Stats 2B lol

capitalising on chance

when you use multiple t-tests rather than ANOVA, the type 1 error chance increases , whilst convienient-lokey immoral

calculating cumulative probability

1-(1-alpha)^n (n being number of tests)

ANOVA

A parametric inferential statistical test used to compare the means of three or more groups

one-way between subjects ANOVA

-one IV

-participant only appears under one condition

variation between groups

how much the group averages differ from one another

error in ANOVA

individual differences + random factors

between groups variance measures

combined effect of error and treatment

within groups variance measures

effect of only "error"

total variance

between groups variance + within groups variance

partition

breaks down total variability into components

grand mean

sum of individual scores from all groups divided by total number of observations

F ratio calculation

between groups variance/ within groups variance

if f value large:

-observed differences among group means are unlikely to be due to chance alone

Assumptions of one way between subjects ANOVA

-DV is interval or ratio data(continuous)

-Independent observations

-normal distribution of residuals (QQplot)

-homogeneity of variance between groups( all groups should have similar variance, so the spread of scores around the mean should be approx the same in each group) boxplot residuals vs fitted plot, Levenes test

if assumptions of one way between subjects ANOVA violated

-if groups have equal sample sizes and effect sizes are relatively large, we can still proceed with ANOVA

-when data has different variance, Welch T-test can be used

-Kruskal-Wallis test

one way between subjects ANOVA df

df1(n-1)

df2 number of observations -n

how to calculate effect size of one way between subjects ANOVA?

partial eta squared

What are the effect sizes for partial eta squared

0.01-small

0.06- medium

0.14- large

omnibus test

this in ANOVa means they do not specify which tests are different , just that one or some are

why we need posthoc tests for ANOVA

Its not specific about which groups without it

post hoc tests for one-way between subjects ANOVA

-Tukeys honestly significant difference

-Bonferroni

repeated measures one way ANOVA

participants in all conditions, only one IV

Evaluation of one way between-subjects ANOVA

+simplicity

-large person to person variability

-needs large sample size for power

evaluation of one way repeated measures ANOVa

+fewer cases

+making contrasts within participant

+relatively precise estimates

-practice effect

-fatigue effect

sphericity

-Variance of differences between any two conditions must be the same as the variance of the differences between any other two conditions

assumptions of one way repeated measures ANOVA

-continuous DV

-normally distributed residuals

-sphericity (Mauchlys test)

test for sphericity

Mauchlys test

p and sphericity

If p<0.05- violation of sphericity

If p> 0.05 satisfaction of sphericity

consequences of no sphericity for repeated measures ANOVA

increased chance of type II error

test loses statistical power

if sphericity is violated

-use greenhouse-geisser correction or huynh-feldt correction

when use green-house geisser

-if epsilon< 0.75

when use huynh-feldt

if epsilon >0.75

DF within subjects anova

Df1 = number of conditions-1 (numerator degrees of freedom)

Df2= (number of participants-1) * (number of conditions-1)

Post hoc within subjects Anova test

Bonferonni

calculate number of t-tests

k(k-1)/2 where k= levels of IV

t

obtained difference between 2 sample means/ standard error

Types of t-test

-student( if equal variance)

-welch(if non-equal variance)

T-test

-parametric

-examines if difference between two means is statistically significant

Non-parametric version of t-test

Mann-Whitney

type 1 error

negative hypothesis is rejected when it is true

Calculate probability of at least 1 type 1 error ( accumulation)

1(1-a)^n where n is number of tests

Why use variance

It is challenging to measure the difference between sample means if more than 2

If between groups variance > within-groups variance

F value is large

Levene's test

looks at homogenity of variance

-if p value > 0.05 , variances ar roughly equal

Tukey HSD test

-look at p value of comparison( p adj)

if less than 0.05, there is a significant difference

Bonferroni test

-comparison is in a lil table of p-values

-cohen's d needs to be found for the write up

evaluate use of one-way repeated measures ANOVA

+ doesn't have to deal with person to person variability

+ fewer cases

+ more accurately detects effect of conditions or treatments being tested

-practice effect

-fatigue effect

generalised effect size

like eta squared but for repeated measures