Is there a statistically significant difference in mean scores between any of th

Question

Is there a statistically significant difference in mean scores between any of the following groups ? calculate and report the mean of each group.If one or more mean differences exists please identify the groups with the significantly different means. Use the most appropriate statistical test to answer this question at the alpha= 0.05 level of significance. Identify the hypothesis statements, test statistics, p-value and your decision.

1              12
1              15
1              18
1              24
1              25
1              21
1              16
2              33
2              35
2              45
2              55
2              44
2              36
2              45
3              65
3              77
3              88
3              67
3              56
3              45
3              67
4              12
4              26
4              33
4              55
4              77
4              89
4              35

Explanation / Answer

One-way ANOVA: response versus factor

Method

Null hypothesis All means are equal
Alternative hypothesis At least one mean is different
Significance level = 0.05

Equal variances were assumed for the analysis.

Factor Information

Factor Levels Values
factor 4 1, 2, 3, 4

Analysis of Variance

Source DF Adj SS Adj MS F-Value P-Value
factor 3 8071 2690.5 10.12 0.000
Error 24 6377 265.7
Total 27 14449

Model Summary

S R-sq R-sq(adj) R-sq(pred)
16.3011 55.86% 50.34% 39.92%

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