HCS 202 Exam 2

what are the steps of hypothesis test

Test, Assumptions, decision rule, hypotheses, Calculate, interpret

Test

choose the right t statistic

assumption

check the assumptions to make sure it is ok to do test

decision rule

find the critical value that determines when to reject the null hypothesis

calculation

calculate the vlaue of test statistic

interpretation

say in plain language what the results mean and find available scientific context

pillar 1 t stat

finds if data supports assumption

pillar 2 effect size

describes the magnitude and importance of data

pillar 3 confidence intervals

estimates likely range that might occur in the population given sampling error

single sample t test

a sample mean to a test vale of interest (ex: population mean)

related sample t test (paired, dependent)

two sample means from the same group or matched group

independent sample t test

two sample means from different groups

4 assumptions and robustness

1. independence of data (not robust)

2.appropriate measurement of variables (not robust)

3. normality of distribution (robust if sample if greater than 30)

4.Homogeneity of variance (robust if group sizes are equal)

independence of data

each participants score must fall within is not influenced by anything and goes with all other participants scores within the same condition (must not be influenced by outside sources)

appropriate measurements of variables

the variable of interest must be measured on the appropriate scale of measurement for the test

normality of distribution

normal distribution

homogeneity of variance

standard deviations are equivalent

non robust

assumption must be met to proceed

robust

can be violated and can continue

what assumption go with single t test

independence of data, normality of dependent variable

appropriate varaible (DV must be continuous and IV grouping variable

what assumptions go with paired t test

independence of data

Appropriate variable (DV continuous, IV grouping)

normality of difference

what assumptions go with independent t test

independence of data

appropriate variable (DV continuous and IV grouping)

normality of DV per group

homogeneity of varaince

3 methods for assessing normality

1. visualize

2. test. the skew

3. conduct Shapiro-wilks

shapiro wilks

is the p value greater than .05 (this can be violated if the sample size is large) if so it is not significant

2 methods for homogeneity

general rule and levenes test

general rule of homogeneity

is the difference between group variance less than 3

- the difference should be no more than triple

levens test

is the p value greater than .05 to be consider equal variance

statistical hypothesis

this examines what the population parameters would be if there were no effect on the population (aka the null hypothesis)

null hypothesis

states no effect

a negative statement

makes a specific prediction (no effect)

alternative hypothesis

states there is an effect

true

non-specific (no directional)

what is the null for a single t test

sample mean = population mean

what is the null for a paired t test

pre mean = post mean

condition 1 mean = condition 2 mean

what is the null for an independent t test

mean 1 = mean 2 (p value is greater than or equal to .05)

what is the alternative for a single t test

sample means x= population mean

what is the alternative for a paired t test

pre mean x= post mean

condition 1 mean x= condition2 mean

what is the alternative for an independent t test

mean 1 x= mean 2 (p less than .05)

if the null is true is there a mean difference

no

if the alternative is true is there a mean difference

yes

what does one tail vs two tail influence

the size of the p value

one tailed test

the direction of the effect is specified ahead of time and there is no effect to the other direction

- easier to reject the null

two tailed test

non directional, the outcome of both directions matter

most common

what does the decision rule determine

whether to accept or reject the nuill

what is the decision rule based on

alpha

two vs one tailed

sample size

what is alpha

your significance level or critical region

when do you reject the null with a critical value

if the observed stat is greater than the critical value, you reject the null

degrees of freedom independent

(n-2)

degrees of freedom dependent

(n-1)

degrees of freedom single

(n-1)

What information do you need to determine the t value of a critical region (also known as tcv)?

alpha, two or one tailed, degrees of freedom

4 outcomes of hypothesis testing

null is really true

- fail to reject (results fall in common zone)

- reject the null (results fall in common zone) type 1 error

null is not ture

- fail to reject (results fall in rare zone) type 2 error

- reject the null (results fall in rare zone) power 1-beta

type 1 error alpha

when we reject the null when we shouldnt

(false positive)

type 2 error beta

when we accept the null when we shouldnt

(false negative)

power (1-beta)

our ability to identify an effect when it exists (we want this to be high 80%) true positive

how to avoid error

we maximize the statisitcal power the power is influenced the alpha (the larger alpha the greater the power)

alpha error and beta error are related

there is a trade off lowering the chances of one can increase the chacnes of another

how to minimize type 1

- lower significance level

how to minize type 2

- increase the significance level

- increase the sample size

p value reject the null

when the p value of our calculated t is less than alpha (p < 0.05)

p value accept the null

when the p value of our calculated t is greater than or equal to the alpha (p> .05)

t test stat reject the null

when our calcualted t score is greater than our critical t value

t test stat accept the null

when our calculated t score value is less tahn our critical value

what is mean difference standardized

cohens d

what does cohens d measure

effect size

what are the cohens d values

=0 none

=.2 small

=.6 medium

=.8 large

standard deviation formula

square root of the sum of the each value - the mean squared divided by (n-1)