Statisticians use Analysis of Variance (ANOVA) to compare three or more groups in a study. It is a powerful approach that enables the testing of differences in three or more groups in a single test. According to Gravetter, (2011), ANOVA is a hypothesis test used with one or more nominal or ordinal independent variables having at least three groups overall and also a scale-dependent variable. The term ANOVA is mostly preceded by two adjectives that show how many independent variables are there and the research design which might be between groups or within groups (Gravetter, 2011).
A one way ANOVA is a hypothesis test that incorporates a nominal independent variable having more than two levels and a scale-dependent variable. Between groups, on the other hand, is a hypothesis test involving two or more samples where each contains different participants. Within groups, ANOVA is a test where there are more than two samples where each sample has the same participants and is sometimes referred to as repeated measures ANOVA. A statistician can also use a two way between groups ANOVA to compare two independent variables. The samples that are to be used are selected independently and randomly (Gravetter, 2011).
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ANOVA has three assumptions which represent optimal conditions for the analysis of data. The three are; random selection is desired if the generalization is to be done beyond the sample. It also uses normally distributed populations thus allowing the examination of the sample. The third assumption is the homogeneity of variance i.e. the samples come from populations with the same variance (Gravetter, 2011).
A t -test or student's T-test is done when the statistician is interested in comparing the means of two groups and establish whether they are different from one another. It is used when a random assignment is available and there are only two and not more sets that are to be compared. The t-test can either be independent measure t-test or matched pair t-test. The population data to be gathered must be normally distributed and compares equal variances of the population under study. A z test is used to test the population mean against a standard or to compare the means of two populations that have large samples whether the standard deviation of the population is known or not (Gravetter, 2011).
Reference
Gravetter, F. J. (2011). Essentials of Statistics for the Behavioral Science . Pacific Grove, CA: Wadsworth.
