¶ … F-ratio is designed in such a way that there is no individual difference with reference to contribution between denominator and numerator. The numerator of F-ratio measures the means difference that exists between one treatment to the other and the F-ratio is designed in such a way that both denominator and numerator measure exactly the same variance and when the null hypothesis is true, and there will be no systematic treatment effect. When there is no treatment effect, the F-ratio balances the numerator and denominator because both are measured exactly in the same variance, making F-ratio to have the value equal to 1.00.
When a research finding concludes that F-ratio is equal to 1.00, the research will conclude that there will be no treatment effect, thus, the research will fail to reject the null hypothesis, and the null hypothesis is true. However, when the treatment effect exists, this contributes to the numerator only, which produces large value for the F-ratio. Thus, the large value indicates that there is a real treatment effect and the research should reject the null hypothesis. The numerator in the F-ratio does not include individual differences and the individual difference needs to be eliminated from the denominator to achieve the balance between numerator and denominator. (Gravetter, 2011).
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The T-test is appropriate to assess whether the means of two groups are statistically different, and t-test is appropriate to compare means of two groups. On the other hand, ANOVA assesses whether the means of three or more group are statistically different. ANOVA assists in comparing the means of three or more group. Thus, ANOVA should be used to carry out a research to determine the statistical differences of the means of the three or more independent (unrelated) groups. However, the t-test will not be appropriate to carry out this type of test because the t-test is only appropriate to test the different of the means of two groups.
Platt, (1998) argues that the t-test is a commonly use statistical procedure to compare the means of two different populations. The difference between the two means divided by standard deviation is known as t-distribution. Platt, (1998) further argues that t-test is appropriate to compare the means of two different group of population, however, ANOVA is an appropriate statistical tool to compare the means of three or more groups. While the t-test is appropriate to carry out the regression of only two values, the ANOVA could be used to carry out the regression...
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