week 7 repeated measures anova

Question 1

sphericity assumption

Answer 1

In repeated measures, anova, we have the equivalent of homogeneity of variance, with the assumption of sphericity. Sphericity exists whenthere is equality of variances over the different treatment levels

ie variance_A-B≈variance_A-C≈variance_B-C

eg if have 3 time points therefore differences between the variances at time 1 and time 2, should be approx equal to differences betweenvariances at time 2 and 3

Question 2

mixed designs

Answer 2

designs which include a combination of at least one between-subjects variable, and at least one within-subjects variable.

Question 3

Mauchley’s test

Answer 3

Mauchley’s Test of Sphericity is used to judge whether any sphericity violation is significant. If Mauchley’s w is significant at

p=/< 0.05 then ad adjustment for sphericity violation is required

Mauchley’s tests the null hypothesis that the variances of the differences are equal.

Question 4

calculations

Answer 4

When correcting for sphericity violation, multiply chosen epsilon by the degrees of freedom, thus resulting in a smaller denominator df and a larger critical F value.

Question 5

lower-bound estimate correction

Answer 5

Third method for correcting sphericity violation.

This estimate tends not to be recommended as is too conservative.

Question 6

Greenhouse-geisser correction

Answer 6

Also known as The Box Correction. When Mauchley’s is significant. how much of a correction is to be performed, is determined by the value of epsilon calculated by Greenhouse-geisser.

Values of epsilon at greenhouse geisser:

A) epsilon=1 thereforeuse sphericity assumed values (no corrections necessary)

B)epsilon>0.75 therefore use Huynh-Feldt correction.

C)epsilon<0.75 therefore use Greenhouse-geisser correction.

Question 7

The Huynh-Feldt correction factor

Answer 7

7

Question 8

Repeated Measures Anova

Answer 8

A repeated measures anova, repeatedly measures THE SAME SUBJECTS. eg.giving same group, 2, 5 and 10 drinks on different occasions, and measuring party enjoyment. CF giving 1 group 2 drinks, one group 5 drinks and another 10 , which is a between subjects one-way anova. In a repeated-measures anova, we are specifically interested in removing any participant differences across the treatments for our error term. Hence, smaller error term, therefore more likely to be able to detect smaller treatment effects. (increased statistical power)

Question 9

treatment vs subject variability

Answer 9

SS_T(total variability in the dv)=SS_B(between person variation)+SS_w(within person variation.

SS_w=SS_M(effect of experiment) + SS_R(error)

SS_W is the extent to which the individual has different scores across different treatments.

in a within-subjects design, because the same subjects are used in all tx groups, correlations b.n tx pairs would NOT EQUAL 0.(ie they will be correlated).

In a repeated-measures anova subjects are treated as an extra variable.Anova will be able to remove the individual differences between sunjects (SS_B )from the within-subjects variability (SS_W).

Question 10

covariance

Answer 10

is an unstandardised correlation, so can think of covariance as a form of correlation.

Question 11

compound symmetry.

Answer 11

Goes a step stricter than sphericity. Must first meet sphericity, plus covariances between pairs of conditions are also approx equal. A co-variance is how much a variance is shared between time points, or how much these time points vary together.

Question 12

variance

Answer 12

Note that variance for repeated measures anova is calculated differently. Just accept spss will calculate.

Question 13

failure of sphericity

Answer 13

Failure of sphericity may be a potential problem in repeated measures anova, as foundation of the analysis is the assumption that multiple measures of the same individual, will be correlated. There is a risk that closer time point measures, will more likely correlate than distant time point measures.

As a consequence, our F-ratio may not be valid, and there is an increased risk of Type 1 error. Failure of sphericity does not increase risk of type 2 error.

If sphericity is violated, it may be necessary to reduce the degrees of freedom in the denominator, in order to reduce risk of type 1 error.

Values of epsilon at greenhouse geisser:

A) epsilon=1 thereforeuse sphericity assumed values (no corrections necessary)

B)epsilon>0.75 therefore use Huynh-Feldt correction. if use greenhouse-geisser here it tends to be unreliable, with too many type 2 errors.

C)epsilon<0.75 therefore use Greenhouse-geisser correction.

D) there will also be a reported Lower bound value for epsilon but this correction in reality is now no longer recommended as tends to be too conservative.

When do the correction for violation of sphericity, multiply degrees of freedom (both numerator df and denominator df)with the chosen method’s epsilon value.

The value of F will remain the same, but because df changed, therefore have adjusted p value. (new df’s need to be rounded to whole number)

Question 14

epsilon

Answer 14

A descriptive statistic which indicates the degree to which sphericity has been violated. Epsilon ranges from 0 to 1. 1=perfect sphericity (no violation) https://statistics.laerd.com/statistical-guides/sphericity-statistical-guide.php