Module 11

Question 1

What is the F-test?

Answer 1

Statistical hypothesis test used to evaluate whether the variances of two groups are different.

Question 2

The ratio of variances is often called what?

Answer 2

F-score

Question 3

What are the four steps that an F-test uses?

Answer 3

• define the null and alternative hypotheses
• establish the null distribution
• conduct the statistical test
• draw scientific conclusions

Question 4

What are the null and alternative hypotheses for the F-test?

Answer 4

non directional:
* null: the ratio of variance is one
* alt: ratio of variance is not one

directional:
* null: F</= 1 or the opposite way
* alt: F>1 or opposite way

Question 5

What is the null distribution for F-tests?

Answer 5

• for the ratio of variances is the sampling distribution from repeatedly sampling a statistical population where the variance was the same for both groups
• since variances can not be negative, the ratio of variances will only ever be non negative
• looks more like a chi-squared distribution
• depends on the sample sizes in each group
• more samples means better estimate and narrower sampling distribution

Question 6

What are the two degrees of freedom?

Answer 6

Group A (dfA)
* degrees of freedom for group A is dfA=nA-1 where nA is the number of sampling units in group A

Group B (dfB)
* degrees of freedom for group B is dfB=nB-1 where nB is the number of sampling units in group B

Question 7

What should the reporting of an F-test include?

Answer 7

• the mean, standard deviation, and sample size for each group
• the observed F-score
• degrees of freedom for each group
• p-value

Question 8

What is the F-test?

Answer 8

• the hypothesis test works by locating the critical F-score that corresponds to the Type 1 error rate on F-distribution and comparing that to the observed F-score
• the statistical decision can be made either by comparing the observed and critical F-score or by comparing the p-value and type 1 error rate

reject: if observed score is greater than the critical score

fail to reject: if observed score is less than or equal to the critical score

Question 9

What is ANOVA?

Answer 9

• analysis of variance
• a statistical mdthod used to work with data that has both numerical and categorical variables
• if there are more than two levels then the data are analyzed using ANOVA (instead of a t-sample t-test)

Question 10

What are the two sources of variation that ANOVA is able to partition (how the test works)?

Answer 10

Group variation: the variation among means of the categorical levels. key to understanding how ANOVA works. if the means of the groups are the same, then the variation among the groups is zero. if they are very different, then the variation among the groups is high. the variation among the groups is a direct indicator as to whether the groups have different means

residual variation: the variation among sampling units within a categorical variable

Question 11

make a flashcard on how group variation and residual variation are calculated.

Question 12

What is the statistical model for ANOVA?

Answer 12

• it compares the group variation to the residual variation
• it looks at the ratio of the group variation over the residual vairation
• if the group variation is about the same size as the residual vaition, then the means of the levels are not overly different
• if the group variation is much larger than the residual variation, then the groups are different

Question 13

How is the F score set up?

Answer 13

group variationd divided by residual variation

F=MSg/MSe

Question 13

What is the ANOVA hypothesis test?

Answer 13

**null and alternative hypothesis
**
* often written twice, first for the means and second for the F-test
* means: null; mean1=mean2, alt; they are not equal
* F-test: null=F less than or equal to 1, alt=F greater than 1

Null Distribution
* the sampling distribution from repeatedly sampling a statistical population where the means are the same across all levels of the categorical variable
* df for group variation: df=k-1, where k is the number of levels in the categorical variable
* df for residual variation: dfe=n-k, where n is the total number of sampling units and k is the number of levels in the categorical variable

F-Test
* same as the others

Question 14

What does the reporting of ANOVA must include/

Answer 14

• the mean, standard deviation, and sample size for each group
• the observed F-score
• degrees of freedom for the group variation and the residual variation
• p-value

Question 15

What are post hoc tests?

Answer 15

• secondary statistical tests designed to indicate what groups have different means in an ANOVA
• only used if the ANOVA F-test indicates to reject the null hypothesis
• evaluare whether groups means are different while controlling for the Type 1 erorr rate for all comparisons among groups

Question 16

What is a contrast statement?

Answer 16

evaluating the mean of any two groups is different, would ask different contrast statements so that one corresponds to each pair wise combination

Question 17

What is the family of contrasts?

Answer 17

the set of contrast statements for a study

Question 18

What are post hoc tests in terms of family of contrasts?

Answer 18

they are designed to evaluate the family of contrasts without inflating the family wise error rate

Question 19

What is the family wise error rate?

Answer 19

the type 1 error rate for the entire family of contrasts

Question 20

What is the TurkeyHSD test?

Answer 20

• type of post hoc test for ANOVA
• compares the mean of all possible combinations of categorical levels in an ANOVA
• it controsl the family wise erorr rate by using a specialized null distribution that accounts for the number of contrasts
• corrects the number of contrasts behind the scenes