# Application of T-Tests and F-Tests

## Application of t-Tests

A research question that can be addressed by using an independent samples t-test about the area of General Psychology is as follows: “Are married couples (both spouses aged 18-25) that have no children and live separately from their parents have fewer quarrels than those married couples (both spouses aged 18-25) that have no children and live with at least one parent of one of the spouses from that couple?”

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An independent samples t-test would be appropriate for the analysis in this case because it is used to compare the means of the same measurement for two different populations to find out whether they are statistically different (Warner, 2013). In this case, the first population (couples who live separately from parents and have no children) is different from the second one (couples that live with parents of one of the spouses and have no children); the populations do not overlap (living or non-living with parents differentiates them into separate sets), but have a common variable (the number of quarrels for the last year), in which cases the t-test is appropriate (George & Mallery, 2016).

The independent variable (according to which the populations will be divided) is “living with or without parents of one of the spouses”; the measurement is nominal. It is possible to assign: 1=live without parents, 2=live with at least one parent of one of the spouses. The second, dependent, variable, the number of quarrels for the last year, will be measured using an interval scale.

It is expected that the group 1 mean score on the second variable will be lower than that of group 2, for an individual often may be able to choose whom to marry and might choose a person with a character that they like, but they may not be able to influence the character of the parents of their spouse, which is why there might be more quarrels in the family if the characters of a person and their parent(s)-in-law conflict.

## Application of F Tests

A research question from the area of General Psychology that may be addressed by the one-way ANOVA is as follows: “Are married couples (both spouses aged 18-30) that have different ethnic/cultural origins (both spouses belong to the same ethnic/cultural group; the groups are: Asian, Black, Hispanic White, Non-Hispanic White) but the same socioeconomic status (the middle class) have different frequency of quarrels?”

A one-way ANOVA would be appropriate for this analysis because it is used to find out whether there is a significant difference between the mean scores of several different populations (usually more than two populations, because for two populations, an independent samples t-test can be conducted) (Weinberg & Abramowitz, 2002). In the offered case, the populations are different and do not overlap. However, they have a common variable (the number of quarrels the couple had over the last year), the means of which may be compared.

The independent variable will be “ethnic/cultural group”; the measurement is nominal. It is possible to assign, for example, Asian=1, Black=2, Hispanic White=3, Non-Hispanic White=4, but any other way of assigning numbers to the categories is appropriate (Greene & D’Oliveira, 2005). The dependent variable will be “the number of quarrels that the couple had over the last year”; it will be measured using an interval scale.

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It is expected that the means of at least two groups will be statistically different, for it appears likely that different cultural origins may have an influence on the way of life of a family and the attitudes of spouses towards one another. Of course, the difference in the number of quarrels may also be correlated with other factors (for instance, to the socio-economic status, which is why it was offered to survey the middle class only), so further studies will be needed.

## References

George, D., & Mallery, P. (2016). IBM SPSS Statistics 23 step by step: A simple guide and reference (14th ed.). New York, NY: Routledge.

Warner, R. M. (2013). Applied statistics: From bivariate through multivariate techniques (2nd ed.). Thousand Oaks, CA: SAGE Publications.

Greene, J., & D’Oliveira, M. (2005). Learning to use statistical tests in psychology (3rd ed.). New York, NY: Open University Press.

Weinberg, S. L., & Abramowitz, S. K. (2002). Data analysis for the behavioral sciences using SPSS. New York, NY: Cambridge University Press.

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