UNIT 1, 2, 3 and 4. Complete mixed set Flashcards
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.
What is the difference between a study and an experiment?
In a study you are basically just watching and in an experiment you are manipulating factors and (hopefully randomly) assigning treatments. Sometimes people call an experiment a study.
how do you interpret slope?
for an increas of 1 [unit of x] there is an (increase/decrease) of [SLOPE] [units of y]
Shape description?
unimodal, bimodal, multimodal, uniform, symmetric, skewed
outliers in regression?
doesn’t follow the “flow” (pinky trick)
RAND VARIABLE:X has mean y and standard deviation of z.A has mean b and standard deviation c.Find: Mean, SD and VAR of: 3X
mean: 3ySD 3zvar 9z2
What is quantitative data?
The actual numbers gathered from each subject. 211 pounds. 67 beats per minute.
What does GSOCS stand for?
Gaps Shape Outliers Center Spread.
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. RETRO-REVERSE, PROspective- PResent and On,
If someone does a pre and post test, what type of experimental design is it?
BLOCK design. Matching with themselves is blocking. Little blocks of two (well, actually one, you and yourself)
If combining 4 random variables with standard deviations of m, p, q, r…. what is the new combined standard deviation?
SQRT(m2 + p2 + q2 + r2)
Can you stratify in an experiment?
NO. stratification is a sampling method, blocking is method used in experiments. They are similar ideas.
When to use general mult and what is it?
AND probability. Use when associated. P(this)*P(that|this). (IT ALWAYS WORKS FOR ALL SITUATIONS. When indep, the P(that|this) = P(that). So you end up with the simpler independent version)
What’s the difference between lurking and confounding?
Lurking varibles, on one hand, infer the assoiation between the two varibles; confounding variables, on the other hand, make it unclear which variable has had an impact on which in an experiment.
What is a big difference between subjects in experiments and members of a representative sample?
In experiments you don’t need a representative sample, you can have volunteers, convenient subjects and that is OK. You are looking at impact of treatment, not at getting a representative sample.
if you switch x and y does r change?
NO. The strength stays the same.
How to describe association on a Scatterplot?
DIRECTION, FORM, STRENGTH
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
How can you match boxplots to histograms?
USE THE FISH TANK METHOD!
what is pythagorean theorem of stats?
st dev of combined model is: sqrt(st dev squared + st dev squared) or more if you combine more?
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)
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)
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? or DISJOINT EVENTS ARE ALWAYS ASSOCIATED!!
What is a great way to assign two treatments to twelve subjects with a random number table/generator
assign each subject a random number, then the lowest 6 get the treatment.
How can you estimate the probability of an event occurring?
run a simulation. Find the percent of trials that you observed the event occur.
what is leverage?
leverage just means it is far away from x-bar? far right or left from the middle, Some leverage points are not influential if they go along with the flow of the scatter.
What is random sampling?
When we use change to select a sample
What type of probability when you are looking for the first success after the fifth attempt?
not on the 4th or before1 - geocdf(p, 4)
What symbols do we use for population mean and sample mean?
Mu for population mean, xbar for sample mean.
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.?
which calculator function gives you a percent?
normcdf
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”
How many ways can I arrange 4 letters?
4!432*1= 24 ways
Gender and Video Game playing are___________ because_______
associated (or not independent) because a higher percentage of males play video games. (think, It depends on gender)
strength?
give the r value (if straight), or say? “tightly packed? loosely packed”
What percentile is the median (aka Q2)?
50th
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, notice they are numbers. Statistics and parameters are summaries like ?the average breath holding time in the sample was 52.4 seconds? notice it is a number (not a %) and a parameter would be ?the average breath holding time in the population was 52.4 seconds?
What does normcdf do?
It gives you the area under the normal curve between any two z scores
Which is more sensitive to outliers and skewed? Mean and SDor Median and IQR
Mean and SD are more influenced by outliers, median and IQR are RESISTANT, RESILIENT, ROBUST!!
probability this AND that . Add or multiply?
MULTIPLY
For information purposes, which gives most, stem-leaf, histogram or box-whisker?
Stem leaf gives the actual values and the shape, histogram just the shape, and box-whisker the least amt, but are great for comparing multiple distributions.
When do we often use mode?
With categorical variables. For instance, to describe the average teenagers preference, we often speak of what ?most? students chose, which is the mode. It is also tells the number of bumps in a histogram for quantitative data (unimodal, bimodal, etc,).
When can you use single digits for simulations?
When the percent is a multiple of ten, like “30% of teachers secretly twerk”, then you would assign 1-3 or 0-2 as twerking teachers.
What is more important, percent of population or size of sample?
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..
How to find likelihood of being pregnant, given the test says you are? (tree)
Split population by %pregnant and %not who take test, then each of those into what test says. Then look just the groups that the test said pregnant. Then find: %pregnant/(total percent in both groups).
If something is correlated is it associated?
Yes
What percent of the data is above Q3?
25%
When would you use two digits instead of a single on a random number table?
When the percent is not a multiple of ten, Like “18% ofdogs eat underwear”, You’ll have to assign 01-18, or 00-17 as undie eating dogs.
What is a contingency table?
A two way table. shows distributions across 2 variables like gender and music pref.
Give example of when you would block
Looking to see impact of different leather preservers on chairs in an airport. You might block according to proximity to window, or proximity to main entrance. The window seats will get more light and the ones closest to entrance may get more use, they will age and wear differently so you want to make sure some in each group get the different treatments.
What are the two major branches of AP STATS?
Inferential and Descriptive
What is a sample?
A subset of a population, often taken to make inferences about the population. We calculate statistics from samples.
Give example of confounding variable
Sunlight and Usage could be confounding variables. Leather preserver, If you randomly choose from all chairs in an airport for treatment and brand A randomly has a lot of chairs near the sun, Brand B randomly gets a lot fo chairs near the main entrance and Brand C randomly gets the chairs that don?t have a lot of sun, or a lot of use, you may think that brand C works the best, when in fact, the results were confounded by sunlight and usage.
How can you straighten data?
Do stuff to the y (L1) (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
What is the area under the normal curve?
1 or 100%
What is the problem with convenient sampling?
The sample may not be representative as it is not randomized to include every type of person. For example, Friends and family are convenient but they likely share similar opinions and thus the sample is not representative of a population.
If you want to find % below a value, what do put into normcdf (? ?)
find z score for value, and then normcdf (-999, Zright)
Do we say things are “dependent?”
NO! we say associated
What does r tell us?
strength of relationship. How strong and positive or negative arelationship is between two QUANTITATIVE variables, It does not tell you about FORM!!
Why do you have to block?
You don’t have to, But you might want to if you feel that the experimental units (subjects) may respond differently to the treatment because of confounding variables.
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 statistics.
how do you describe form in a scatterplot?
straight or curved
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.
What are humans bad at ?
Humans are bad at generating random numbers.
What is prospective study?
Prosepctive study is when you study the experimental unit’s present and future response variable.
How can you simulate a coin flip with random number table?
Assign heads to odd numbers and tails to even numbers.
What is control?
Control is just that. Controlling stuff, as much as you can. (the environment, the subjects, the wording, the people involved). You try to keep factors constant in each trial if you believe it would effect the outcome of the experiment. Also having a group that is not getting treatment helps to control because it measures the effects of the natural environment.
what does influential mean?
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.
What is the “mean of a random variable?”
The expected value. sum of probs times values
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.
What is systematic sampling?
Systematic Sampling is one of four different ways to make a survery sample random. Systematic sampling includes picking every Nth number of what you are sampling (for example people.). You must still start on a random person and then from then on take every Nth person. So you can take every 10th person in a line in order to take a survey as long as you also start on a random individual.
What is the placebo effect?
When those who get the placebo (instead of treatment) show improvements, or show the effects of the treatment. This often happens to up 20% of participants!
What if a scatterplot goes straight across horizontally?
NO ASSOC. That would be like height and IQ. they are independent so each height has about the same IQ.
will residual plots always show outliers? (will outliers always have large residuals?)
Not necessarily, but usually. Some points have so much leverage, they pull the line up to it?
What is probability first success is on 7th try?
qqqqqq p (q^6*p). (this is a GEO prob)
what’s the difference between response bias and nonresponse bias?
response bias is anything in a survey design that influences responses (wording of questions, person asking, time of day, location, temperature). Nonresponse bias is bias introduced to a sample when a large fraction of those sampled fails to respond.those who respond are likely to not represent the entire sample.
how do you describe direction o fa scatterplot?
positive or negative
If a distribution is skewed left, what will be greater, the mean or median? WHY?
Median. The mean moves left to keep balance.
what is b1 and bo ?
b1 is the SLOPE, and bo is the intercept. Remember that bo can be thought of as “b old” it is the old b? the intercept in y=mx+b? so it is still the intercept.
What is a census?
Like a sample of the entire population, you get information from every member of the population
What values can r be?
from -1 to +1
How do you use a table of random digits?
FIRST, Make a key showing what the digits represent, whether you will use single, double or triple digits, and which, if any will be ignored. SECOND, Decide when a trial will end (after 12 events, or after 12 successes), THIRD, Make sure to clearly label the successes and where the trials end.
binopdf(inputs)
EXACTLY X successes in N triesbinopdf(n,p,x).Probability of exactly X successes in N trials. (PARTICULAR probability)
Sample size compared with the fraction of a population: For instance, do you need like 10% or 20% to have a good sample?
percent of popluation is irrelevent (as long as you have less than 10% for our procedures), The sample size determines how well the sample represents the population, not a fraction of the population sampled. The fraction of the population that you’ve sampled doesnt matter. Its the sample size its self thats most important. A sample of 100 people can tell you as much about a population of 10,000 as it can about a population of 2 Billion.
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. Not true, 5 flips is not the long run. Infinity is. The next flip still has a 50% chance of being another head. You may hear someone say “he’s do for a hit” or “it’s bound to rain soon” both bad.
What’s the difference between cluster and stratified?
Stratified- you take from each strata, cluster you just grab a couple clusters. In stratifying, the strata are all different from eachother, so you need a bit from each strata, in clustering the clusters each have all of the traits of the population, so yoy can grab 1 cluster and it will be representative. If you grabbed just one strata, you’d just have a bunch of freshmen boys instead of a sample of the entire school…
How can you simulate rolling 1 die with a random number table
use only the digits 1-6, ignore 0, 7, 8, 9
What type of probability when you are looking for exactly 5 or less successes in twelve attempts?
binocdf(12, p, 5)
Give three examples of variables that are not independent (associated)
- Playing video games and gender (Knowing male makes itmore likely theyplay)2. Whether it is snowing and the month you are in (some months are more rainy than others, knowing what month changes likelihood of snowing)3 If a pet is a dog and if it is a cat (knowing it is a dog makes it certain that it is not a cat).(notice, knowing one bit of information changes the likelihood of the other being true also).
RAND VARIABLE:X has mean y and standard deviation of z.A has mean b and standard deviation c.Find: Mean, SD and VAR of: X + X + X
mean: y+y+ysd SQRT(z2+z2+z2) ….var(z2+z2+z2)
What is the variance?
The average squared distance to the mean (It is the SD before you take the square root, so it is the stuff under the radical in the formula)
how can you check for “straight enough?”
residuals plot fool!
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, how do you feel about the border wall? “
When to use general add and what is it?
OR probability. Use when not disjoint. (subtract overlap)P(this OR that) = P(this)+P(that) - P(this and that)(IT ALWAYS WORKS IN ALL SITUATIONS, when disjoint, P(this and that)= 0, so you end up with the simpler disjoint version)
What is the difference between confounding and lurking?
Confounding is with experiments, it is the thing that may be causing the different effects instead of the treatment (sunlight instead of leather preserver). Lurking is with regression, it is when something is causing things to go up and down together like how the weather impacts ice cream sales and beach injuries (rise and fall when more people are at the beach). Confounding is a vocab word for this course, lurking IS NOT.
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.)
For information purposes, which gives LEAST, stem-leaf, histogram or box-whisker?
Box/Whisker, BE CAREFUL, you really don’t know how things are distributed. The fish tank gives a very GENERAL look. There can be little modes in any of the quarters?
What is frequency?
How often something comes up
How is clustering and stratifying different when doing a sample?
Clustering is when chosen at random a group from the population that looks like the population, clusters should be heterogenous. While Stratifying is slicing a population into homogeneous groups(strata). Then randomly sample within each stratum before the results are combined.
Do we add or subtract st dev when combining models?
neitheryou always just add variances. Square the st devs, add them, then take sqrt.
what is a clear example of where the mean would change but median wouldn’t? (this would show its resilience)
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 if one of them just got back from the casino, and instead it 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 carries, 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.
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 is from __ to __ and the other from about __ to __”
What type of study would find relationship beween Verbal and Math SAT?
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. If you had the database, it would be easy to do a census.
What is the median?
the middlest number, it splits area in half (always in the POSITION (n+1)/2 )
What do we sometimes call a categorical variable?
qualitative
What is homoscedasticity?
equal scatter along the regression line
What if the scatterplot is curved?
either straighten it and fit a line, or keep it and fit a curve (quadreg, cubicreg, lnreg, logreg)
Why blind the subject?
When people know they are getting a treatment, they may feel better even if the treatment doesn’t work. Their previous experience with the brand might bias their reporting or something,
What is a quantitative variable?
Quantitative variables are numeric like: Height, age, number of cars sold, SAT score, weight.
What is the mode?
the most common, or the peaks of a histogram. We often use mode with categorical data
We are curious about the average wait time at a Dunkin Donuts drive through in your neighborhood. You randomly sample cars one afternoon and find the average wait time is 3.2 minutes. What is the population parameter? What is the statistic? What is the parameter of interest? What is the data?
The parameter is the true average wait time at that Dunkin Donuts. This is a number you don’t have and will never know. The statistic is “3.2 minutes.” It is the average of the data you collected. The parameter of interest is the same thing as the population parameter. In this case, it is the true average wait time of all cars. The data is the wait time of each individual car, so that would be like “3.8 min, 2.2 min, .8 min, 3 min”. You take that data and find the average, that average is called a “statistic,” and you use that to make an inference about the true parameter.
What is a quality of SRS that is not a quality of Systematic, Stratified or Clustering?
In an SRS, all groups (samples) are possible, and ALL POSSIBLE GROUPS have the same chance of being picked. The other methods have lots of “impossible groups” SRS has no impossible groups.-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 4 people that are right next to eachothe (you are taking every nth person)
What is a level in an experiment?
A level is a specific value(s) that the experimenter chose for a factor that is manipulated.ex. Factor is sleep, level(s) would be how many hours the subjects were aloud to sleep, 4 hours, 6 hours, 8 hours, so 3 levels of the factor sleep.
If the distribution is unimodal and symmetric, what would you use for center and spread statistics?
Mean (center) and Standard Deviation (spread)
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 you use that to __________ about the flavor of the entire pot of soup, which would be the__________.
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.
Give a simple example showing that multiplying by a constant changes both the spread and the center. (this always happens)
Data set: 1,2,3,4,5 Spread:4, Center: 3 mult by three and get new data set: 3,6,9,12,15 spread:12 Center:9 (both center and spread were multiplied by three) IQR and SD will be multiplied by 3.
Why do you have to Stratify?
You don’t have to, But you might want to if you feel that a simple random sample might not be representative of the population . You want your sample to be like the population, a representative sample (it represents the population well). We stratify to make sure that all qualities of population are represented
How to make TREES with screening tests????
SPLIT UP POPULATION FIRST»_space;»» then split the groups by outcomes of the test
binocdf (inputs)
EXACTLY X OR LESS successes in N triesbinocdf(n,p,x)..Probability of X OR LESS successes in N trials. (CUMULATIVE probability)
What do you call things that are not independent?
associated
If asked to compare distributions, what should you write about?
Compare Shapes, Centers, Spreads, and Stranges. gaps The GSOCS
When can you round?
AT THE VERY END!!! (keep 3 significant digits until end!)
When we say “the average teenager” are we talking about mean, median or mode?
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.
What are the two types of observational studies?
Retrospective, and Prospective
How are mean, median and mode positioned in a skewed left histogram?
goes in that order, mean median mode
What is Placebo used for?
Placebo is used for control in an experiment. the purpose of placebo is to determine the change between the controlled treatment and the other treatments
How do you undo a log when solving?
10^ stuff
what are the percentiles from left to R on normal model?
2.5-16-50-84-97.5
if you mult or divide the x’s or y’s in regression (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)
Samplin Method Types?
SRS, stratified, clustered, systematic, multistage, convenience, voluntary
Why blind the treatment givers?
The treatment givers may behave differently as they administer the actual stuff vs when they administer the placebo. They could cue the subjects unknowingly.
