Lecture 15 - Stats

Anovs

What do you use Anova for

Comparing 2+ groups

True or false: A one-way anova is NOT similar to a t-test

False. In fact, it can handle more groups than a t-test

What is the Null Hypothesis for a One-Way Anova

μ1=μ2=μ3

What is the Alternative Hypothesis for a One-Way Anova

Ha: It is not true that μ1=μ2=μ3

What is the ratio used for an Anova Test

F Ratio

How do we see if the differences are big or small

Effect Size

Define Test Wise a-level

The risk of a type 1 error (false positive) in one hypthoesis test

Experiment-wise a-level

The total probability of a type 1 error, from all of the individuals test in the experiments (look at slide 16 for example)

A dependant variable is…

continuous (uses numbers)

An independant variable is…

a factor (not numbers)

“Individual conditions/ values that make up a factor” is…

levels of a factor (e.g how many treatments)

The grouping/predictor is made up of…

k groups

The continous/outcome varible is made up of

1. All the means for the individual groups

2. The grand mean (all the means added together)

Between-Groups Variance has the F variance in the…

numerator (top number)

Within-Groups Variance has the F variance in the…

F ratio

Define Between-Groups

Comparing different groups in a population (e.g middle class, upper class)

Define Within-Groups

Comparing INSIDE a group (e.g races, sexuality, gender IN the middle class)

Define Total Variability

The total number of the sum of squares. It represents overall variability with one number

What is the Formula for Total Variability

SST = SSB + SSW (SS = sum of squares).

What is the formula for the degrees of freedom for SSB (Sum of Squares Between?)

K - 1 (number of levels - 1)

What is the formula for the degrees of freedom for SSW (Sum of Squares Within?)

N – k (Total number of participants – Number of levels)

What is the formula for the TOTAL degrees of freedom ?

N – 1 (Total number of participants – 1)

F Ratio formula is…

F= MSB / MSW (MS = mean squares)

F distribution is ___________ skewed

Positively

“As the degrees of freedom get larger, the curve approximates a ___________ distribution”

Normal

What does “ETA Squared” Stand for?

measure of effect size

What is the Formula for ETA Squared

N2 = SSb / SSt

ETA helps explain ___________ found in Anova

Variance

True or false: 0.01-0.10 is a small effect size

False, 0.01-0.08 is a small effect size

What is the number for a large effect size for ANOVA

0.25

True or False: There are tests we can do after our experiments to see if the mean differecnes are/aren’t significant

True

True or False: These test are completed when you fail to reject the null hypothesis, and there are two groups

False, when you reject H0 (because that means one of the means is different) , and when they’re three or more groups

True or false: the Tukey test is the most used in psychological research

True

In the Tukey test, you have more _____ when testing ______ ______ of means

1. Power

2. Large Numbers

What does the Tukey test do for experiment wise error rate?

“Sets experiment-wise error rate at the error rate for the collection for all pairwise comparisons”

The Bonferrioni test uses ___________ to perform pairwise comparison between groups

T-tests

The Bonferroni test has more power when the number of comparisons is ________

small

How does the Bonferroni controll the overall error rate?

It sets the error rate for each test to the experiment-wise error rate divided by the total number of tests

The scheffe tests is the best method for reducing risk of _______________

Type I error

Which test is the safest out of all possible post hoc test

Scheffe

The Dunnett’s C Test is a pairwise comparison test based on _____________ range

studentized

The Games-Howell test is based on ________ ____ and uses the ___________ __________statistic

1. Welch’s correction

2. Studentized range

The Dwass-Steel-Critchlow-Fligner is a pairwise comparison used with the _______________ test

Kruskal-Wallis Test

True or false: Dunnett’s C, Games-Howell, and Dwass-Steel-Critchlow-Flinger are all test to use when you assume variance.

False, those tests are when you do NOT assume variance. Tukey, Bonferroni, and Scheffe are the tests when you do assume varriance

Define: Independence

No data in the sample affects each other

Define: Normality, and which test is used if significant if assumption is not met

Two populations, and the same both are normally distributed, Shapiro-Wilk test is used

Homogeneity of Variance and which test is significant if assumption is not met

The true population variance for each group is the same. Any difference, is because of chance. Brown-forsythe and Levene’s Test

What Non-parametric test do you use if you violate the assumption of normality?

Kruskal-Wallis Rank Sum Test: it uses a ranked order of the OUTCOME variable

What test do you use if you violate the assumption of homogeneity of variance? (When the Levene’s Test or Brown Forsythe Test is significanT)

Welch’s One-way Test

What’s the three assumptions?

1) Random Selection

2) Normal Distribution

3) homoscedasticity

What’s another word for homoscedasticity

Homogeneity of Variance

What is the first step when conducting an ANOVA

Identify populations (what you’re comparing), distributions (z, t, or f) and assumptions

What is the second step when conducting an ANOVA

State null and alternate hypothesis

What is the third step when conducting an ANOVA

Determine Characteristics of the comparison distribution (is it z, t, or f, and what are the degree of freedoms)

True or false, each estimate has its own degrees of freedom

true

What is the fourth step when conducting an ANOVA

Determine the critical value/ cutoff

The critical value for a F distribution will always be _________

positive

What is the fifth step when conducting an ANOVA

Calculate the T statistic

What is the sixth step when conducting an ANOVA

Make a decision