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 refer to when dec hypotheses

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