PSCL 282 Exam

Post Hoc Tests

1. Tukey's Honestly Significant Difference test 2. Scheffe test

hypothesis for related samples test

H0: μD=0 H1: μD ≠ 0

Table of F values organized by 2 df

df numerator-between df denominator-within

when treatment effect is inconsistent

difference scores are more scattered and variability is high

when treatment has a consistent effect

difference scores cluster together and variability is low

variability as a measure of consistence

treatment effect may be significant when variability is low, but not significant when variability is high

matched subjects design

two separate samples are used (each individual in a sample is matched one to one with an individual in the other sample, matched on relevant variables) participants not identical to match-ensure that samples are equivalent with respect to some specifica variables

how to evaluate F

use F distribution table- set alpha and find critical value

Scheffe Test

uses F ratio to evaluate signifcance of the difference between two treatment conditions

related samples design

uses statistically equivalent methods. Uses a different number of subjects-matched samples has twice as many subjects as repeated measures design

between-treatments variance

variability results from general differences between the treatment conditions; variance between treatments measures differences among sample means

within treatments variance

variability within each sample; individual scores are not the same within each sample

Effect size-ANOVA

Compute percentage of variance accounted for by the treatment conditions- η2

difference score

D = X2—X1

f-ratio

F=variance between sample means/variance from sampling error

Tukey's Honestly Significant Difference test

a single value that determines the minimum difference between treatment means that is necessary for significance-HSD

test statistic for ANOVA

f ratio is based on variance instead of sample mean difference(variance is used to define and measure the size of differences among the sample means (numerator), and variance in the denominator measures the mean differences that would be expected if there is no treatment effect)

disadvantages of repeated measures design in related samples t tests

factors besides treatment may cause subject's score to change; participation in first treatment may influence score in the second treatment (order effects)

ANOVA similarity

for 2 samples, ANOVA will give you the same results as a t-test

Hypothesis tests & Effect Size

if the null hypothesis is rejected, the size of the effect should be determined

distribution of F-ratios

if the null hypothesis is true, the value of F will be around 1.0 since F ratios are computed from 2 variances, they are ALWAYS POSITIVE

ANOVA

it is NOT POSSIBLE to compute a sample mean difference between more than 3 samples

homogeneity of variance

need to find F-max F-max=s2 largest/s2 smallest large value indicates large difference between sample variance small value (near 1.00) indicates similar sample variance

sources of variability within-treatments

no systematic differences related to treatment groups occur within each group; random, unsystematic differences (individual differences, experimental error)

n

number of scores within a treatment

k

number of treatment conditions

hypothesis tests and effect size for repeated-measures design

numerator of t statistic measures actual difference between the data MD and the hypothesis μD denominator measures the standard difference that is expected if H0 is true

assumptions of the related samples t test

observations within each condition MUST be independent; population of distribution of difference scores must be normal (this assumption is not a concern unless the sample size is small, so with samples of n>30 this assumption can be ignored

advantages of repeated measures design in related samples t tests

requires fewer subjects, are able to study changes over time, and reduces or eliminates influence of individual differences

stats for repeated-measures research design

structurally similar to the other t statistics, only difference is that it is based on difference scores (D) rather than raw scores (X)

T

sum of all scores within a treatment mean and SS within each treatment

G

sum of all the scores (G = sumnationT)

sources of variability between treatments

systematic differences caused by treatments; random unsystematic differences (individual differences, experimental error)

t test

t = mean difference between samples/standard error

estimated standard error

the measure of standard or average distance between sample statistic (M1-M2) and the population parameter

N

total number of scores

when to use a post hoc test

when you reject H0 and H1 states that at least one of the treatment means is significantly different but you don't know which one or how many are different

Assumptions for Independent Measures ANOVA

1. The observations within each sample must be independent 2. The population from which the samples are selected must be 3. The populations from which the samples are selected must have equal variances (homogeneity of variance)

Assumptions for the Independent Measures t-test

1. The observations within each sample must be independent 2. The two populations from which the samples are selected must be normal 3. The two populations from which the samples are selected must have equal variances

Computing new ratio using Scheffe's test

1. Use the same df in the numerator as the original F 2. Use the same critical value as in the original F to evaluate the Scheffe F 3. Recalculate the SS between to reflect only the two treatment groups you are testing against each other 4. Start by comparing the two groups with the largest mean difference. If the first comparison is significantly different, then test each progressively smaller set of means until you no longer obtain a significant difference.

Assumptions for ANOVA

1. observations are independent 2. populations are normal (samples are larger than 30) 3. homogeneity of variance (you must test that this assumption has not been violated using F-max

Structure for testing a hypothesis

1.Form your hypothesis 2. Define your critical region 3. Calculate your t statistic 4. Make a decision to reject or accept the null hypothesis

repeated-measures

also known as within-subjects design two separate scores are obtained for each individual in the sample same subjects are used in all treatment conditions no risk of the treatment groups differing from each other significantly

one-tailed tests

critical region is located in only one tail, called a directional hypothesis