Question

1.Interpret the following results of analysis of variance. Interpret each statistic including post-hoc comparisons. Provide a complete interpretation using the five-step model of hypothesis testing.

Oneway: Relationship Between Lab Section and Score on Stat Final

                                                                               Descriptives

Score on Stat Final

	N	Mean	Std. Deviation	Std. Error	95% Confidence Interval for Mean		Minimum	Maximum
					Lower Bound	Upper Bound
1	22	40.68	13.892	2.962	34.52	46.84	14	65
2	22	32.59	12.015	2.562	27.26	37.92	7	55
3	24	29.83	12.910	2.635	24.38	35.28	4	55
Total	68	34.24	13.580	1.647	30.95	37.52	4	65

                                                          ANOVA

Score on Stat Final

	Sum of Squares	df	Mean Square	F	Sig.
Between Groups	1438.811	2	719.406	4.283	.018
Within Groups	10917.424	65	167.960
Total	12356.235	67

Post Hoc Tests

                                                              Multiple Comparisons

Dependent Variable: Score on Stat Final

Scheffe

     

(I) Lab Section	(J) Lab Section	Mean Difference (I-J)	Std. Error	Sig.	95% Confidence Interval
					Lower Bound	Upper Bound
1	2	8.09	3.908	.125	-1.70	17.88
	3	10.85(*)	3.825	.023	1.27	20.43
2	1	-8.09	3.908	.125	-17.88	1.70
3	2.76	3.825	.772	-6.83	12.34
3	1	-10.85(*)	3.825	.023	-20.43	-1.27
2	-2.76	3.825	.772	-12.34	6.83

* The mean difference is significant at the .05 level.

Homogeneous Subsets

                               Score on Stat Final

Scheffe

  

Lab Section	N	Subset for alpha = .05
		1	2
3	24	29.83
2	22	32.59	32.59
1	22		40.68
Sig.		.775	.118

Means for groups in homogeneous subsets are displayed.

a Uses Harmonic Mean Sample Size = 22.629.

b The group sizes are unequal. The harmonic mean of the group sizes is used. Type I error levels are not guaranteed.

Answer 1

The five step model of hypothesis testing is describe below,

Step 1: The null hypothesis for the test is define as,

Null hypothesis: such that group means are all equal.

Step 2: The alternative hypothesis for the test is define as,

Alternative hypothesis, : such that not all group means are equal.

Step 3: The significance level for the test, is the maximum acceptance level at 5% risk which means null hypothesis will be rejected beyond this level ( such that if P-value is less than 0.05 null hypothesis will be rejected)

Step 4: The test statistic is the F-value which is obtained in ANOVA table, The F-value is used to calculate the P-value. (Whereas F-value determine whether the means among two or more populations are significantly different if compare against the F-critical value). Here the P-value is used to make a decision about the statistical significance of the means. From the ANOVA model summary,

Step 5: The decision for the statistical significance in mean is determine by the P-value. The P-value can be define as the probability that measures the evidence against the null hypothesis If the P-value < alpha: The differences between some of the means are statistically significant and if P-value > alpha: The differences between the means are not statistically significant. from the model summary,

Hence the differences between some of the means are statistically significant.

Post hoc test

If the null hypothesis is rejected, ANOVA only tell there is atleast one group statistically different. ANOVA doesn't compare means individually hence the post hoc test is reqired to see which means are statistically different

The Scheffe test for multiple group comparison is used here. From the test result summary, The P-value

(I) Lab Section	(J) Lab Section	Mean Difference (I-J)	Sig.
					Significance Level
1	2	8.09	0.125	>	0.05	Not Significant
	3	10.85(*)	0.023	<	0.05	Significant
2	1	-8.09	0.125	>	0.05	Not Significant
3	2.76	3.825	-6.83	>	0.05	Not Significant
3	1	-10.85(*)	0.023	<	0.05	Significant
2	-2.76	3.825	-12.34	>	0.05	Not Significant

The P-value for group comparison 1 and 3 (or say 3 and 1, same thing) is significant at 5% significance level.