EOYR UNIT 1-4 ALL Flashcards
what does “regression to the mean” mean?
preditions for y are closer to the mean y (y bar) than the actual x is to the mean x (in s.d). Sons were closer to average height than the dads. Super tall dads had tall sons, but not super tall sons, on average.
what is a z score?
the number of standard deviations away from the mean
what is a simulation?
Basically a test based on reality with a sequence of random outcomes that model it. Like an imitation.
What is statistically significant?
When an observed difference is too large 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 something is less than 5% likely to have happened by chance alone.
What if the scatterplot is curved?
either straighten it and fit a line, or keep it and fit a curve (quadreg, cubicreg, lnreg, logreg)
How many ways can I arrange 4 letters?
4!432*1= 24 ways
Who chases the tail?
The mean chases the tail, the mean chases the tail, high-ho the derry-oh the mean chases the tail, and outliers,,.
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.
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”
What percentile is Q1?
25th
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 variability?
Differences, how things differ. There is variability everywhere, We all look different, act different, have different preferences, Statisticians look at these differences.
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 percentile is the median (aka Q2)?
50th
What type of probability when you are looking for exactly 5 successes in twelve attempts?
binopdf (12,p,5)
What is the difference between discrete and continuous variables?
Discrete can be counted, like “number of cars sold” or shoe size, school grade they are generally integers (you wouldn’t sell 9.3 cars), while continuous would be something like weight of a mouse, 4.344 oz.
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.
What do you call things that are not independent?
associated
What is it called when knowing one event happened does not change the probability of another event occuring?
independent events
How can you match boxplots to histograms?
USE THE FISH TANK METHOD!
probability this AND that . Add or multiply?
MULTIPLY
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)
How can we use Pascal’s Triangle?
To find probability of x successes in K trials.. BINOMIAL BABY!!!
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).
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.
If the distribution is unimodal and symmetric, what would you use for center and spread statistics?
Mean (center) and Standard Deviation (spread)
What is the difference between a cluster sample and random sample?
A cluster sample is when the population is first divided into sections of clusters that have all of the traits that the population has, so the clusters are representative. You grab a cluster as your sample. A random sample is all names in a hat so you could get any group.
probability this and that when they are not independent? How?
probability A times probability B (knowing A is true) called general multiplication ruleP(A)P(B given A)P(this)P(that given this)
Association and Independence,. How are they related?
Variables are either independent or associated. Associated means there is some relationship, independent means there is none.
How do you match OGIVES to histograms?
RECTANGLE DROP!!
What is an example of blocking that people often miss?
Matching, Like when someone does a pretest, treatment and then post test, they are blocked with themselves, aka matched to themselves
mean/SD/median/IQR, How do I know which ones to use?
when unimodal and symmetric, mean and sd. When skewed or outliers use Median and IQR, when bimodal talk about the MODES and maybe range or iqr
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).
does high r squared mean a good model?
CHECK STRAIGHNESS FIRST. you should check your plot and residuals to make sure model is appropriate and no outliers present? then it means something
What is the purpose of matching?
Matching, like blocking, reduces unwanted variation. In a retrospective or prospective study, subjects who are similar in ways not under study may be matched and then compared with each other on the variables of intrest.
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 called ____?
a datum, or a data value.
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.
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).
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.
Example of how not blocking would backfire
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,
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 type of probability when you are looking for the first success on or before the fifth attempt?
Geocdf(p, 5)
when does a trial of a simulation end?
Generally there are two cases:1. You want to know the probability of having x successes in n attempts (getting 3 smokers in a group of 5 students). Trials end when you get to n (get to 5 students). You record the number of smokers for each trial.2. You want to know how many attempts it takes to get f successes. Trials end when you get f successes. Record the number of attempts.
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
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.
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)
How is r calculated?
r= sum(ZxZy) / (n-1)—- the sum of rectangle areas on standardized axes
What is homoscedasticity?
equal scatter along the regression line
What are the 3 ways we used random numbers?
- To simulate the likelihood of an event occurring. (ch 11) 2. To choose a sample that is representative of the population and avoid bias.(Ch 12) 3. To assign subjects (experimental units) to treatments to evenly distribute variability and help reduce possible confounding variables.(Ch 13)
What type of probability when you are looking for exactly 5 or less successes in twelve attempts?
binocdf(12, p, 5)
Give some examples of response variables in an experiment
To test a medication, blood pressure might be response variable. To test and SAT course effect, SAT score might be response variable. To test a diet, “weight lost” might be a response variable.
Is it always better to do a census or a sample?
It depends, generally, it is better to do a sample since a census is expensive to execute, and because popultaions are always changing it is hardly more accurate then a sample. BUT,. For small populations, a census is fine.
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
What is a random sample?
When you choose a sample by 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.
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 marginal distribution? How does it differ from a conditional distribution?
overall distributions of a single variable in contingency table (out in margins) For instance, in a gender vs music preference, the overall distribution of gender would be a marginal distribution, like “22 males and 18 females”. A conditional distribution is within the table, a distribution along the given condition, for instance:” of the country music lovers, 8 were male and 3 were female”
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 frequency?
How often something comes up
what’s up with extrapolation?
not a good idea?? sometimes it’s all you can do, but still, NOT GOOD
Give three examples of independent variables
- Being tall and having a high GPA2. If it is snowing and whether it is a Thursday or not3. Whether a person likes pizza and their gender(notice, knowing one bit of information does not impact the likelihood of the other being true also)
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 disjoint?
can’t be joined?. They can’t both happen at the same time! (being over 5 feet and under 4 feet)
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.
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
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”
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.
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 is the expected value?
The mean of the random variable. What you’d AVERAGE if you played the game A LOT!!!!!!!!!
what is a linear model?
it is an equation you can use or a line of a graph, it describes a relationship, but it is just a model that says what kind of happens, and can be used to ESTIMATE WHAT MIGHT HAPPEN
What is a sample?
A subset of a population, often taken to make inferences about the population. We calculate statistics from samples.
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? (categorical) 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? (quantitative)
What are the two types of observational studies?
Retrospective, and Prospective
What is a statistic?
A numerical summary of a sample. Like a mean, median, range, of a sample.
How is blocking different from stratifying?
Blocking is in an experiment, when you want to tease out a possible confounding variable, stratifying is in sampling when you want to make sure to get units with a specific characteristic so your sample is representative.
How many SD wide is the IQR in a normal distribution?
NOT 2!!!! The middle 68% is 2 sd wide, since the IQR is only the middlest 50%, it is less than 2. try [invnorm(.75)] x2 (about 1.35 sd)
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.
Give three examples of disjoint events
- A card being a CLUB and a RED2. A student being a SENIOR and a FRESHMAN3. An animal being a CAT and a GOLDFISH(both can’t be true)
What is a frequency distribution?
A table, or a chart, that shows how often certain values or categories occur in a data set.
what is the best way to reduce bias?
randomness. sophisticated answer: make as many things as random as possible
What is probability first success is on 7th try?
qqqqqq p (q^6*p). (this is a GEO prob)
geopdf (inputs)
FIRST SUCCESS ONgeopdf (p,x)probability of FIRST SUCCESS being ON the Xth trial
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!
If a distribution is skewed left, what will be greater, the mean or median? WHY?
Median. The mean moves left to keep balance.
What are the percentiles for Q1, med, and Q3?
25, 50 and 75
What is the five number summary?
min- Q1 - Q2(median)- Q3 and max
What symbols do we use for population mean and sample mean?
Mu for population mean, xbar for sample mean.
how do you describe direction o fa scatterplot?
positive or negative
what is a complement?
the probability that it doesn’t happen. 1-P(it happens). (together they add to 100%)
how do you interpret slope?
for an increas of 1 [unit of x] there is an (increase/decrease) of [SLOPE] [units of y]
Use the following words in one run on sentence: inference, sample, statistic, parameter, population, census, data
I was curious about a population parameter, but a census was too costly, so I collected data for a sample, calculated a statistic and used that to make an inference about the parameter of interest.
What is a conditional distribution?
A distribution within the table, along only one row or one column, NOT OUT IN THE MARGINS. So, on a table about food preference and grade in school, a conditional distribution would be “of the freshmen, 20% liked pizza, 50% tacos and 30% pasta”, a marginal distribution would be “overall, 25% liked pizza, 45% liked tacos and 30% liked pasta”
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 is the law of large numbers?
states that in the long run.. (NOT SHORT 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)
When can you round?
AT THE VERY END!!! (keep 3 significant digits until end!)
When comparing boxplots, what do you compare?
Medians and IQRS, ALSO, you might want to compare medians to quartiles if you can. For instance, if one has a median above the others Q3, you might say, Half of the first group scored over 80 while less than 25% of the second did.
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 + 5A + 12
mean: 3y+5b+12sd:sqrt (9z2 +25c2)var 9z2+25c2
what is the LSRL
the “least squares regression line”? that line, That equation
are any populations actually normal?
no, nothing is normal, just normalish. The only normal thing is the model we use.
what is probability?
THE LONG RUN RELATIVE FREQUENCY!!
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.
What is a simple random sample?
A sample where every possible group has the same chance of becoming a part of a sample.
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.
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 happens if you multiply all of a data set by a constant?
it is scaled, Everything is effected. Mean/ median/ stand dev/ iqr/ quartiles all multiplied by that constant. Center, spread and all individual values are changed.
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.
how do you combine probability models?(play more than one game)
add or subtract the means, and thenADD THE VARIANCE
What is Statistics?
The study of variability
How can you simulate a coin flip with random number table?
Assign heads to odd numbers and tails to even numbers.
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 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.
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”
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”
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: 5A
mean: 5bsd: 5cvar: 25c2
what should we look for in resid plot?
curve or pattern, Also, it should have equalish scatter from left to right
strength?
give the r value (if straight), or say? “tightly packed? loosely packed”
Center description?
mean (balance), median (splits area in half), mode (peaks, if bimodal, talk about both modes) or ,. “centered around ____”
what does binomial model tell us about?
exactly x successes in K trials. What is likelihood of exactly 3 heads out of 13 flips?
What is the “hot hand?”
a misinterpretation of the law of large numbers. Using this law, if you flipped 4 tails in a row, you’d expect the next one to be another tails, because tails is “hot.” A baseball player who gets three hits in a row, you expect another hit? wrong. Streaks happen randomly.
Give three examples of events that are not mutually exclusive
- Being a DOG and being SMELLY2. Being a FRESHMAN and being FEMALE3. Liking ICE CREAM and liking HAMBURGERS(both can be true simultaneously)
Why is it called “binomial”
These numbers come from the coefficients of expanded binomials..(x+y)1, (x+y)2, (x+y)3
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.
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)
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?
when can you expect the first success if thereis a 30 percent chance of success?(mean of geo)
1/por 1/.30.Which is 3.333 so around the 3rd or 4th try.1/ptells you, on average, when the first success will occur1/p is the mean of the geometric distribution
What is area under ANY probability curve?
1 (or 100%)
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 is the main purpose of a placebo ?
To blind the subject that is being experimented on to avoid influence to the given variable therefore altering the response variable . When people think they’re getting help, they often improve anyway,
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 + 12
mean: y+12SD zvar: z2
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!!
What is diff between 3X and X+ X+ X(mean and st. dev)
3X is just tripling one play. Mult mean and SD by 3.X+X+X is playing 3 times, must add variances, square SD’sadd 3 times thensqrt.
what about your calculator for using curves to fit curved data?
sure, Quadreg, cubicreg, lnreg, etc. just be careful when substituting while writing the equation given. Often you have to put the X into a few places.
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 do you find relative frequency?
just divide frequency by TOTAL,.
If you want to calculate % between two values what do you do?
find z scores for both value, and then normcdf (Z LOW, Z HIGH )
How can you think about the mean and median to remember the difference when looking at a histogram?
mean is balancing point of histogram, median splits the area of the histogram in half.
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.
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 contingency table?
A two way table. shows distributions across 2 variables like gender and music pref.
Probability of THIS AND THAT?
MultiplyP(this)*P(that) works when independent only, when not, then P(that) should be p (that|this)
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
What four things do you need in an experimental design? (trick)
NEED only 3: control , randomization, replication, BUT, Use blocking when appropriate. Don’t for get to COMPARE and identify RESPONSE VARIABLE
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, treatment givers, evaluators,
How many ways can you choose 3 books to take with you on a trip out of the 7 books on the shelf?
7 choose 3. 7!/(3! * 4!)notice that the two factorials on bottom add to the top.
are there any normal samples?
no, nothing is normal, just normalish. The only normal thing is the model we use.
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
How do you describe distributions (histograms)?
Shape-Cener-Spread- and STRANGE (Outliers and gaps) some say GSOCS. where’s yo GSOCS?
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.
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 point is on every regression line?
the mean-mean point. (x bar, y bar)
What is a factor?
A variable in an experiment that the experimenter manipulates
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
If asked to compare distributions, what should you write about?
Compare Shapes, Centers, Spreads, and Stranges. gaps The GSOCS
What is wrong with using volunteers in a survey?
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!
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?
where are the “outlier fences?”
1.5 IQR above Q3 and 1.5IQR below Q1,. Just a rule of thumb,
What is the mean?
the old average we used to calculate. It is the balancing point of the histogram
What is the mode?
the most common, or the peaks of a histogram. We often use mode with categorical data
binopdf(inputs)
EXACTLY X successes in N triesbinopdf(n,p,x).Probability of exactly X successes in N trials. (PARTICULAR probability)
Year in school (F,S,J,S) and Pizza Preference (pepperoni or cheese) are __________ because _______________
independent because they all have the same preferences, it doesn?t depend on grade, 80% of each group likes cheese better.
Explain two types of experimental design.
1.)Randomized Block Design: randomization occurs within the blocks only. (this includes matching or pre-post testing which is matching/blocking the person to herself)2.) Completely Randomized Design: all of the experimental units have the same chance at recieving a treatment.
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.
Which calculator function gives you a z score?
invnorm(%ile)
What is quantitative data?
The actual numbers gathered from each subject. 211 pounds. 67 beats per minute.
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)
What is “mutually exclusive?”
same as disjoint
Why blind those doing the analysis?
Researchers like to see results, they want to see an effect. If they know which treatment is the actual medicine, then they might be “looking” for it, We want the data to say it works, not the person.
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.
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
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.
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,
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.
What is sampling error?
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 the STATISTICS is called sampling error. (not the variability of the data).
what do we call it when events are not associated?
independent
How do you find percentiles and make a boxplot from OGIVE?
Go across from .25, .5, and .75 till you hit the curve and then STRAIGHT DOWN!
How can you tell if variables in a contingency table are independent?
If you look at the percents across the table or up and down. Like if 30% of males and 30% of females would both consider getting a pet pig, then you say gender and pet pig consideration are independent.
if you switch x and y will slope change?
YES- slope is rsy/sx? to get new slope you do: (r sqared)/old slope
is r sensitive to outliers?
yes. A single outlier can make it seem like there is a relationship (out in x direction,), or that there is none.
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.
How to describe association on a Scatterplot?
DIRECTION, FORM, STRENGTH
You want to simulate the likelihood of more than 4 psychology majors being on a full bus that seats 30. Suppose that 1 in 9 students are psych majors. Use a random nunmber table.
use single digits on a random number table. Each digit represents a student on the bus. Ignore the zeros. Let 1 be a psych major, and 2 through 9 be other students. Trials end when you have reached 30 students. Count the number of psych majors (ones) in the trial. Record this. Do this 20 times. Find the percent of times there were 4 or more psych majors on the “bus.” If this occured in 5 trials, then the likelihood is 5 in 20, or 25%
what is the mean/median/mode helper diagram?
a skewed left distribution with mean/median/mode labeled in order from L to R
What is a quantitative variable?
Quantitative variables are numeric like: Height, age, number of cars sold, SAT score, weight.
How to make TREES with screening tests????
SPLIT UP POPULATION FIRST»_space;»» then split the groups by outcomes of the test
What type of probability when you are looking for exactly 5 or more successes in twelve attempts?
(more than 4)1 - binocdf(12, p, 4)
How do you undo sqrt when solving?
^2 (square both sides)
How can you estimate the probability of an event occurring?
run a simulation. Find the percent of trials that you observed the event occur.
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 + A
mean: y+bSD SQRT(z2+c2)var z2+c2
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 of the other to 0
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!!”
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? “
what is independent? What are the two equations to test for independence?
when P(A)=P(A|B) OR P(A)*P(B)=P(A and B)When the probability of A is the same even when B is also true.Knowing B does not affect the probability of A.
Look for lurking variables?
think hot chocolate sales in caf at wachusett mountain and ski accidents at wachusett mountain. Did the chocolate cause the accident??????
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. There’s two forms: prospective and retrospective. A prospective observational study is when you identify subjects in advance and record data as you go along. A retrospective observational study is when you analyze observations from the past.
What is the total area under the normal curve?
one , or 1.000
What is the median?
the middlest number, it splits area in half (always in the POSITION (n+1)/2 )
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)
what is the emperical rule?
mean, 68-95-99.7 yeahh,,
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)
What are the two major branches of AP STATS?
Inferential and Descriptive
What are INFERENTIAL STATS?
Look at your data, and use that to say stuff about the BIG PICTURE, like tasting soup, a little sample can tell you a lot about the big pot of soup (the population)
how can you check for “straight enough?”
residuals plot fool!
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
What do we call it when two things can’t happen at the same time?
disjoint OR mutually exclusive
What is a control group?
A group in an experiment without the treatment that is compared to groups with treatments to make results or conclusions. The control group helps us see what would happen anyway, without any treatment so that we can see the true effect of the treatment.
how do you describe form in a scatterplot?
straight or curved
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!
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 + 5A
mean: 3y+5bsd: SQRT(9z2+25c2)var: 9z2+25c2(same as (3z)2 + (5z)2)
which is explanatory variable?
x. horizontal axis. it “explains” what happens to y
Is matching blocking?
YES, little tiny blocks of one.
What is undercoverage?
Undercoverage is when either one part of the population is not included in a survey or is underrepresented in the survey
what happens if you ADD a constant to each value in a data set?
it is SHIFTED only. Spread doesn?t change, but 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).
Why is it calle d “least squares regression line?”
Because, after you find the mean-mean point, you fix the line so that it minimizes the squared vertical distance to that line (minimizes the squared residuals)
Why randomize in an experiment?
To avoid bias. An experimenter might want their treatment to work, so may chose the subjects that might respond best.
What is the “mean of a random variable?”
The expected value. sum of probs times values
what is representative?
It means that the sample statistics will be kind of like the population parameters.. The sample “looks like” the population.
What does GSOCS stand for?
Gaps Shape Outliers Center Spread.
Can you stratify in an experiment?
NO. stratification is a sampling method, blocking is method used in experiments. They are similar ideas.
What is retrospective study?
A retrospective study is a study that looks backwards in time. They focus on estimating differences between groups or some association between.
What percent of the data is below the median?
50%
Probability of THIS OR THAT?
ADD P(this) + P(that) works when disjoint only, when not, subtract overlap.
Ho w are the good sampling methods similar?
In all of them, all members of population have equal chance of being selected.
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”
how do you describe the SPREAD of a distribution?
range, IQR, stand dev, variance, or simply say, From here, to about here,.
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.
How to find P(at least 1)?
1-P(none)
If something is correlated is it associated?
Yes
Why do we plug 999 into normcdf?
normcdf needs two z scores, but we can’t plug in infinity. So we go down or up 999 standard deviations and that pretty much gets everything,.
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)
How many successes can you expect?(mean of binormial)
np.Makes sense, if 30% like butter, out of 50 people you would expect (50)(.3)= 15 to like butternp is the mean of the binomial distribution
What percent of the data is between Q1 and Q3?
50%
the output for normcdf(Zleft, Zright) is_______
A PERCENT, or a probability, it is the area under the normal curve between the given z scores. The total area is 1 (or 100%)
What values can r be?
from -1 to +1
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!!
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 are mean, median and mode positioned in a skewed left histogram?
goes in that order, mean median mode
outliers in regression?
doesn’t follow the “flow” (pinky trick)
association or correlation?
association is talking about a relationship? correlation is an actual calculated number
does correlation mean causation?
NO WAY DUDE
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 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..
What do we sometimes call a categorical variable?
qualitative
How can you simulate on your calculator
RANDINT( lowest, highest, how many you want to grab)
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!!!
What is prospective study?
Prosepctive study is when you study the experimental unit’s present and future response variable.
Samplin Method Types?
SRS, stratified, clustered, systematic, multistage, convenience, voluntary
How do you undo squares or cubes?
^ 1/2 or ^ 1/3
does high r value mean anything?
An r value alone tells little? CHECK THE SCATTER, IS IT LINEAR?? make sure it’s linear first?
What is a mutlistage sample?
A sample that combines several sampling methods
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.
What are humans bad at ?
Humans are bad at generating random numbers.
If you want to find % below a value, what do put into normcdf (? ?)
find z score for value, and then normcdf (-999, Zright)
what is the line that you plot?
IT IS A MODEL!
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)
What are DESCRIPTIVE STATS?
Tell me what you got! Describe to me the data that you collected, use pictures or summaries like mean, median, range, etc,
What is a parameter?
A numerical summary of a population. Like a mean, median, range, of a population
How do you undo an ln when solving?
e^stuff
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.
Compare Descriptive and Inferential STATS
Descriptive explains the data that you have: summaries, bar charts, scatterplots, regression, mean, st. deviation etc? , inference uses that data you have to try to say something about an entire population,.
What is the IQR?
Interquartile range, a measure of spread, Q3-Q1, The distance from Q1 to Q3. It is a single number.
How do you find Q1 and Q3?
Q1 is the median of the bottom half (25th %ile) and Q3 is the median of the upper half (75th %ile)
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 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,
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 is Blocking in an Experiment Similar to Stratifying in a Sample?
The two are similar because they divide the subjects groups according to traits where the subjects are all similar
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.
Do we say things are “dependent?”
NO! we say associated
What is a census?
Like a sample of the entire population, you get information from every member of the population
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.
What is meant by relative frequency?
The PERCENT of time something comes up (frequency/total)
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.
what is a residual?
ACTUAL-PREDICTED A-P like this class, AP (get it?)
geocdf (inputs)
FIRST SUCCESS ON OR BEFOREgeocdf(p,x).Probability of the FIRST SUCCESS being ON OR BEFORE the Xth trial.
If the distribution is skewed (or outliers/not symmetric) what would you use for center and spread statistics?
Median (center) and IQR (spread)
how to interpret slope EQUATION? R Sy / Sx
for each increase of 1 st dev in x direction, you go r st dev in y direction.
Probability this OR that when they are not disjoint? How?
probability A plus probability B minus the double counted (the ones that are both A and B) called “general addition rule”P(A)+P(B)-P(A and B)P(this)+P(that)-P(this and that)
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,).
What do we call it when events are not independent?
associated
What is a standard deviation?
average distance to the mean
what does geometric model tell us about?
it is about FIRST SUCCESSWhat is likelihood first success is on 5th trial?
which calculator function gives you a percent?
normcdf
What type of probability when you are looking for at least one success in twelve attempts?
1 - p(NONE)not zero1-binopdf(12, p, 0)
What is random sampling?
When we use change to select a sample
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.
How are mean, median and mode positioned in a skewed right histogram? goes in the opposite order, Mode-median-mean
mode- median- mean (mean chases the tail)
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 burger at FIVE GUYS, the true average number of pickles is considered a ______?
parameter, a one number summary of the population. The truth. AKA the parameter of interest.
What percentile is Q3?
75th
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 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.
What type of probability when you are looking for less than 5 successes in twelve attempts?
4 or lessbinocdf(12, p, 4)
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 many trials in simulation?
At least 20-30.
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.
How do you find the median fro man OGIVE?
go halfway up the y axis, shoot across to the curve, then straight down. It’s at the 50th percentile (halfway up)
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)
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: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 +3
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!!
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.)
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 is categorical data?
The actual individual category from a subject, like “blue” or “female” or “sophomore” the raw data are words or symbols representing categories.
which is response?
y, Vertical axis, It “responds” to the x
interpret r squared
r squared % of variability in y can be explained by the model WITH X. The rest is in residuals?
Can you predict an X by using a Y?
NOT WITH THE SAME EQUATION! BE CAREFUL!! You have to change the entire equation and start from scratch? Switch and run linreg with L2 v L1
if you switch x and y does r change?
NO. The strength stays the same.
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
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.
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
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.?
What is the area under the normal curve?
1 or 100%
What is a population?
the group you’re interested in. Sometimes it?s big, like “all oysters in wellfleet” Or “all teenagers in the US” other times it is small, like “all AP Stats students in my school” or “my toes”
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.
How do you undo a log when solving?
10^ stuff
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.
What is the sure way to assign treatments correctly?
throw names in hat and pick.
How do you find mean and sd of discreet random variable ?
put values in L1, probabilities in L2, and run “1-var stats L1,L2” and you get it!
What percent of the data is above Q3?
25%
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 does normcdf do?
It gives you the area under the normal curve between any two z scores
what are the percentiles from left to R on normal model?
2.5-16-50-84-97.5
what is n! ?
it is “n factorial” example: 5! = 54321= 120. tells you how many ways you can arrange n objects.
Shape description?
unimodal, bimodal, multimodal, uniform, symmetric, skewed
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 a categorical variable?
Qualitative variables are like categories: Blonde, Listens to Hip Hop, Female, yes, no, etc.
What is response bias? How do you avoid it?
Response bias is any influence that may sway the respondent to give a more favorable answer 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.
Who can be blinded?
Subjects. Those delivering treatments. Those assessing effectiveness of treatments. and three mice.
What type of probability when you are looking for more than 5 successes in twelve attempts?
6 or more same as not 5 or less1 - binocdf(12, p, 5)
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 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.
What is bias?What are some common errors?
It’s any systematic failure of a sampling method. COMMON ERRORS: Voluntary response, undercoverage of the population, nonresponse bias and response bias. We use randomness and methods like stratifying to reduce these.
