Scenario Background
Using statistical analysis to make informed and data-driven decisions makes critical practical sense to minimize the probabilities of error, bias, and risk. Statistical analysis is profoundly essential to the social and psychological sciences, whose goal is to investigate patterns of human behavior in groups, in society, and at the individual level (Privitera, 2022). In this scenario of a four-group experiment, a researcher calculated an F ratio of 4.86 with degrees of freedom of 3 in the numerator and 16 in the denominator. The ANOVA test was used to calculate the statistical difference in mean values between groups.
The Use of One-Way and Two-Way ANOVA Tests
Strictly speaking, one-way ANOVA is used when there are more than two groups (in practice, three or more) for which continuous data on the dependent variable of interest are obtained. For each group, the mean is calculated, and the result is the F-value for the overall statistic. Thus, for the current scenario, the results of the ANOVA test resulted in the following result: F(3, 16) = 4.86.
The Significance of the F Ratio
Using the standard distribution tables, we can calculate the p-value at the current setting to determine statistical significance. The general rule is that if the calculated p-statistic for a data set is below the selected critical significance threshold, the null hypothesis is rejected, and the result is accepted as statistically significant. For the current results, the calculated p-value is.013698. Concerning the significance threshold alpha of.05, it can be seen that this result is statistically significant because p < α. The conclusion is that there is at least one statistically significant difference in the mean values between the four groups under study.
However, it is essential to emphasize that the classical ANOVA test does not provide the location of this difference, so an additional post hoc test is needed. On the other hand, when α is.01, the result is not statistically significant, and the null hypothesis cannot be accepted because p > α. It is essential to clarify that the higher the level of α is accepted, the less accurate the results are because the probability of type 1 errors increases.
The Use of Various Types of T-Tests
To select the optimal t-test, it is necessary to understand how the samples were formed: whether they are paired (paired t-test), independent (independent t-test), or only one sample (one-sample t-test). Each methodology has a different version of the corresponding t-test, and mixing these variants cannot be done technically. There is also a difference between one-way and two-way ANOVA: a one-way ANOVA is used if there is only one dependent variable. In contrast, a two-way ANOVA is used if there are two dependent variables.
In addition, based on the nature of the data available, the type of sample(s) collected, and the research question, different non-parametrically t-tests can be used. There are analogs for each of the above tests: Wilcoxon signed-rank for paired t-test, Mann-Whitney U for independent t-test, Sign test for one-sample t-test, Kruskal-Wallis test for one-way ANOVA and Friedman test for two-way ANOVA (Privitera, 2022). In other words, when the data violate normality requirements, classical tests can be replaced by non-parametric variants.
Reference
Privitera, G. (2022). Research methods for the behavioral sciences (3rd ed.). Sage.