Computing and Interpreting ANOVAs

When To Use Univariate Analysis

Student’s Name

Institution Affiliation

The t-test analysis compares the average means of two unrelated groups. This analysis is also known as student t-test that shows how significant the difference between the two separate groups could be and if it happened by chance (Kim & Kohout, 1975). The ratio difference between the two unrelated groups is measured using the t-score scale. Larger t-score shows that the groups are different while the similarity is shown when the t-score is small. For instance, if we want to test the number of Masters Students enrolled in two universities assuming that the conditions of the two institutions are different, we take the random sample of various courses and run an independent t-test. The independent variable would be the two levels of Categorical Students from University A and University B. On the other hand, a p-value is the probability test to prove whether the results happened by Chance. They are measured from 0-100% and written in decimals. Low p-values show that the results are correct and indicate that they did not occur by chance.

The test hypothesis will be null hypothesis stating that the means are equal, i.e. (Ho µ1 = µ2). The test runs to see if we can reject the null hypothesis and accept the alternate hypothesis which shows that the two means are not equal, i.e. (Ha µ1 ≠ µ2). To do this test, it’s advisable to set a significance level alpha at (αp<.05) this allows the test to be either accepted or rejected. A t-test requires that in each group the independent variables appear normally and approximately distributed.

Presenting the result of a t-test from above example would state as follows. An independent sample t-test was conducted to evaluate the number of students enrolled in the two different universities. It was found that the computed p-value was t-value (-2.740) which was greater than the table value at an Alpha level: (p<.05). This shows that there is a difference between the two means indicating a null hypothesis.

On the other hand, the analysis of variance, ANOVA, helps statisticians to compare the means of three or more groups (Kim & Kohout, 1975). From the above case, comparing the random number of students enrolled in each university from different courses to their gender regarding the number of males to Female would require an ANOVA analysis. The ANOVA analysis compares the differences within the groups also known as variations. There is a statistical significance if at all what occurs by chance is different. The null hypothesis in ANOVA would show that the population mean for all the groups is the same; that is, the average value is the dependent value. The null hypothesis states that there is no difference among the group’s means, while the alternative hypothesis indicates that the group means are not equal. The null hypothesis is rejected when f-test is significant. If the f-ratio is large, then the alternative hypothesis is correct. When the null hypothesis is rejected in ANOVA, then it’s concluded that at least two groups differ from each other.

Reference

Kim, J. O., & Kohout, F. J. (1975). Analysis of variance and covariance: subprograms ANOVA and ONEWAY. Statistical package for the social sciences, 2, 398-433.