2 stat

test stats

when we are hypothesis testing, what exactly are we testing?

groups, comparing the difference of means

what are we determining when we do a hypothesis test

the relationship between 2 variables, a difference between 2 groups, if a variable has an effect on another variable

what are the 6 steps to a standard hypothesis test?

1. state the null hyp

2. state the alternative/research hyp

3. choose a test statistic, justify

4. determine if we meet the assumption

5. calculate the test statistic, solve the problem

6. state the conclusion

what do ALL test statistics have that we need to determine before we can even use it

ASSUMPTIONS.

what is a hypothesis

an educated guess about how something works in the real world, translating a problem statement into something testable, to which we can generalize to a population

big 3 of a hyp (what it is and adresses)

educated guess, testable, generalize to population

what is a null hyp (H_O)

hyp where nothing interesting happens, everything is the same—no relationships exist

what does null hyp significance testing refer to the act to

taking a sample and comparing it to the null hyp

what does the null universe refer to

a made-up region where null hyp “originates” from, in which no variables have relations to one another and no effects exist

null universe or not? how old you are does NOT correlate with how tall you are

null universe

null universe or not? as you get older, you get taller

not null universe

what is a alternative hyp (H_A)

hyp where differences exist and changes CAN occur (interesting things yes)

which hypothesis refers to what we think something is happening in the world

research hyp

in what type if hypothesis do group differences exist and talk about effect we have

alternative hyp

what do null hyp determine about 2 groups

that they are the SAME

how do you write symbolically for null hyp

H_O : mu_{2 =} mu₁ OR H_O : mu₂ = [benchmark value]

how would you verbally describe the null hyp

there IS NO DIFFERENCE between [population 2] and [population 1] in terms of [variable]

how do you write symbolically for research hyp

H_A: mu₂ DOES NOT EQUAL mu₁ OR H_O: mu₂ DOES NOT EQUAL [benchmark value]

how would you verbally describe the alternative hyp

there IS A DIFFERENCE between [population 2] and [population 1] in terms of [variable]

what does mu 2 refer to when desc hypotheses

the mean for the hypothesis population the sample comes from

what does mu 1 refer to when dec hypotheses

the mean for a population we r comparing our sample to

what does the benchmark value represent

actual numeric value of mu 1

when you look choosing a test statistic, what do we need to understand about it before we can determine if it fits the variable of interest?

understand what the assumptions are AND when to use them

what are the assumptions of a z test

1. observations r independent of one another

2. random sampling

3. population data is normally distributed

4. population variance is known

when determining if the observations are independent of one another, what are we attempting to find to be able to use a z-test

if each person’s score ISNT affected by another individual

if every individual in data set ISNT affected by one another, what can we determine?

that the observations ARE INDEED independent of one another

in a random sample, what individuals are we looking at? what is the probability of being selected?

every person in sample has a known, non-zero probability of being chosen

when looking at a random sample, does the population have the SAME probability of selection or a non-zero probability of selection?

NON ZERO

what is the probability of selection of a population in a random sample

KNOWN NON ZERO

what do ALL test stats have

THEIR OWN ASSUMPTIONS

how do we determine if the population’s data is normally distributed

using central limit theorem we use n >/= 30

if n is greater than or equal to 30, what can we determine

population data IS NORMALLY DISTRIBUTED

how do we determine if the population variance is known

if we are given/aware of the standard error (SE known)

what are z tests considered for single sample hyp tests

the golden standard

what are simple sample hypothesis tests

hyp tests in which we compare our known population (or benchmark)

what are the 2 simple sample hyp tests we #use

t-tests and z-tests

what are rejection regions

area of probability (tails of distributution) where we can say our sample is significantly different from the null universe

what is the goal of a hyp test

to reject the null hypothesis

if out test statistic falls into the rejection region, what can we reject?

the null hypothesis

what do we use the rejection region to determine

if we can reject or fail to reject the null hypothesis

what do we calculate to figure out if our test statistic (p-value) falls into rejection region

z-score

what is the rejection region often discussed as the probability of

alpha; a

what is the value of a? (always for the course)

.05

if our p-value for our test statistic is less than a, where are we on the distribution of a graph

rejection region

is the p value greater or less than a if we are the rejection region

less than

symbol of what we are looking for when determining if we are in the rejection region?

p < .05 if a .05 (p < (less than) a)

what can we do if the p-value IS LESS THAN a

we can reject H_O and support H_A

if my p-value IS NOT LESS THAN a, what can we do?

fail to reject the null hypothesis

what does the p value refer to

the probability of getting our test stat results if the null hyp were true

what is the easiest way to tell if ur test stat is in the reject region?

comparing the p value to alpha = .05

if our z-score were positive what would that mean for the variable to which we are comparing populations to

would indicate that our sample is higher than the benchmark

if our z-score were negative what would that mean for the variable to which we are comparing populations to

would indicate that our sample is lower than the benchmark

what the heck is a type I error

chance of the probability that we reject the null hyp when its actually true

what the hell is a type II error

chance of the probability that we fail to reject the null hyp when its actually false

a= .05 refers to what type of error

type I error

1-a ; 1-.05

type II error

what type can we use test is it if we do not know the population variance

single sample t-test

what do t-tests give us that allows to solve the issue in which we do not know the variance? what do we use to solve this issue?

give us a way to approximate the population variance using the info from our sample

what does i mean when we consider t-tests to be more conservative

it is more difficult to reject the null hyp w a test compared to a z-test

what do the values in the denominator refer to of the calculation of a single sample t-test: s / the square root of N

a estimation/approximation of the population variance

what do t-tests heavily rely on? how come? (think about what we are looking at!)

the sample size as it directly effects the denominator

what does the data have to be in order for us to be able to reject the null hypothesis?

more extreme

what is the t-distribution (shape) depended on

the sample size

what is the resulting t-distribution if we have a SMALL SAMPLE SIZE

looks platykurtic, “pushed down”, tails are bigger and rounder

what is the resulting t-distribution if we have a LARGER SAMPLE SIZE

looks more bell shaped, “lets up” on the distribution as the sample goes up

the shape of the t-distribution changes based on the ________

number of people in the sample (sample size)

when the t distribution has a sample of n that is close to 30, what is the general shape

bell shaped ish

when the t distribution has a sample of n that is smaller than 30, what is the general shape

platykurtic

as the n inc, the t-distribution begins to look like the z-distribution w its bell shape. So, what tells us what the shape of our t-distribution will be?

degrees of freedom (df)

what do degrees of freedom (df) tell us

how our p-value and t-values are connected, what the shape of our distribution is

for t-tests, how are the degrees of freedom calculated?

df = n - 1

what are the degrees of freedom directly related to?

sample size

why do we care about the degrees of freedom? what is their relevance (for t-tests in this case)

tell us where the rejection region is and the relation between t and p, helping us figure out p value as we are always looking for p < a

in t-tests, what is the relationship between t-score and p-values

1 p-value is attached to various t-scores (vv.)

what determines which t-score a p-value is attached to

the degrees of freedom (df)

what is the only way we can figure out what t-score is paired with probability

the df

if we have 2 p-values where p= .025, will we have the same t-score for both? how come

no, a p-value is associated with various t-scores not just one so the t-score can vary

if we have 2 p-values where p= .025, what will allow us to ultimately determine what the t-score is?

the value of the degrees of freedom

what are the assumptions of a t-test

• observations are independent from one another

• random sampling

• population data is normally distributed

if we are given the benchmark value but do not know the population variance, what test statistic can we justify the use of?

single sample t-test

if we are NOT given the benchmark value, do not know the population variance, but are comparing 2 groups what test statistic can we justify the use of?

independent sample t-test

when we reject the null hypothesis what are we saying about the benchmark value

that the benchmark value is NOT actually our given benchmark value but another

how do we estimate/determine the “actual” benchmark value

95% confidence interval of difference

what do we use if we don’t want to compare our sample to a hypothesis benchmark (or cant in some cases) and want to compare one group to another?

two sample tests

what are two sample tests

tests that directly compares the mean of group 1 and the mean of group 2

what type of test do we call the direct comparison the mean of group 1 and the mean of group 2? (think broadly…)

a Difference of Means test

what type of statistic is a (or i guess use?) two-sample t test

a bivariable test

what is a bivariable statistic

a stat that looks at 2 variables at once

what are the 2 ways we are able to distinguish between the 2 variables of a bivariate statistic

experimental, IV and DV; correlational, predictor and outcome

what do independent variables define

your groups

are independent variables quantitative or qualitative?

qualitative

which variable has categories that we can put people in

independent variables

what variables do experimental experiments use

independent variables and dependent variables

what variables do correlational experiments use

predictor variables and outcome variables

if we are able to either randomly assign or manipulate the category someone is in, what would be the variables we can use?

IV and DV

if we are unable to either randomly assign or manipulate the category someone is in, what would be the variables we can use?

predictor variables and outcome variables

what does the dependent variable refer to

what we are interested in

is the dependent variable qualitative or quantitative?

quantitative

in single sample t tests when we want to know the mu—what exactly are concerned with knowing?

want to know the population mean of our sample!

in independent sample t tests—what exactly are concerned with knowing?

the difference between means of 2 samples