Question

1. Perform a Two-way analysis of variance (ANOVA) and report the results using correct APA style; report whether significance was found for Factor A, Factor B, and/or an interaction between Factors A and B was found.
2. If the test statistic is significant, run a post hoc test to determine between what groups significance was found.
3. Report an effect size for all significant results.

This is all the information they gave me.

Answer 1

• (a) The output is:

  			Factor 2
  	Means:
  		< 30 % fat	30% - 60% fat	> 60% fat
  	< 60 minutes	3.4	2.2	1.8	2.5
  Factor 1	60 minutes or more	4.8	7.4	5.6	5.9
  		4.1	4.8	3.7	4.2
  	5	replications per cell
  ANOVA table
  Source	SS	df	MS	F	p-value
  Factor 1	90.13	1	90.133	135.20	2.39E-11
  Factor 2	6.20	2	3.100	4.65	.0196
  Interaction	18.47	2	9.233	13.85	.0001
  Error	16.00	24	0.667
  Total	130.80	29

  The hypothesis being tested is:

  H₀: There is no main effect of Factor A

  H_a: There is a main effect of Factor A

  The p-value from the output is 0.0000.

  Since the p-value (0.0000) is less than the significance level (0.05), we can reject the null hypothesis.

  Therefore, we can conclude that there is a main effect of Factor A.

  The hypothesis being tested is:

  H₀: There is no main effect of Factor B

  H_a: There is a main effect of Factor B

  The p-value from the output is 0.0196.

  Since the p-value (0.0196) is less than the significance level (0.05), we can reject the null hypothesis.

  Therefore, we can conclude that there is a main effect of Factor B.

  The hypothesis being tested is:

  H₀: There is no interaction effect of Factor A and B

  H_a: There is an interaction effect of Factor A and B

  The p-value from the output is 0.0001.

  Since the p-value (0.0001) is less than the significance level (0.05), we can reject the null hypothesis.

  Therefore, we can conclude that there is an interaction effect of Factor A and B.

  (b) The output is:

  Post hoc analysis
  p-values for pairwise t-tests for Factor 2
  		> 60% fat	< 30 % fat	30% - 60% fat
  		3.7	4.1	4.8
  > 60% fat	3.7
  < 30 % fat	4.1	.2842
  30% - 60% fat	4.8	.0060	.0672
  Tukey simultaneous comparison t-values (d.f. = 24)
  		> 60% fat	< 30 % fat	30% - 60% fat
  		3.7	4.1	4.8
  > 60% fat	3.7
  < 30 % fat	4.1	1.10
  30% - 60% fat	4.8	3.01	1.92
  critical values for experimentwise error rate:
  		0.05	2.50
  		0.01	3.21

  There is a significant 30% - 60% fat & > 60% fat.

  (c)

  Source	effect size
  Factor 1	0.689
  Factor 2	0.047
  Interaction	0.141