DECK 13 FINAL 500 - ENTIRE COURSE MIXED Flashcards
1
Q
What do observational studies and experiments have in common?
A
In both, you are making OBSERVATIONS. recording data. doing statistical analysis.
2
Q
If you have multiple groups and ask them one question, what Chi-squared test is it?
A
Test for homogeneity.
3
Q
Give example of confounding variable.
A
fertilizer A vs B. If you have two tables in a room with tomato plants and and one table gets A and the other gets B, but later you realize that the table with A was near the windows. You say that SUNLIGHT IS A CONFOUNDING FACTOR in that experiment.
4
Q
What are conficence intervals for?
A
PARAMETER CATCHERS. They are an attempt to say what the true population parameter is.. It is our best guess. “We think that there will be between 8 and 12 inches of snow”
5
Q
What does r 2 tell us? (r-squared)
A
It tells us the percent of variablility of y that is explained by the model with x.
6
Q
What is “mutually exclusive?”
A
disjoint. Can’t happen at the same time.
7
Q
Will larger samples reduce BIAS?
A
No, bias is a systematic flaw, even large samples will still have bias. If you ask more people outside of McDonalds, you still only get answers from people who eat at McDonalds (large samples can reduce error, however)
8
Q
Suppose you are doing a weight loss experiment with 2 diets (A low carb and B low fat), and three medications (1 NUTRI LOSS 2 POUND DROPPER and 3 SLIMMERLY). What is the response variable?
A
weight loss (pounds)
9
Q
What is a Chi squared model?
A
A sampling distritubion. If you took a bunch of samples and calculated a bunch of Chi-square statistics, the pile of chi squareds would look like that.
10
Q
What is a quality of SRS that is not a quality of Systematic, Stratified or Clustering?
A
In an SRS, all groups are possible, and ALL POSSIBLE GROUPS have the same chance of being picked (like all senior male students.).The other methods have lots of impossible groups. SRS has no impossible groups. Example: -Stratified- an impossible group would be all girls (you’re taking some boys and girls)-Clustered- an impossible group would be all girls (each cluster has boys and girls)-systematic- an impossible group would be first 10 people that are right next to each other (you are taking every nth person, so you will skip)
11
Q
Is a confidence interval a PROBABLILITY?
A
NO
12
Q
When drawing a normal model, what are the PERCENTILES from left to right?
A
2.5, 16, 50, 84, 97.5
13
Q
How do you find 5 number summary from OGIVE?
A
Split the y axis into quarters. Shoot out to the right from 0, .25, .50, .75 and 1.00 till you hit the line in the ogive, then go straignt down. Those numbers on the x axis below correspond to the 5 numbers.
14
Q
What type of study would find relationship beween Verbal and Math SAT?
A
You could take all of the SAT Math and Verbal scores and run a regression and find the r-quared value and linear model. This would be a Retrospective Study.
15
Q
How do you find the median from an OGIVE?
A
go halfway up the y axis, then shoot across to the curve, then straight down. It’s at the 50th percentile (halfway up)
16
Q
How do you write “A BINOMIAL MODEL WITH p=.35 and n=12?”
A
B(12, .35) B(N, P)
17
Q
which is response?
A
y variable, the Vertical axis.. It “responds” to the x
18
Q
In which sampling methods do the subjects have equal chances of being selected?
A
SRS, Stratified, Clustered, Systematic, and multistage. In all of these, the subjects have an equal chance (but groups have different chances)
19
Q
Gender and Video Game playing are___________ because_______
A
associated (or not independent) because a higher percentage of males play video games. (think.. It depends on gender)
20
Q
If the p-value is high, (above alpha), how do you write conclusion?
A
With a p-value this high(show p value < alpha) I fail to reject the null. There is not enough evidence to say that more students like eggs now.
21
Q
Can you prove a null hypothesis true?
A
NO.. We just fail to reject it.
22
Q
How to find P(at least 1)?
A
1-P(none)
23
Q
How can you think about the mean and median to remember the difference when looking at a histogram?
A
mean is balancing point of histogram, median splits the area of the histogram in half.
24
Q
For information purposes, which gives LEAST stem-leaf, histogram or box-whisker?
A
Box/Whisker, BE CAREFUL. you really don’t know how things are distributed. The box and whisker and fish tank give a very GENERAL look.
25
interpret this 90% confidence interval for avg weight of mice (2.3, 3.5) in ounces
I am 90% confident that the mean weight of mice is between 2.3 and 3.5 ounces
26
How is a paired T test different from a 2 sample mean T test?
A paired test talks about an AVERAGE OF DIFFERENCES from one list, whereas a 2 sample mean t-test talks about a DIFFERENCE OF AVERAGES between two samples.
27
What is undercoverage?
Undercoverage is when a group of the population is not represented in the sample. When the sampling frame isn't representative.
28
what is disjoint?
can't be joined . They can't both happen at the same time! (being over 5 feet and under 4 feet)
29
What values can r be?
from -1 to +1 (r near 0 is WEAK)
30
What is the placebo effect?
When those who get the placebo show improvements, or show the effects of the treatment. This often happens to up 20% of participants!
31
What does Central Limit Theorem Say?
It basically says.. NO MATTER WHAT SHAPE THE POPULATION IS (normal, bimodal, uniform, skewed, crazy.. ) If you make a histogram of a bunch of means taken from a bunch of samples, that histogram will be unimodal and symmetric WITH LARGE ENOUGH SAMPLES.. Close to normal. So.. A nerdy way to say it is: The sampling distribution of means is approximately normal no matter what the population is shaped like. The larger the sample size, the closer to normal. (the normal curve is just a model.. the sampling distribution is close to it, but not it! we use the model anyway!)
32
What is the null model(the sampling distribution) in a 1-sample mean T test?
A pile of means from a bunch of samples.
33
Can you stratify in an experiment?
NO. stratification is a sampling method, blocking is method used in experiments. They are similar ideas.
34
If you want to find percentile for a value, what do you put into normcdf (? ?)
find z score for value, and then normcdf (-999, Zright) like going from negative infinity up to the z score
35
What does r tell us?
The direction (+/-) and how strong a LINEAR relationship is between two QUANTITATIVE variables (when linear)
36
How are we manipulating the environment differently in experiments and studies?
No manipulation or treatments in an observational study. You only manipulate environment in an experminet.
37
What is BIAS in sampling?
A systematic FLAW in your method.
38
Which is explanatory variable?
the x the horizontal axis. it "explains" what happens to y
39
Use the following words in one sentence: population, parameter, census, sample, data, statistics, inference, population of interest.
I was curious about a population parameter, but a census was too costly so I decided to choose a sample, collect some data, calculate a statistic and use that statistic to make an inference about the population parameter (aka the parameter of interest).
40
What is the problem with convenience sampling?
The sample may not be representative as it is not randomized to include every type of person. Friends and family are convenient but they likely share similar opinions and thus the sample is not representative of a population.
41
What is the mode?
the most common, or the peaks of a histogram. We often use mode with categorical data
42
Give example of factors and levels
Factor: medication. Levels: 50mg, 100mg and 200mg.
43
What is difference between population of interest and parameter of interest?
Population is the WHO (subjects you measure, beads people) Parameter is the actual number you want (like % of or AVG)
44
What is the five number summary?
min, Q1 , Q2(median), Q3 and max
45
What percent of the data is between Q1 and Q3?
50%
46
How can the WORDING of the question lead to response bias
Words or phrases that impact your feelings tend to influence responses. Look for "devastating, horrific, wonderful etc." Sometimes there is a background story like "Many americans lose jobs to illegal aliens every year, do you feel this is fair"
47
What is stratified sampling?
When you break the population into groups with similar attributes and randomly select from each strata.
48
Compare population to sample
populations are generally large, and samples are small subsets of these population. We take samples to make inferences about populations. We use statistics to estimate parameters.
49
What is the difference between quantitative and categorical variables?
Quantitative variables are numerical measures, like height and IQ. Categorical are categories, like eye color and music preference
50
What is a probability distribution?
A table or graph showing all of the probabilites of certain occurances. THE PROBABILITIES HAVE TO ADD TO ONE!
51
How is r calculated?
r = sum(Z x Z y ) / (n-1) it is the sum of rectangle areas on the standardizes Z axes
52
What is a representative sample?
A sample that looks like the population. It has similar characteristics.
53
A bag has 3 red chips and 4 blue chips.. WTPT you grab a red first, then put it back in and then grab a red again?
3/7 * 3/7 = 9/49 (indep events)
54
What is the null for a chi squared GOF test?
The distribution fits [the expected distribution]
55
Why randomize in an experiment?
To reduce confounding variables (and bias).
56
Think of the minimum value, the mean and the standard deviation, what is impacted by shifting (adding a constant)
adding a value shifts the entire histogram to the right, so the min and the mean will increase by that amount, BUT THE SD WILL NOT CHANGE.
57
what does influential mean?
It impacts the SLOPE. It means that the point, when added or removed to data, will influence the SLOPE. Generally these are outliers in the x direction. Far left or right.
58
When your sampling frame is different from the population, then you risk ____
undercoverage
59
What is the standard sampling method?
A Simple Random Sample (SRS) is our standard. Every possible group of n individuals has an equal chance of being our sample. That's what makes it simple. Put the names in a hat.
60
Example of response bias
A teenager goes to the doctor's office with their parents. The doctor asks the teen if they vape. The teen may say "no" because their parent's are there, even though they do vape.
61
What should we look for in resid plot?
Curve or pattern. Also, it should have equalish scatter from left to right It should look RANDOM
62
Can there be a correlation between grade and music preference?
No, music preference is categorical. There is an association, however.
63
Compare data to parameters
Data is each little bit of information collected from the subjects?. They are the INDIVIDUAL little things we collect? we summarize them by, for example, finding the mean of a group of data. If it is a sample, then we call that mean a "statistic" if we have data from each member of population, then that mean is called a "parameter"
64
What does normcdf do?
It gives you the area under the normal curve between any two z scores , or percent between 2 values if you use the shortcut normcdf (low, high, mean , sd)
65
Which is more sensitive to outliers and skewed? Mean, median. Sd or IQR?
Mean and SD are most influenced by outliers. median and IQR are RESISTANT, RESILIENT, ROBUST!!
66
What is extrapolation?
Making predictions outside of the x values you have.
67
using calculator: suppose 30% of dogs have fleas. WTPT first dog with fleas was the fifth you checked?
not, not, not, not, yes. .7x.7x.7x.7x.3orgeopdf (.30, 5
68
What is a confidence interval?
it is a parameter catcher.. Like a fishing net. We stand at our statistic, and reach up and down a margin of error, and hope to CATCH the parameter? sometimes we do, sometimes we don't? but we never know.. Mooo hooo hooo haaaa haaa haaa (evil laugh)
69
4 INGREDIENTS TO EXPERIMENTS
Compare, control , randomization, replication (and BLOCKING when you need to)
70
A 4 year high school of 2000 students, sampling 40 high students : Describe a systematic sample
Get an alphabetical list of all of the students, 2000/40=50. Randomly choose one of the first 50 students and then every 50th student after that.
71
How is BIAS different from SAMPLING error
Bias is a systematic flaw in your sampling method. Sampling error is always present even with the best methodology.
72
What is the mean and mode of a chi squared model? What is the 5% cutoff chi-squared?
The mean is the degrees of freedom and the mode is df-2. The cutoff is at 1.5df+3.
73
notation: what is p
true population proportion (percent in the population)
74
describe a scatterplot's strength?
give the r value (if straight), or say "tightly packed loosely packed"
75
If you want to calculate % above a value, what do you put into normcdf(? ?)
find z score for value, and then normcdf (Z left, 999)
76
In order to reject a null hypothesis, you need ___________
evidence
77
What are the three chi-squared models?
goodness of fit, test for homogeneity, test for independence
78
What are the two types of observational studies?
Retrospective, and Prospective
79
what happens if you multiply all of a data set by a constant? Think of an example
it is scaled Both center and spread are impacted. Mean/ median/ stand dev/ iqr/ quartiles all multiplied by that constant. Center, spread and all individual values are changed. Consider 1,2,3,4,5 mean of 3 and range of 4. Now multiply by 3: 3,6,9,12,15 and you get a mean of 9 and a range of 12. both multiplied by three.
80
What percentile is Q3?
75th
81
If you are tasting soup.. Then the flavor of each individual thing in the spoon is the ________, the entire spoon is a ______.. The flavor of all of that stuff together is like the _____ and
If you are tasting soup. Then the flavor of each individual thing in the spoon is DATA, the entire spoon is a SAMPLE. The flavor of all of that stuff together is like the STATISTIC, and you use that to MAKE AN INFERENCE about the flavor of the entire pot of soup, which would be the PARAMETER. Notice you are interested in the parameter to begin with. that is why you took a sample.
82
What symbols do we use for population proportion (%) and sample proportion (%)?
p for population and p-hat for sample
83
What is the main purpose of a placebo ?
to see how the environment impacts the subjects. How do all of the other factors impact the subject.
84
using calculator: suppose 30% of dogs have fleas. WTPT less than 4 out of 10 have fleas?
less than 4 is the same as 3 or less.binocdf (10, .30, 3)
85
What is sampling error?
same as sampling variability.. The natural variability between STATISTICS.. NOT DATA!!! . We call it error EVEN THOUGH YOU MADE NO MISTAKES!!!
86
Does high r squared mean a good model?
CHECK SCATTER FIRST.. Make sure model "FITS" the data. You should check your scatterplot and residuals plot to make sure model is appropriate and no outliers present then it means something So YES, but after you check the resids.
87
the (n over k) thing has a (5 over 2), how would you do it? What is it called?
Also known as "5 choose 2" or "5 C 2".. 5! / 3!2! (notice the bottom two add to the top)
88
notation: what is mu
true population mean (average)
89
you fail to reject when ____________ evidence
you fail to reject when you DON'T HAVE EVIDENCE
90
What is a standard error?
The typical, or expected, error. The spread of a pile of stats. It is how far off you are expecting your statistic to be from the parameter. It is calculated like the standard deviation, but we are using sample statistics.. We don't know the true parameters, so we estimate with statistics adding error to our calculation
91
What is the general formula for ALL CONFIDENCE INTERVALS?
STAT +/- CRIT SE
92
What is probability first success is on 7th try?
qqqqqq p (q^6*p). (this is a GEO prob)
93
Suppose you are doing a weight loss experiment with 2 diets (A. low carb and B. low fat), and three medications (1. NUTRI LOSS, 2. POUND DROPPER and 3. SLIMMERLY). How many treatment groups would there be?
there would be 6: A1, A2, A3, B1, B2, B3
94
what is another name for alpha level?
a significance level
95
N ( ?1 , ?2 ) what does this mean?
it means NORMAL models centered at 1 With a standard deviation of 2
96
What's up with extrapolation? Is it OK?
Not ideal. Sometimes it's all you can do, but state CAUTION.
97
Height and weight has an r value of 0.7. You would expect a person with a height that is 2 st. dev above the mean in height to have a weight that is only___St. Dev above the mean weight.
only 1.4 S.D above the mean for weight. (for each SD in the x direction you change r SD in the y direction)
98
geocdf
(p,x) . Probability of the FIRST SUCCESS being ON OR BEFORE the Xth trial.
99
What is a Z score?
The number of standard deviaiton away from the mean
100
What is the median?
the middlest number, it splits area in half (always in the POSITION (n+1)/2 )
101
A 4 year high school of 2000 students, sampling 40 high students: Describe a convenience sample
Ask the first 40 students coming to the locker rooms after school. This is problematic because athletes may not have the same preferences as non athletes.
102
Association and Independence. How are they related?
Variables are either independent or associated. Meaning: if one impacts the other then we say there is an association. If not, Then they are independent.
103
Compare DATA-STATISTIC-PARAMETER using quantitative example
Data are individual measures, like how long a person can hold their breath: ?45 sec, 64 sec, 32 sec, 68 sec.? That is the raw data. Statistics and parameters are summaries like ?the average breath holding time in the sample was 52.4 seconds? and a parameter would be ?the average breath holding time in the population was 52.4 seconds?
104
what is leverage?
Far right or left from the middle. leverage just means it is far away from x-bar Some leverage points are not influential if they go along with the flow of the scatter.
105
how do you interpret y intercept?
The model predicts that if there were no [x stuff] this is how much [y stuff] you'd have
106
What is the difference between a sample and a census?
With a sample, you get information from a small part of the population. In a census, you get info from the entire population. You can get a parameter from a census, but only a statistic from a sample.
107
using calculator: suppose 30% of dogs have fleas. WTPT exactly 5 out of 12 have fleas?
binopdf(12, .30, 5)
108
What is a point estimate?
Your statistic, the sample p-hat or your x-bar. Your best guess. What you got in your sample. It is in the middle of the interval.
109
What is the line that you plot?
IT IS A MODEL! It is the LSRL and it is the model we are talking about
110
How are statistics and parameters different?
A statistics is a numerical description of a sample, and a parameter is a description of a population. The difference between these is called ERROR (sampling error).
111
How do you find a certain percentile on an OGIVE?
Start at the % on the Y axis.. travel horizontally to the right until you hit the line, then straight down to the X axis. That data value is the percentile.
112
does correlation mean causation?
NO WAY DUDE
113
What is the " large enough sample" condition for Chi Square?
Make sure that there are at least 5 in each expected cell.
114
How are voluntary and convenience samples similar
With voluntary, people choose them selves, with covenience, the people are just chosen by researcher, neither uses randomness and both are prone to BIAS.
115
How can you match boxplots to histograms?
USE THE FISH TANK METHOD!
116
Which calculator function gives you a z score?
invnorm(%ile),
117
What is a factor? give example
DIET PLAN would be a factor and levels could be: low carb, low fat, and no diet
118
How are we making inferences differently in experiments vs studies?
In observaional studies, you make and inference about the population, in an experiment you make an inference about a treatment.
119
What is the null model (the sampling distribution) in a 1-proportion Z test?
A pile of proportions (%) from a bunch of samples.
120
If you have one group and ask them one question, what type of chi-squared test is it?
Goodness of fit test.
121
using calculator: suppose 30% of dogs have fleas. WTPT exactly 7 or less out of 20 have fleas?
binocdf (20, .30, 7)
122
What percent of the data is above Q3?
25%
123
A 4 year high school of 2000 students, sampling 40 high students: Describe a cluster sample
Imagine that all of art classes have 10 students and they are mixed with fr, so, jr and srs. You would randomly choose 4 classes and survey everyone in each of the 4 classes.
124
DEGREES OF FREEEDOM: one sample t, two sample T, regression, chi square gof, chi square hom/indep
one sample t: n-1two sample t: calc or smaller n-1regression: n-2Chi square GOF: cells-1CHi square hom/indep: ROW-1 x COL-1
125
What is the law of averages?
a misinterpretation of the law of large numbers. Using this law, if you flipped 4 heads in a row, you'd expect the next one to be a tails because it should even out in the long run, as if the coin remembers that it "owes you" something NOT TRUE
126
How do you undo squares or cubes? like if you have x 2 = stuff or x 3 = stuff
^ 1/2 or ^ 1/3 (raise stuff to these powers to get x)
127
What is statistical inference?
Using a statistic to infer something about a parameter.. Basically, using a sample to say something about a population.
128
What is the null model (the sampling distribution) in a chi squared test?
a pile of chi-squared statistics calculated from a bunch of samples
129
What percent of the data is between Q1 and Q3?
the middle 50%. That is the IQR
130
What is a residual?
Vertical distance to the LSRL. ACTUAL-PREDICTED, A-P, like this class AP (get it?) Take y data found and from that, subtract the y you get from plugging the x into the model (equation).
131
What's the difference between a prospective and a retrospective study?
A retrospective study takes a group and looks back at its history while a prospective study watches a group for a period of time and records the data along the way into the future.
132
What is alpha?
It is the rejection threshold. You reject p-values below it.. It is how willing you are to make a Type 1 error? alpa=P(Type I error)
133
A 4 year high school of 2000 students, sampling 40 high students: Since ALL GROUPS (samples) are possible and equally likely, show some groups that you could get randomly from and SRS that would not be representative of the entire school.
all female, all freshmen, all seniors, all athletes.. these could happen in an SRS (but they are not likely to)
134
notation: what is p-hat
sample proportion (percent in our sample)
135
What is a parameter?
A numerical summary of a population. Like a mean, median, range? of a population
136
4 ingredients: What is "control?"
You want to control the environment as best as you can so that the only difference between groups is the treatment, and the treatment only. Everything else should be similar.
137
What is the difference between response bias and nonresponse bias?
Response is when the person's response is influenced by the question or questioning method (like if a parent asks if you use drugs, as opposed to a friend. there is only one answer to this, but one might respond differently to them), non response is is when the people who don't respond might have different opinions/views than the people who did.
138
Control group vs Experimental group
The experimental group gets the treatment (pill, fertilizer) while the control gets placebo or nothing. You compare the experimental group to control group.
139
What is difference between completely randomized and random block design?
Completely randomized takes all units and puts them in a hat and randomly chooses treatments, blocked puts them all in different hats first (blocks) and then chooses
140
What percent of the data is below the median?
50%
141
CONDITIONS: What are the three conditions that you have to check with pretty much every inference procedure (every test and every interval)
1. Randomly chosen sample (or assigned treatment). Circle the word random or explain why you think it is. 2. Sample size is less than 10% of the population. Show that 10n is less than N. Example, for 50 students, write 10(50)=500 is less than all students.3. Nearly normal (or large enough sample)- this differs based on the type of data and test.
142
What is the difference between a bar chart and a histogram
bar charts are for categorical data (bars don't touch) and histograms are for quantitative data (bars touch)
143
What is categorical data?
The actual individual category from a subject, like "blue" or "female" or "sophomore"
144
What is the difference between quantitative and categorical data?
The data is the actual gathered measurements. So, if it is eye color, then the data would look like this "blue, brown, brown, brown, blue, green, blue, brown? etc." The data from categorical variables are usually words, often it is simpy "YES, YES, YES, NO, YES, NO" If it was weight, then the data would be quantitative like "125, 155, 223, 178, 222, etc.." The data from quantitative variables are numbers.
145
is r sensitive to outliers?
yes. A single outlier can make it seem like there is a relationship ( if way out in x direction), or even seem like there is no relationship.
146
Can you accept a null hypothesis? Can you say "keep the null?"
Never accept a Ho, don't keep the Null. simply "FAIL TO REJECT THE NULL"
147
A 4 year high school of 2000 students, sampling 40 high students: Explain how stratifying has "impossible groups"
You couldn't get all freshmen in your sample
148
What point is on every regression line?
the mean-mean point. (x bar, y bar). This point is generally not one of the points on the scatterplot. Usually none of the scatterplot points are on the regression line.
149
What is the "mean of a random variable?"
The expected value sum of probs times values
150
What's the difference between stratified and cluster sampling?
Stratified- you divide the population up into groups with similar traits, called strata (homogeneous groups) and randomly choose a few from each strata.
151
How do you interpret slope?
For an increase of 1 [unit of x] there is an (increase/decrease) of [SLOPE] [units of y]. You can write "SLOPE UNITS Y/ ONE UNITS X" to help
152
when do you need crits?
in confidence intervals (and old fashioned hyp tests.. We look at Z to see if greater than crit.)
153
What is the mode?
the peaks of a histogram (the humps). or with categorical data, the most popular category
154
What is "statistically significant?"
When our sample statistic is so far away from what we were expecting that we don't think that it was due to random sampling error. Then is statistically significant. When p-value is below the alpha, we say "statistically significant".. Low p-values are statistically significant.
155
To make a survey to tell of a restaurant is good, would you ask the people coming out of the restaurant?
People at the restaurant are probably there because they already like it. If you asked the question "Is this your first time dining here?" and if they say "yes" you survey them, that would be a better method. But then again.. the people wouldn't go into an Italian restaurant if they didn't like that type of food.
156
Who can be blinded? ( two groups)
1. Subjects (and dog owners..). The poeple getting treatment and 2. administrators. Those delivering treatments and assessing effectiveness of treatments.
157
what is a probability model?
a list of all possible values of random variable with respective probabilities. The probabilities should add to 1! Normal model is one
158
If you want to find % below a value, what do put into normcdf (? ?)
find z score for value, and then normcdf (-999, Zright) or shortcut normcdf(-99999, value, mean, sd)
159
What is the variance?
The average squared distance to the mean. Or the SD2 (It is the SD before you take the square root, so it is the stuff under the radical in the formula)
160
using calculator: suppose 30% of dogs have fleas. WTPT AT LEAST ONE OUT OF 10 has fleas?
1-none= 1-.7^10or1-binopdf( 10, .30, 0)or1-binocdf( 10, .30, 0)
161
Does r 2 tell direction?
NO r 2 is always positive, so you can't use it to see if the relationship is negative.
162
Give example of correlation without causation and explain the lurking variable.
Ski accidents are higher on days with more hot chocolate sales, therefore, hot chocolate must cause ske accidents. (lurking variable: the number of people on the mountain). What is happening is that on days when the mountain is crowded, there are more hot chocolate sales and more ski accidents. So the population on the mountain is causing both to rise and fall together.
163
What do you know about the sign of r and the slope of the regression?
they have the same sign. Both will be positive or both will be negative.
164
Does the IQR capture 68% of the data?
NO. it catches the middle 50%.
165
If I take a random sample 20 hamburgers from FIVE GUYS and count the number of pickles on a bunch of them? and the average number of pickles was 9.5, then 9.5 is considered a _______?
statistic. (t is a summary of a sample.)
166
When do you know it is GOF test?
When you have ONE ROW or ONE COLUMN… then it gives you a ratio , like 1:2:5 or it gives you expected percents.
167
Another name for "skewed right" is
positively skewed
168
what does "95% confidence" in a 95% confidence interval mean? (explain the confidence level)
It means if we took a ton of samples, and made confidence intervals from each of them,ABOUT 95% of the intervals would contain the parameter, 5% would not.
169
If you are doing a 2 tailed test with alpha=.05.. What confidence interval goes with that?
95% confidence interval (there is .025 in each tail)
170
are there any normal samples?
no, nothing is normal, just normalish. The only normal thing is the model we use.
171
which calculator function gives you a percent?
normcdf(Z left, Z right)
172
What's a useful alternative when you can't run an experiment? What are they useful forms of this, and how do you preform them respectively?
An alternative of an experiments could be an observational study. t.
173
using calculator: suppose 30% of dogs have fleas. WTPT no more than 8 out of 15 have fleas?
not more than 8 is the same as 8 or less.binocdf(15, .30, 8)
174
What is data?
Any collected information. Generally each little measurement? Like, if it is a survey about liking porridge? the data might be ?yes, yes, no, yes, yes? if it is the number of saltines someone can eat in 30 seconds, the data might be ?3, 1, 2, 1, 4,3 , 3, 4?
175
Computer ouput: What does "constant" mean?
It is the y intercept
176
Can you eliminate sampling error?
Only if you take a census. Larger samples have less error.
177
What is the other conditions for regression inference?
Random residuals (equal random scatter, no pattern).
178
Give example of incorrectly using the word "correlation"
"there is a correlation between gender and video game playing" This person should say "association." You can't say correlation because gender is categorical.
179
what is a clear example of the medians resiliance and when you would use the median instead of the mean?
(change just the top value). Imagine if we asked eight people how much money they had in their wallet. We found they had {1, 2, 2, 5, 5, 8, 8, 9}. The mean of this set is 5, and the median is also 5. You might say "the average person in this group had 5 bucks." But imagine the same group the next week, but one of them just got back from the casino and the dist was (1, 2, 2, 5, 5, 8, 8, 9000}, in this case, the median would still be 5, but the mean goes up to over 1000. Which number better describes the amount of money the average person in the group this time? 5 bucks or 1000 bucks? I think 5 is a better description of the average person in this group and the 9000 is simply an outlier.
180
How can you turn OGIVES into histograms?
RECTANGLE DROP! (bin drop)
181
What symbols do we use for population mean and sample mean?
Mu for population mean, xbar for sample mean.
182
How do you find outliers in regression?
they don't follow the "flow" (pinky trick, cover with you pinky.. Then uncover.. Does it follow the flow?)
183
notation: what is p - p
true difference between two population proportions (percents).
184
If I take a random sample of 20 hamburgers from FIVE GUYS and count the number of pickles on a bunch of them? and I do this because I want to know the true average number of pickles on a bur
parameter, a one number summary of the population. The truth. AKA the parameter of interest.
185
when is data "paired"
when you have 2 measurements of the same variable on the same subject (or matched subjects)
186
using calculator: suppose 30% of dogs have fleas. WTPT first dog with fleas was ON OR BEFORE the fifth you checked?
geocdf (.30, 5)
187
When we say "statistics vary" or the "variablility of statistics" are we talking about data from an individual?
NO. we are stating that summaries of samples (statistics) will vary from sample to sample. Statistics from one sample will differ from statistics from another sample and they will also differ from the parameters. The distance your statistic is from the parameter is called the ERROR. Larger samples will give piles of statistics that will be narrower (less variability).
188
When you are doing PAIRED or MATCHED or BLOCKED tests.. What are you finding?
The average difference.. You are doing 1 sample procedures on a NEW THIRD LIST OF DIFFERENCES
189
what is df for chi squared homogeneity or independence?
(rows-1)(columns - 1) (remove a column and row.. Count boxes)
190
What is the expected value?
The mean What you'd AVERAGE if you played the game A LOT!!!!!!!!!
191
Compare DATA-STATISTIC-PARAMETER using categorical example
Data are individual measures? like meal preference: ?taco, taco, pasta, taco, burger, burger, taco?? Statistics and Parameters are summaries. A statistic would be ?42% of sample preferred tacos? and a parameter would be ?42% of population preferred tacos.?
192
What is statistically significant?
When an observed difference is too odd for us to believe that it is likely to have occurred naturally (or just randomly). Basically it is Statistically Significant when we don't think it happened randomly. when you think "something's up" or "something's fishy"
193
what is the law of large numbers?
guarantees that in the long run.. The relative frequency settles down to true probability.. (you'll have 50% heads after an infinite number of coin flips with a fair coin)
194
How do you undo an ln (natural log) when solving? ex: ln x = stuff or: ln x = m
e stuff or e m
195
An unbiased sampling method will eliminate error
No, error is always there. Error is not a mistake.
196
You own a bike shop and order your tires from 2 companies (A and B). You order 80% from A and 20% from B. 1% of the tires from A are defective, while 4% from B are defective What is the probability that a defective tire is from company A? How would you do this?
Tree diagram. Split up by company first, then use conditionals. A BAD (.8)(.01)= .008A GOOD (.8)(.99)= .792B BAD (.2)(.04)= .008B GOOD (.2)(.96)= . 192It seems that .008/(.008+.008) or 50% are bad
197
What is variability?
Differences? how things differ. There is variability everywhere.. We all look different, act different, have different preferences? Statisticians look at these differences.
198
How do you write conclusion if you reject?
With such a low p-value, (p-value < alpha) I reject the null hypothesis. There is strong evidence that the proportion of students who eat rice has changed.
199
Example of undercoverage
You only ask people who go to Home Depot about their views on school lunches.
200
binopdf
(n,p,x) .. Probability of exactly X successes in N trials. (PARTICULAR probability)
201
if you mult or divide the x's or y's (shift/scale) does r change?
no. the strength remains the same. (If you log or square it, it will change, but just adding or multiplying won't change it)
202
If I take a random sample of 20 hamburgers from FIVE GUYS and count the number of pickles on a bunch of them? and one of them had 9 pickles, then the number 9 from that burger would be calle
a datum, or a data value.
203
mean/SD/median/IQR. How do I know which ones to use?
when unimodal and symmetric, mean and sd. If skewed or outliers? Median and IQR. If bimodal? Talk about the MODES
204
If the distribution is skewed (or outliers/not symmetric) what would you use for center and spread statistics?
Median (center) and IQR (spread)
205
How do we use representative samples in experiments and studies?
You don't need a representative sample in an experiment. You are not making inferences about a population, just about a treatment.
206
Does a high r value mean anything? (can it look strong, but not be?)
Sure. It can. It tells you strength of LINEAR relationship. BUT CHECK THE SCATTER. One outlier or typo can make it look STRONG.
207
How do you interpret slope EQUATION? rSy/Sx
for each increase of 1 st dev in x direction, you go r st dev in y direction. 2st dev in x, you go 2r st. dev in y. 3st dev in x, you go 3r st. dev in y.
208
How is a confidence interval made?
statistic +- margin of error. Statistic +- (crit * s.d ). Stand at the statistic, reach out up and down a margin of error, and hope that you catch the parameter.
209
WHat is the null model (the sampling distribution) in a paired T-Test?
A pile of average differences. Remember that in a paired test, you are getting an individual differenc from each pair of data, then finding the average of differences.
210
Give a quick example of associated variables
A higher percentage of boys play video games than girls so we say "gender and video game playing are associated" or "gender and video game playing are not independent"
211
notation: what is z*
critical z, how many SE you are reaching up and down in a confidence interval for proportions
212
What is the null for a 2 prop Z?
p1=p2 OR. p1-p2=0, there is no diff
213
What percent of the data is above Q3?
25%
214
What is the difference between a parameter and a statistic?
BOTH ARE A SINGLE NUMBER SUMMARIZING A LARGER GROUP OF NUMBERS?. But pppp parameters come from pppp populations? sss statistics come from ssss samples.
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What happens to a pile of statistics if you take larger samples?
All of the x-bars or all of the p-hats will get closer to eachother, and closer to the parameter ( mu or p)
216
Interpret residual: Points above the line/positive resid
"the model underpredicted" or "actual performance was above the expected performance
217
What is the differnce between standard error and standard deviation?
Standard error is the typical distance a STATISTIC is from the mean in a sampling distribution (pile of a bunch of sample's statistics) and Standard Error is the typical distance a DATUM is from the mean in a pile of raw data.
218
What is the "nearly normal" condition for proportions? (aka large enough sample)
np>10 and nq>10. actually Show this calculation
219
What symbols do we use for population mean and sample mean?
Mu for population mean, xbar for sample mean.
220
A bag has 3 red chips and 4blue chips.. WTPT you grab a blue then a red? (without replacing)
4/7 * 3/6 (notice that there were only 6 in the bag)
221
When we say the average teenager are we talking about mean
It depends, if we are talking height, it might be the mean, if we are talking about parental income, we'd probably use the median, if we were talking about music preference, we'd probably use the mode to talk about the average teenager.
222
How are power and alpha related?
they go up and down together, unless you get a larger sample, then power increases. You can set the alpha to anything you want.
223
A bag has 3 red chips and 4 blue chips.. WTPT you reach in and grab 2 reds?
3/7 * 2/6 = 6/42 or 3/21 (notice the denominator changed)
224
What is a sampLING distribution?
a pile of statistics. A pile of p-hats or x-bars.
225
What is a t-crit?
It is the same as z crit. It is the number of sd you reach out in your CI. To find it, do INVT(area in one tail, degrees of freedom)
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In which sampling methods do all subjects have the same probability of being chosen?
SRS, cluster, systematic and stratified all give subjects equal likelihood of being chosen.
227
What is a p-value
It is the probability of getting your sample randomly if the null were true. Basically, how likely is it that your sample statistic came from the Null Model.
228
What are the names of four two-sample procedures we do?
2 proportion Z interval2 proportion Z test2 sample mean T interval2 sample mean T test
229
what is a biased estimator?
When the sampling distribution (pile of sample stats, x bars or p hats) is NOT centered on the true population parameter. If you were weighing people and there was a 1 pound weight on the scale, the pile would be centered 1 pound higher. Baised.
230
What if you want more confidence?
get a bigger net.. (wider conficence interval) (or increase sample size)
231
Can you draw the alpha/beta/power diagram?
BE ABLE TO SKETCH THE ALPHA BETA POWER DIAGRAM from the original pregnancy worksheet. Know where everything is. This helps you understand how alpha, beta and power interact.
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What is wrong with using volunteers in a survey?
(Volunteers are often upset or emotionally attached) Those who volunteer may not be like the rest of the population. An example may be, if you're trying to find our how often people volunteer for things. So you ask for volunteers to take the survey. A question may be "when was the last time you volunteered for something?" Well. they all just volunteered for the survey!
233
What is a critical value?
It is the amount of standard errors you'll reach out, depending on your confidence (a t or z). Example.. 68% crit z = 1 .. For 95% crit z = 2 (well, 1.96).. For means.. Use t crits
234
What is a margin of error?
critical * s.d. It is how far you reach out in a confidence interval.. You reach up and down one of these, so the interval is actually 2 margins of error wide.
235
What symbols do we use for population standard deviation and sample standard deviation?
Sigma for population and s for sample.
236
What is a simple random sample?
put all of the names in a hat. every group is possible. pull the numbers
237
How to make TREES with screening tests or tests that give you conditionals????
SPLIT UP POPULATION FIRST >>>>>> then split the groups by outcomes of the test
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How is undercoverage different from non response
undercoverage you don't even ask people, non-response you ask, but they don't answer.
239
what is a conditional distribution?
A distribution with a condition (within the table), along only one row or one column. What percent of the 8th graders liked bacon. The condition is 8th graders, so you are only interested in 8th graders. NOT IN THE MARGINS. You are given a condition.. Then read along that row or column.
240
Suppose you sample 150 people randomly from a city to make an inference about the city, and then you sample 150 people randomly from around the country to make an inference about the entire country, which will you be more confident in????
It will tell you just as much about both. Same reliability (if sample is representative). Sample size determines confidence. To get more confidence you need a larger sample (not a smaller population)
241
What is a control group?
The group that doesn't get a treatment (or gets the old treatment). It helps us see the impact of the environment. It gets the placebo or standard care but goes through all of the motions
242
What percentile is Q1?
25th
243
What does mutually exclusive mean?
Same as disjoint.. Can't both happen.
244
Can numbers be CATEGORICAL?
sure. Zip codes, sports jersey numbers, telephone numbers, social security nunmbers, area codes these are categorical.
245
How can you decrease sampling error?
Get a larger sample
246
Will 95% of other statistics be within my interval?
NO!!! You have no idea where your statistic is (or your interval) in regards to true parameter
247
How do you describe a scatterplot?
DIRECTION FORM STRENGTH and STRANGE
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If the p-value is low, (below alpha), how do you write conclusion?
With p-value this low (show p value < alpha) I reject the null hypothesis. There is strong evidence that the proportion of students who eat rice has changed.
249
if you switch x and y does r change?
NO. The strength stays the same.
250
when can you expect the first success? (mean of GEO)
1/p this tells you, on average, when the first success will occur .
251
What is a continuous probability function or curve?
A line or curve (like the normal model) that has an area of exactly one. The probability is found by finding the area between the boundaries given.
252
Does a census make sense?
A census is ok for small populations (like Mr. Nystrom's students) but impossible if you want to survey "all US teens"
253
Does sample size matter, or percent of population?
Sample size. A sample of 150 will say as much about a population of 2,000 as it will about a population of 2,000,000. The sample size determines level of confidence and interval widths..
254
what is the best way to reduce bias?
randomness and good sampling methods.
255
How do you describe distributions (histograms)?
Shape-Cener-Spread- and STRANGE (Outliers and gaps) some say GSOCS. where's yo GSOCS?
256
What is the sure way to assign treatments correctly?
throw names in hat and first half in group 1 and the rest group 2. . Or number subjects from 1-n and use randint until you get half for group 1.
257
Can you make a 100% confidence interval?
Sure, I'm 100% confident that it will snow between 0 and 500 feet tomorrow.
258
Do parameters vary?
NO!!! Statistics do because they are calculated from samples, different samples have different statistics. they vary from sample to sample. The parameter doesn't vary because there is only one.
259
What is the null for a 2 sample mean T?
mu1=mu2 OR mu1-mu2=0 there is no diff
260
What is the difference between single-blind and double blind?
Single blinding is when all individuals in either one of the classes are blinded; double-blinded is when everyone in BOTH classes are blinded. Classes are: subjects and the other is treatment givers + evaluators
261
A bag has 3 red chips and 4 blue chips.. If you grab a red one on the first try and keep it, WTPT the next one is red?
2 out of 6
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How do statistics from big samples compare to small? (notice this doesn't ask about DATA)
Larger sample statistics have less variablility, so statistics from larger samples are closer to eachother and to the parameter. Statistics from smaller samples are more spread out, further away from true parameter.
263
what is pythagorean theorem of stats? (variances add)
st dev of combined model is: sqrt(st dev squared + st dev squared) or more if you combine more
264
What is a census?
Like a sample of the entire population, you get information from every member of the population
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What is cluster sampling?
Cluster- grab clusters of the population. Usually for convenience. GO to 20 randomly chosen schools and sample 50 students in each. each cluster should be representative ( like the population) use a few clusters.
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What is a random sample?
When you choose a sample by using randomness… rolling dice, choosing names from a hat, or other REAL RANDOMLY generated sample. Humans can't really do this well without the help of a calculator, cards, dice, or slips of paper.
267
If you switch x and y will slope change?
YES (but not just reciprocal) slope is rsy/sx , to get new slope you can use shortcut: r 2 /old slope (reciprocal times r 2 )
268
How do students often mix up IQR and St. Dev
They INCORRECTLY think that Q1 is 1sd below the mean and Q3 is 1sd above the mean. THIS IS NOT TRUE!!! Q1 is only .67 sd above the mean and Q2 is .67 below
269
What is the "nearly normal" condition for regression? (aka large enough sample)
Make sure the histogram of the residuals is normalish.
270
Why do we plug 999 into normcdf?
It needs a z score, but we can't plug in infinity. So we go down or up 999 standard deviations and that pretty much gets everything
271
What does the CLT say about the distribution of actual sample data?
Nothing? The sample will be distributed similar to the population. Bimodal populations have bimodal samples. The CLT only talks about distributions (histograms) of sample statistics, of summaries, which are groups of means.., NOT OF INDIVIDUALS!!!! NOT DATA
272
What are the two (three) types of experiments?
1. Completely randomized 2. Randomized block (and matched pairs which is just blocking by pairs)
273
How are we using random numbers in experiments vs studies?
In a study, we randomly choose subjects to survey from the population as a whole. In an expermint we
274
What do OGIVES look like?
They all start at the bottom left (0%) and go to top right (100%)
275
A 4 year high school of 2000 students, sampling 40 high students: Explain how clustering has "impossible groups"
You couldn't get 2 people from each classroom, because you would be randomly choosing classrooms and asking everyone in those classes.
276
What is the null for a chi squared test for homogeneity?
The [samples of ---] are similarly distributed.
277
What is the difference between a completely randomized and a randomized block?
In a completely randomized experiment, all of the subjects names go into ONE HAT and you pick for treatment groups. In a randomized block design you have more hats (a hat for males, a hat for females etc) and pick for treatments from each.
278
Why does it make sense to double-blind an experiment?
It reduces bias in an experiment. If subjects don't know what treatment they're receiving, they won't change their habits based on that knowledge. If evaluators don't know which treatment each subject is receiving, they won't bias the true results based on the results they expect to see
279
Diff between association or correlation?
association is talking about a relationship. If you see a pattern in the scatterplot, there is an association. Correlation is an actual calculated number (two quantitative variables) . NEITHER MEAN ONE CAUSES THE OTHER!!!
280
How do you describe CENTER for unimodal and symetric distributions?
use the MEAN
281
notation: what is t*
critical t, how many SE you are reaching up and down in a confidence interval for means
282
A bag has 3 red chips and 4 blue chips.. WTPT you reach in and first grab a blue and then grab a red without replacing?
4/7 * 3/6 = 12/42 or 6/21
283
Example of wording bias
Do you support food assistance and nutrition programs for children living in poverty? VS. Do you approve of supporting lazy people on welfare?
284
WHat is the null for a chi squared test for independence"
The [two variables in context] are independent.
285
can disjoint events be independent? EXPLAIN
NO.. If they are disjoint then knowing one tells you that the other couldn't happen so they are always NOT INDEPENDENT
286
are any populations actually normal?
no, nothing is normal, just normalish. The only normal thing is the model we use.
287
A 4 year high school of 2000 students, sampling 40 high students: Explain how systematic has "impossible groups"
You couldn't get the first 40 people alphabetically (because you are taking every nth)
288
Describe the distribution of a sample vs the population
It will look like the population. The distribution of a sample is a histogram made from the sample, which will look kind of like the population. If the population is bimodal, then the distribution of the sample is bimodal. The SAMPLING distribution of a bunch of means, however, will look normalish.
289
In the fertilizer experiment, how could you plan to eliminate the confounding variable?
USING RANDOMIZED BLOCK DESIGN. Make each table a block, and then randomly assign fertilzer A and B to the plants at each table. Compare the fertilizers for table 1, then compare the fertilizers on table 2.
290
What is the IQR?
Interquartile range a measure of spread. Q3-Q1. The distance from Q1 to Q3. The regular range is Hi-Lo, this is the inner range, the interquartile range.
291
If you are testing to see if a math program works in your town (that will cost 4 million to implement) describe a type 1 and type 2 error.
Type 1: you think it worked, but it didn't so you spend 4 million on a program that isn't good.Type 2: It worked, but you didn't notice, so you miss the opportunity to adopt a good math program.
292
what does geometric model tell us about
it is about FIRST SUCCESS What is likelihood first success is on 5th trial?
293
what does " 90% confidence" mean in a 90% interval for avg weight of mice (2.3, 3.5) in ounces
90% of intervals made this way would catch the true mean weight. If you took 1000 samples and made 1000 intervals, about 900 intervals would catch the true weight, 100 would not.
294
What is retrospective study?
A retrospective study is a study that looks backwards in time (or at the present moment).
295
What is area under ANY probability curve?
1 (or 100%)
296
what is independent?
when P(A)=P(A|B) When the probability of A is the same even when B is also true Knowing B does not affect the probability of A. (can also be checked by P(A)*P(B)=P(AandB))
297
what is a test statistic?
a t or z score (or chi squared) that you use to find a p value
298
What is a way to think about the three conditions?
1. Sample is random2. Sample is small enough (<10%)3. Sample is large enough (np&nq>10 for props, n>30 for means or the histogram is normalish)EXTRAS: chi squared exp at least 5 in each cell, regression- random resid
299
What is difference between subject and experimental unit?
Humans who are experimented on are commonly called subjects in an experiment. Subjects like dogs, days, plants and anything not human are called Experimental Units
300
Why is it called the "least squares regression line?" the LSRL?
Because, after you find the mean-mean point, you fix the line so that it minimizes the squared vertical distancesto that line from each point. It minimizes the squared residuals, the least squares..
301
what is the shortcut invnorm?
gives data value from percentile, skips Z score. Invnorm (percentile, mean, sd)
302
Are models what really happen?
No. A model train is not a real train. We use models to say what kind of happens.
303
give an Example of a MULTISTAGE sample
Suppose you want to poll urban, suburban and rural citizens, you can divide a map into those strata, and then randomly choose neighborhoods or streets in each and ask everyone on those streets. Here you stratified by community type and then clustered by street.
304
Q: How can you get a parameter? A: By taking a ___________
Census
305
When there is no relationship between two variables, we say they are
independent (or not associated)
306
What is the null for a paired T test?
xbar diff=0 (the average diff is zero)
307
notation: what is mu - mu
true difference between two populatinon means
308
What is matched pair design?
A type of blocking where you match subjects to other "like" subjects MOST OFTEN SEEN WHEN YOU COMPARE A SUBJECT TO ITSELF!! (like pre-post tests)
309
what does binomial model tell us about?
exactly x successes in K trials. What is likelihood of exactly 3 heads out of 13 flips?
310
What do you have to look for with two sample procedures:
1. You have to check the conditions for each sample AND2. The samples have to be independent from eachother
311
What is a "percentile?"
It tells you the percent of data BELOW a certain value
312
If you take two bits of information from each subject there are two possible tests you could do. If the data is quantitative, you can do___ and if it is categorical, you can do a ______
regression t test, chi-squared test for independence.
313
What is the difference between categorical VARIABLES and categorical DATA?
The Variable is the overall category. Like "EYE COLOR". The data is the actual measurement from the subjects. Like "blue, brown, blue"
314
How can you describe spread?
range, IQR, stand dev, variance, or simply say: From here, to about here
315
What if a scatterplot goes straight across horizontally?
NO ASSOCIATION. That would be like height and IQ, they are independent so each height has about the same IQ.
316
What are random variables?
If you randomly choose people from a list, then their hair color, height, weight and any other data collected from them can be considered random variables.
317
Do we add or subtract st dev when combining models?
neither you always just add variances. Square the st devs, add them, then take sqrt.
318
How can you tell if variables in a contingency table are independent?
If the distributions are the same across the variables.. Then it doesn't DEPEND so INDEPENDENT. Ex: 30% of freshman and 30% of seniors like cabbage.
319
notation: What is Ha
The alternative. This is what you are trying to prove.
320
IF you are testing to see if a marketing program increases sales, describe a type 1 and type 2 error.
Type 1: you think it increased sales but it didn'gType 2: It actually increased sales but you didn't notice
321
One tail or 2 tailed? How do you tell?
if it just says "changed" or "different".. Then it is 2 sided.. DOUBLE THE P VALUE!If it says "more" "less than" "greater" etc.. Then it is just one sided..
322
How can you describe shape?
TWO THINGS: modes and symmetry.unimodal, bimodal, multimodal AND uniform, symmetric, skewed
323
What is systematic sampling?
collecting data from every nth subject.
324
What is "probability of at least one" the same as?
1-probability of NONE.
325
What does invnorm do?
It gives you the Z SCORE from a percentile
326
What is difference between 2 Samp T test and a PAIRED T Test
In a two sample T test you are comparing TWO SAMPLE AVERAGES to eachother. In a PAIRED T test you are looking just at JUST ONE average of the THIRD LIST… They are paired.. So you find each individual BEFORE-AFTER and take the average of all of those differences. You do ONE SAMPLE T TEST on it because you really have one mean. You just the average or the difference list.
327
How do you match OGIVES to histograms?
RECTANGLE DROP!!
328
how do you find z and t crit?
for z crit.. INVNORM(area in 1 tail) for t crit. INVT(area in 1 tail, deg freedom). area in 1 tail is just ( 1-CL) / 2
329
What is response bias? How do you avoid it?
Response bias is any influence that may sway the respondent e.g wording of the question, interviewer's behavior/background. Therefore, in a survey, ask questions that allow respondents to answer comfortably and honestly. Keep the wording "indifferent" or neutral in some way in order to unduly favor one response over another.
330
If you have one group and ask them two questions, what type of chi squared test is it?
Test for independence.
331
you reject when _____________ evidence
you reject when YOU HAVE EVIDENCE
332
If you are doing a one tailed test with alpha=.05.. What confidence interval goes with that?
90% confidence interval tests a one tailed test. There is 5% in the tail.
333
How do you find point estimate from an interval?
It is in the dead center of interval, so take the average of the upper and lower bounds.
334
What is the missed opportunity error? (the "I didn't notice" error)
Type 2
335
What do you call things that are not independent?
associated. Or not independent. We generally don't say DEPENDENT (unless talking about y variable on a scatterplot).
336
How do you describe SPREAD for bimodal or multimodal?
talk about the outer edges of the clusters "from here to here" or use the IQR.
337
what is the emperical rule?
mean 68-95-99.7 yeah!
338
How do you find relative frequency?
just divide frequency by TOTAL?.
339
not associated is the same as being ____________
independent
340
Is it always better to do a census or to sample?
depends on the availablility of the data. If the you want to look at SAT vs GPA, you may easily be able to get all of the school's data and do that study (a census). If you have to go out and get the info, you may want to take a sample to save time and energy.
341
What's wrong: Age and height have a correlation of 2.7
WRONG. Correlation must be between 1 and -1
342
If the distribution is bimodal or multimodal, what would you use for center and spread statistics?
Talk about each mode (center) and maybe use the range or IQR. You could also say "one group seems to go from __ to __ and the other from about __ to __"
343
Why are there different standard deviation formulas for population and sample? Arent they the same thing?
Both equations are actually doing the same thing. They both attempt to calculate the true population proportion. When you have all of the data from the population you just divide by n and get the actual SD. BUT If you only have a sample then you are using that to make a guess (inference) at what the population standard deviation is.. What happens is that samples tend to have less spread so their SD underestimates the population, BUT, when you divide by n-1 instead of n, It gives you a better estimate of what the population standard deviation is.
344
Year in school (F,S,J,S) and Pizza Preference (pepperoni or cheese) are __________ because _______________
independent because all grades have similar preference distributions.. 40% cheese, 30%pepperoni, 20% veggie 10% other
345
What is a null model?
It is a sampling distribution. It tells us how sample statistics would vary if the null were true. It is centered at the null. A pile of p-hats or x-bars.
346
How can you check for "straight enough?"
Residuals plot fool! check the resids
347
What is a standard deviation?
average (typical) distance to the mean (about). It is how far you expect a random value to be away from the middle.
348
What is the "you think it worked but it didn't" error?
Type 1
349
what happens to t models as n gets larger?
The models look more like the normal model. An infinite sample size would give a t model identical to the normal model.
350
What is the "nearly normal" condition for means? (aka large enough sample)
If n>30, good to go. If n<30, then you have to make sure the histogram of the sample looks normalish.
351
What does a "significance level of .02" mean?
set alpha= .02 and reject only p-values below that
352
How do you describe CENTER for skewed or distributions with outliers?
use the MEDIAN
353
What do we sometimes call a categorical variable?
qualitative
354
marginal distribution
distribution in the margins (outside of the table). The overall distributions of a single variable in contingency table.
355
What is the total area under the normal curve?
1 or 1.000
356
How do you find the mean of a random variable if it is in a table?
values in L1, percents in L2, run 1-VAR STATS L1, L2.
357
What is the difference between confounding and lurking?
Confounding is in experiments, like sunlight confounding a fertilizer experiment. Lurking is when you think hot chocolate causes ski accidents. "lurking"is actually a word not even used in AP STATS.
358
what is representative?
It means that the sample statistics will be kind of like the population parameters.. The sample "looks like" the population.
359
Lurking variable: Why are there more ice cream sales on days that there are more surfing accidents? Is the ice cream putting surfers at risk?
The WEATHER is the lurking variable. When it is a nice day, more surfers and more ice creams are sold. So, the WEATHER causes both to go up and down together.
360
How else can you explain power?
The likelihood you correctly reject a false null.. The likelihood you correctly detect what you were trying to detect
361
How can you increase power?
Increase alpha or increase sample size..
362
what is df for goodness of fit?
cells - 1
363
How do you undo a log when solving? log x = stuff or log x = m
10^ stuff 10 stuff that will get you x or x= 10 m
364
What are the xbar and mu in t-test? (on calc)
xbar is your sample mean, mu is your hypothesized population mean
365
Computer Output: What is "S"
The average, or typical residual.. Standard deviation of the residuals typical distance from actual value to the model's prediction. About how far off your prediction is likely to be.
366
What is difference between non response bias and undercoverage?
You may ask someone to take a survey, they may say no. They may feel differently than the people who decide to take the survey. In this case, that is non-response bias. Undercoverage happens when you didn't even ask some people to take the survey. The people you didn't even ask might feel different.
367
When there is a relationship between two variables, we say that they are
associated (or not independent)
368
What is a level in an experiment? give example
Example. For the Factor "SLEEP" the, level(s) would be how many hours the subjects were alowed to sleep.. 4 hours, 6 hours, 8 hours.. 3 levels
369
4 ingredients: What is "compare?"
Having something to compare your treatment with helps you see its effectiveness. Usually you compare to a control group (or a previous value when the subjects are their own control group).
370
what is probability?
THE LONG RUN RELATIVE FREQUENCY!!
371
Think of the minimum value, the median and the IQR, which is impacted by shifting (adding a constant?)
adding a value shifts the entire histogram to the right, so the min and the median will increase by that amount, BUT THE IQR WILL NOT CHANGE.
372
What are the 3 steps in hypothesis testing AFTER YOU CHECK CONDITIONS?
1. Make your Ho and Ha 2. Make a Null Model (centered at null, use your Ho as center and in calculations, use your sample size).. This is a sampling distribution for the statistics if the null were true. 3. THINK then CHECK. use your statistic (p-hat, x-bar, phat1-phat2, xbar1-xbar2) to calculate your test statistic and then p value
373
If something is correlated is it associated?
Yes. If it is correlated then it must be associated. However, if it is associated, it may not be correlated.
374
If you take two bits of information from each subject there are two possible tests you could do. If the a chi squared test would be for _____ data and a regression t-test would be for ______ data
categorical, quantitative.
375
4 ingredients: What is "randomization?"
You want to randomly assign subjects to treatment groups.
376
If you want to calculate the probability (%) something falls between two values in a normal model, what do you do?
find z scores for both value, and then normcdf (Z LOW, Z HIGH )
377
binocdf
(n,p,x) .. Probability of X OR LESS successes in N trials. (CUMULATIVE probability)
378
What is the null model (the sampling distribution) in a 2 sample mean t-test?
a pile of differences of TWO MEANS samples, taken from a bunch of PAIRS of samples. Take two samples, calculate two means, subtract to get a difference, PUT THE DIFFERENCE IN THE PILE.
379
What is meant by cumulative frequency?
ADD up the frequencies as you go. Suppose you are selling 25 pieces of candy. You sell 10 the first hour, 5 the second, 3 the third and 7 in the last hour, the cumulative frequency would be 10, 15, 18, 25
380
How do you find mean and sd of probability model?
put values in L1, probabilities in L2, and run "1-var stats L1,L2" and you get it!
381
What are the "good" sampling methods?
SRS (simple random sample), stratified, clustered, systematic, multistage
382
What is Q2 also known as?
the median
383
the output for normcdf(Zleft, Zright) is_______
the area under the normal curve between the given z scores
384
How do you write conclusion if you fail to reject?
With a p-value this high (p-value > alpha) I fail to reject the null. There is not enough evidence to say that more students like eggs now.
385
Systematic, how do you find the N for every nth subject, and then how do you proceed?
TOTAL POP/SAMPLE SIZE= your n (round down). Then use RAND INT to Randomly choose first. RANDINT(1, n). And then take every nTH.
386
In which sampling methods do all GROUPS have the same probability of being chosen?
Only in SRS do all GROUPS have the same probability of being chosen, all of the other methods have IMPOSSIBLE GROUPS.
387
how do you describe direction? (in regression)
positive or negative
388
Name types of bias
undercoverage, non response, response, voluntary
389
When drawing a graph or chart, what do you have to remember to do?
LABEL AXES, make a KEY(if needed ) AND GIVE IT A NAME!!! "Figure 1: Age and Food Preference"
390
independent is the same as __________
not associated
391
notation: what is phat - phat
difference between two sample proportions
392
name 2 differences between observational studies and experiments
1. Experiments can prove causation (studies can't) . 2. In experiments, you assign treatments (studies you just watch)
393
notation: what is x-bar
mean of your sample
394
What is the null model (the sampling distribution) in a 2-proporiton Z test?
a pile of differences of TWO PROPORTIONS, taken from a bunch of PAIRS of samples. Take two samples, calculate proportions, subtract to get a difference, PUT THE DIFFERENCE IN THE PILE.
395
What if you want more cofidence with same size interval?
increase your sample size
396
What are the differences between the subjects in strata and the subjects in clusters?
the "strata" are homogeneous, or have similar traits. The clusters are heterogeneous, or mixed traits.
397
How are mean, median and mode positioned in a skewed left histogram?
goes in that order, mean median mode
398
What is a categorical variable?
Qualitative variables are like categories: Blonde, Listens to Hip Hop, Female, yes, no? etc.
399
Give an example of independent variables
If 80% prefer cheese and only 20% prefer pepperoni IN EACH GRADE AT BHS then they all have the same preference, so grade doesn't matter. We say "school year and pizza choice are independent"
400
how do you combine probability models?
add or subtract the means, and then ADD THE VARIANCES ALWAYS
401
how do you find deg freedom?
n-1 for one sample, for 2 samples you must use calculator. For PAIRED use n-1, REGRESSION IS n-2
402
what is n! ?
it is "n factorial" example: 5! = 5*4*3*2*1= 120. tells you how many ways you can arrange n objects.
403
What is beta?
It is probability that you'll make a Type II error.. P(Type II error)
404
Interpret r squared
r squared % of variability in y can be explained by the model with x. The rest is in residuals
405
how do you describe form of a scatterplot?
straight or curved?
406
Do you use p-hat or p-null when you calculate your standard error in a null model?
use p-null..
407
How do you find Margin of Error from an inteval?
It is half the width.. (HI-LO divided by 2) Remember you stand at statistic (point estimate) and reach up and down a Margin of Error. So an inteval is always exactly 2 margins of error wide)
408
Give example of a matched pair design study for fuel efficiency
Testing fuel efficiency of different gasolines. Subjects use both fuel A for a month and fuel B for a month and compare, based on their driving habits and vehicle, which was more efficient. BE SURE TO RANDOMLY CHOOSE WHICH ONE GOES FIRST FOR EACH SUBJECT.
409
What are the mean and standard deviation of a sampling distribution for a mean?
mean is mu and standard deviation is sigma/root n (look at formula sheet) N(mu, sigma/rootn)
410
data or datum?
datum is singular.. Like "hey dude, come see this datum I got from this rat!" data is the plural.. "hey look at all that data Edgar got from those chipmunks over there!!"
411
What is the "hot hand" view of probability?
Misrepresentation of the law of large numbers. If someone flipped a coin and it landed on heads 4 times in a row you'd expect it to be heads again because "heads is hot".. NOT TRUE..
412
If asked to compare distributions, what should you write about?
A sentence comparing the SHAPES. A sentence comparing the CENTERS. A center comparing the SPREADS. and a sentence comparing the STRANGE STUFF. (GSOCS)
413
Compare data to statistics
Data is each little bit of information collected from the subjects?. They are the INDIVIDUAL little things we collect? we summarize them by, for example, finding the mean of a group of data. If it is a sample, then we call that mean a "statistic" if we have data from each member of population, then that mean is called a "parameter"
414
what is the LSRL
the "least squares regression line" that line you plot OR That equation
415
How many SD wide is the IQR in a normal distribution?
NOT 2!!!! Think about it. The middle 68% is 2 sd wide, since the IQR is only the middlest 50% it must be less than 2. try [invnorm(.75)] x2. You find that it is only 1.35 SD wide if the distribution is nearly normal.
416
A 4 year high school of 2000 students, sampling 40 high students: Describe a stratified sample
Stratify by year. Randomly choose 10 FR, 10 SO, 10 JU and 10 SENIORS
417
What is a statistic?
A numerical summary of a sample. Like a mean, median, range? of a sample.
418
what is a parameter?
some numerical summary of a population. Often called "the parameter of interest." It is what we are often trying to find.. It doesn't vary. It is out there and STUCK at some value, it is the truth, and you'll probably not ever know it! We try to catch them in our confidence intervals, but sometimes we don't (and we don't know it!). It Could be the mean of a population, the standard deviation of a population, the proportion of successes in a population, the slope calculated from a population, a difference of 2 means from 2 population, a difference of 2 proportions from population
419
What does GSOCS stand for?
Gaps Shape Outliers Center Spread (put on your gsocs when comparing distributions) be sure to talk about each one clearly (make a list)
420
What percentile is the median (aka Q2)?
50th
421
What is a quantitative variable?
Quantitative variables are numeric like: Height, age, number of cars sold, SAT score
422
What is a CUMULATIVE FREQUENCY GRAPH?
An OGIVE. It shows the added up totals as you go left to right.
423
If something is associatied is it correlated?
Not necessarily. It can be associated and have a zero correlation ( parabolic scatterplot) or categorical variables.
424
what is the shortcut normcdf?
gives % from raw data, skips Z score. normcdf (low VALUE, high VALUE, mean, sd)
425
If there is a screening test for mathphobia, describe a type 1 and a type 2 error
Type 1: You think the person has mathphobia, but they don'tType 2: They have mathphobia, but you didn't notice
426
If a distribution is skewed right, what will be greater, the mean or median? WHY?
Mean. The mean moves further to the right to keep balance.
427
When can you round?
AT THE VERY END!!! (keep at least 3 digits until end!)
428
how are t models like Normal models?
both are unimodal and symmetric. T models aren't as high and have more area in tails, that’s why you have to reach out a little further than z for same confidence.
429
Give a simple example showing that adding a constant doesn't change the spread, but changes the center. (this always happens)
Data set: 1,2,3,4,5 Spread (range):4, Center: 3 add three and get new data set: 3,4,5,6,7 spread:4 Center: 5 (center went up, spread stayed the same). The IQR and SD will stay the same, but median and mean go up 3. Called shifting, or sliding the data.
430
notation: what is xbar- xbar
difference between two sample means
431
How is Blocking in an Experiment Similar to Stratifying in a Sample?
The two are similar because they divide the subjects into homogenous groups where the subjects are all similar (these traits were already present in the population)
432
Which hypothesis shows what you are trying to prove?
The alternative.
433
what happens if you ADD a constant to each value in a data set?
it is SHIFTED only. Does not impact spread. This effects all of the data values and measures of center (mean, med) and quartiles, deciles, etc, IT DOES NOT CHANGE THE SPREAD! (IQR, St Dev, Range all stay the SAME).
434
How do you describe SPREAD for skewed distributions (or distributions with outliers?)
Use the IQR
435
How do you make confidence interval for slope?
STAT +/- CRIT SE of slope
436
where are the "outlier fences?"
1.5 IQR above Q3 and 1.5 IQR below Q1. Just a rule of thumb.
437
What is diff between homogeneity and test for independence?
homogeneity is more than one sample and asking about one variable, independence is just one sample with two variables.
438
How can you describe the center of a distribution?
OPTIONS: give the mean (balance), median (splits area in half), mode (peaks, if bimodal talk about both modes) or say "centered around ____"
439
What is the purpose of matching?
it isolates the differences between subjects so help see the impact of the treatment.
440
Make a guess as to what relative cumulative frequency is?
It is the ADDED up PERCENTAGES.. An example is selling candy, 25 pieces sold overall., with 10 the first hour, 5 the second, 3 the third, and 7 the fourth hour, we'd take the cumulative frequencies, 10, 15, 18 and 25 and divide by the total giving cumulative percentages. .40, .60, .64, and 1.00. Relative cumulative frequencies always end at 100 percent.
441
4 ingredients: What is "replication?"
Having enough subjects. You don't want to test fertilizer on just one plant.
442
What is sampling variability?
same as sampling error. The natural variation of sample statistics.. NOT DATA.. Samples vary. so do their statistics.. Parameters do not vary!
443
If r= 0.8. An x value that is 2 standard deviations above the mean will have a predicted y value that is _______
1.6 standard deviations above the mean in the Y direction
444
using calculator: suppose 30% of dogs have fleas. WTPT more than 10 out of 40 have fleas?
1 - 10 or less1-binocdf(40, .30, 10)
445
What is quantitative data?
The actual numbers gathered from each subject. 211 pounds. 67 beats per minute.
446
How is a sampling frame different from the population?
Suppose you are wondering how elderly people on the cape feel about a new medicare law. If you go to nursing homes and randomly sample residents, then the frame is "elderly people at those nursing homes." Your population is still elderly people on cape cod.
447
How can you use random numbers to sample?
Number the subjects 00-99 (if less than 100) or 000-999 (if less than 1000) or 0000 to 9999 etc.. then use a random number table taking one, two, three or four numbers at a time. Throw out repeats.
448
What are we confident in?
our confidence lies in our interval. if we took another sample.. We'd have a different interval..
449
Example of nonresponse bias
In a survey, a person does not answer a few questions (or a person is on your list and you can't get a hold of them)
450
What is frequency?
How often something comes up
451
How do you find df in 2 samples?
USE CALCULATOR.(or smaller sample-1). you have to run an interval or a test on your TI and read the output (unless you want to use the equation.)
452
What is a mistake that people make with the law of large numbers?
they make short term predictions. The law of large numbers talks about the LOOOOOOONG run relative frequency.
453
How do you find Expected Count?
for GOF: Exp %(total).. For indep and homog: ROW*COL/TOTAL
454
What are the mean and standard deviation of a sampling distribution for a proportion?
mean is p and sdandard deviation is root pq/n (look at formula sheet) N(p, root (pq/n) )
455
When sampling, what kind of sample are we striving to get?
A representative sample, we want our sample to have similar charactaristics as the population
456
How do you find Q1 and Q3?
Q1 is the median of the bottom half and Q3 is the median of the upper half (they are the 25th and 75th percentiles)
457
How do you descrive SPREAD for unimodal and symmetric distributions?
use the standard deviation
458
what are the names of four one-sample procedures we do?
1 proportion Z interval1 proportion Z test1 sample mean T interval1 sample mean T test
459
WHAT ARE THE TWO INDEPENDENCE EQUATIONS USED FOR CHECKING?
P(A)=P(A|B) or P(A)*P(B)= P(A and B)
460
How many ways can I arrange M N W Z ?
4! 4*3*2*1 = 24 ways
461
For both a chi squared test for independence and a regression t test you are looking for an association, how do the null hypotheses differ?
The chi squared will be in words.. Ho: the variables are not associated. The regression t test will be with symbols (and words). Ho: Beta = 0 (the slope is zero) . Saying "beta=0" is the same as saying "there is no association"
462
What are the "bad" sampling methods.
convenience samples, voluntary samples
463
When are box plots used most often?
When comparing a bunch of different sets of data.
464
How does multiplying by a constant impact the summary statistics of a data set? (or random variable)
It is SCALED. Both center and spread are effected. They all (mean, median, IQR, SD, range) get multiplied by three. (BE CAREFUL, remember the variance is the SD squared, so the variance gets multiplied by 9).
465
How do you describe CENTER for bimodal or multimodal?
talk about the modes (the lumps, the clusters)
466
What is a sample?
A subset of a population, often taken to make inferences about the population. We calculate statistics from samples.
467
Is sampling error a mistake?
IT IS NOT A MISTAKE!!! Because the data in samples are generally different, the statistics calculated from one sample to another vary and are generally not equal to the parameter. This variablilty of STATISTICS is called sampling error.
468
not independent is the same as
associated
469
notation: what is Ho
The NULL, the dull, the "things haven't changed" hypothesis
470
What is the NULL HYPOTHESIS?
The DULL HYPOTHESIS, the nothing changed hypothesis, the no-difference hypothesis, the "he's telling the truth" hypothesis, the "No trickery" hypothesis
471
How do you do the tricky reverse tree problems (like test says pregnant.. What is probability you actually are?)
SPLIT UP POPULATION FIRST >>>>>> then split the groups by outcomes of the test.. BE SURE TO LABEL THE OUTCOMES and multiply the branches to the end To find P(pregnant|test says pregnant), only look at the 2 branches that end with test saying pregnant.. put the actual pregnant over the sum of both pregnant and non.
472
What "designs" are there for experiments?
completely randomized, random block, and matched pair design(type of block)
473
How is a margin of error different from a standard error?
A margin of error is a NUMBER OF STANDARD ERRORS. It is how far up or down you go in a confidence interval. A standard error tells you about the spread of a pile of statistics (a sampling distribution).
474
How can you straighten data?
Do stuff to the y (square it, root it, log it, etc) and recheck the plot. Remember to put the transformation into your equation. Example Sqrt y = 4.33 - 2.03 x
475
how can you decide the right test? What are the 3 questions?
1 or 2 samples? Proportions (z) or Means (t)? Test or Interval?(YES/NO/PROP/Z)
476
how are beta and power related
as one increases, the other decreases, and vice versa. They have to because they BOTH ADD TO ONE!!! Power + Beta = 1
477
What is the Fundemental Theorem of Statistics?
The CLT!! The Central Limit Theorem!
478
What is meant by relative frequency?
The PERCENT of time something comes up (frequency/total)
479
How do you undo sqrt when solving? like sqrt(x) = stuff
^2 (raise stuff to power of 2 to get x)
480
Can you predict an X by using a Y?
NOT WITH THE SAME EQUATION! BE CAREFUL!! Don't just solve for x. You have to change the entire equation and start from scratch. (run LinReg L 2 , L 1 )
481
What if the scatterplot is curved?
Either straighten the scatter and fit a line, or keep it and fit a curve Try quadreg, cubicreg, lnreg, logreg and check the graph and the r.
482
what is that (n over k) thing in the binomial equation?
n choose k it tells you how many ways you can choose k objects from a set of n things. The formula is n!/(n!(n-k)!) the two numbers on bottom add to the number up top. These are coefficients in expanded binomials and can also be found in Pascal's Triangle
483
What is wrong with using voluteers in an experiment?
Not much. In an experiment, we are not looking for a sample that is like the population. We just want to see the effectiveness of a treatment. It is fine if the subjects are all similar. In fact it is best sometimes when they are!
484
Give example of randomized block design for a new anxiety med vs placebo with 100 volunteers (60m and 40f)
Block by gender. Randomly assign 30m to new and rest placebo. Randomly assign 20w new and rest placebo.
485
What is prospective study?
Prospective study is when you study the experimental unit's present and future.
486
What are some strong r values and some weak r values
Strong r values are close to 1 or -1, like -0.83 or 0.94. Weak r values are close to zero like 0.10 or -0.06
487
geopdf
(p,x) probability of FIRST SUCCESS being ON the Xth trial
488
Why don't we always use the mean, we've been calculating it all of our life ?
It is not RESILIENT, it is impacted by skewness and outliers
489
Interpret residual: Points below the line/negative resid
"the model overpredicted" or "Actual value was below the the expected (or predicted)"
490
What is the difference between discrete and continuous variables?
Discrete can be counted, like "number of cars sold" they are generally integers (you wouldn't sell 9.3 cars), while continuous would be something like weight of a mouse? 4.344 oz.
491
What is a weakness of a SRS?
Suppose you want a sample of 50 high school students, with an SRS, although unlikely you could get "all freshmen" which wouldn't be representative.
492
If the mean is above the median, the distribution may be
skewed right. the mean follows the tail
493
What is an unbiased estimator?
When the sampling distribution (pile of sample stats) is centered on the true population parameter. Basically, the pile of x bars should be around mu.
494
What is the difference between a population mean and a sample mean?
population mean is the mean of a population, it is a parameter, sample mean is a mean of a sample, so it is a statistic. We use sample statistics to make inferences about population parameters.
495
4 ingredients: What is "BLOCKING?"
If you think different groups of subjects may respond differently to treatments because of location, gender, age, then you make BLOCKS, and make sure to compare the treatments within each block.
496
First step in interpreting slope
Write "slope units y over 1 unit x" and look at it.
497
can independent events be disjoint? EXPLAIN
NO, if they are independent, then knowing one doesn't change the probability of the other, but if they are disjoint, knowing one makes the other impossible, so it does change the probability to 0
498
What is the difference between the distribution of a sample and a sampling distribution?
A distribution of a sample is just a histogram of the DATA in a sample. A sampling distribution is made from an bunch of sample STATISTICS. It is the distribution of the statistic that was calculated from those many many samples.
499
Give an example of matched pair design for comparing a new blood pressure medication to an older version?
Have subjects use the new medication for a month and the old one for a month and compare. Be sure to randomize which month and blind.
500
What is wording bias
A type of response bias, When the wording of the question impacts response to it. (type of response bias)
