Please answer the following in 60 or more words per topic. W…

Please answer the following in 60 or more words per topic. When would a researcher use a t test of independent means? Provide an example. When would a researcher use a t test of dependent means? Provide an example. What is an analysis of variance (ANOVA)? Describe the theory underlying it. When would a researcher use ANOVA for data analysis? Provide an example Purchase the answer to view it

A researcher would utilize a t test of independent means when comparing the means of two independent groups. This statistical test aims to determine if the means of the two groups are significantly different from each other. For example, a researcher may want to investigate if there is a difference in test scores between male and female students. By conducting a t test of independent means, the researcher can determine if the gender of the student has an impact on the test scores.

A t test of dependent means, on the other hand, is employed when comparing the means of two related or dependent groups. This test assesses if the means of two related groups are significantly different from each other. For example, a researcher may want to examine if there is a difference in the anxiety levels of individuals before and after a relaxation intervention program. By conducting a t test of dependent means, the researcher can determine if the relaxation program had a significant impact on anxiety levels.

An analysis of variance (ANOVA) is a statistical technique used to compare the means of more than two groups simultaneously. ANOVA assesses if there are any significant differences between the means of the groups being compared. The theory underlying ANOVA is based on the partitioning of the total variance into different sources of variance, namely, the variance between the groups and the variance within the groups. The main assumptions of ANOVA include the normality of the data, homogeneity of variances, and independence of observations.

Researchers employ ANOVA when they have more than two groups and want to determine if there are significant differences among the means. For example, a researcher may be interested in comparing the effectiveness of three different teaching methods on student learning outcomes. By conducting an ANOVA, the researcher can determine if there are significant differences in the mean scores of the three teaching methods. If there are significant differences, further post-hoc tests can be conducted to identify which specific groups differ from each other.

In summary, a t test of independent means is used when comparing two independent groups, while a t test of dependent means is used when comparing two related groups. ANOVA, on the other hand, compares the means of more than two groups simultaneously. Researchers utilize these statistical tests based on the nature of their research design and the specific research questions they aim to investigate.