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.
