T Tests and ANOVA Statistics

Statistics: T-Tests and ANOVA

T-Tests and ANOVA: Statistics

Independent sample t-tests and ANOVA are both used to test for differences in means of unrelated, independent groups. However, ANOVA has been shown to be more effective than the t-test when the number of groups is more than two. This is because ANOVA controls the risk of type I error by holding the probability constant at a .05 significance level. This text explores the differences between the two tests, and the specific situations when each one is more effective.

Independent Sample t-Tests

My week 1 research questions were geared at assessing the impact of community youth sporting programs on adolescents' academic performance, discipline, and social well-being. RQ4 was selected to be used for this particular analysis. It read:

"Are there any significant differences between the levels of discipline of adolescents who engage in community youth sporting activities and those that do not?"

Well, this research question lends itself effectively to both ANOVA and the independent sample t-tests. However, ANOVA is preferred when the number of groupings being tested is more than 2; that is, when three or more unrelated groups are being measured on the same independent variable (Sukal, 2013). In our case, however, there are only two groupings of data -- i) adolescents who engage in community sporting activities and ii) adolescents who do not engage in community sports activities, which implies that the sample t-test can be used effectively (Sukal, 2013).

Variables and their Attributes: it is evident, from the research question, that community youth sporting activities is the independent variable, whereas the level of discipline is the dependent variable. The independent variable would be measured based on whether or not a participant engages in any of the state-funded youth sporting events in their community, be it rugby, football, tennis, hockey or basketball. The variable will be composed of two groups -- 1) a Yes group, for adolescents who participate in any of the aforementioned sporting events; and 2) a No group for adolescents who do not participate in any youth sporting event in the community. This would make the variable a discrete, nominal variable because there is a finite number of possible options (just two) and the numbers 1 and 2 are nothing but category identifiers with no quantitative significance.

The dependent variable, level of discipline, on the other hand, would be defined in terms of an individual's ability to self-regulate their performance, impulses, emotions and thoughts. We will measure this using the Brief Self-Control Scale questionnaire survey, which measures one's level of self-discipline on the basis of the aforementioned four domains. The BSCS requires respondents to respond to a set of 13 questions by selecting their most preferred option for each from a 5-point Likert scale answer list. The questions include, 'I am good at resisting temptation', 'I am not lazy', and so on. The responses to choose from, on the other hand, include a) very much like me; b) mostly like me; c) somewhat like me; d) a little like me; and e) not like me at all. We will assign each response a numerical value: 2, 1, 0, -1, and -2 respectively. The individual's level of discipline will then be obtained by summing up their points in all the 13 questions. This would make the variable a continuous, interval variable as a score of 0 would not necessarily imply no discipline. The actual levels of discipline for all participants will be recorded alongside the option of whether or not they engage in community sporting activities, and the t-test run to determine whether there any significant differences in discipline levels between the two groups.

Variables Qualifications for the t-Test: there are a number of major assumptions that a set of data must pass in order for it to qualify to be tested using the independent sample t-test. The test can only be conducted if the variables fit the qualifications for these six assumptions. Three of these assumptions can only be tested using SPSS statistics once actual data has been collected; since no data has been collected, we will disregard these three assumptions. As such, we will only focus on the remaining assumptions. First, the test can only be used if the independent variable comprises of two categorical, independent groups -- our independent variable comprises of the 'Yes' and 'No' groups, which are unrelated and independent from each other, implying that this assumption has been satisfied (Sukal, 2013). Secondly, the dependent variable should exhibit the characteristics of a continuous, interval or ratio variable -- ours satisfies this condition as described in the preceding section (Sukal, 2013).

The Null and Alternative Hypotheses: the study is guided by the following null and alternative hypotheses:

H0: µA= µB

There are no significant differences between the levels of discipline of adolescents who engage in community sports activities and those that do not H1: µA ? µB

There are observable and significant differences between the discipline levels of adolescents who engage in community sporting activities and those that do not.

If the test yields significant results (p

Type 1 Errors: type I errors are a wild possibility in this case. A type I error occurs when one falsely rejects the null hypothesis; that is, when one rejects the null hypothesis yet it is true. Most studies are conducted at a 95% confidence level, which implies that there is a 5% chance of making a type I error. In our case, we will conduct two independent t-tests, implying that we have a 10% chance of making a type I error. This would not be the case if ANOVA had been used instead because ANOVA controls for the type 1 error such that the probability remains at 5% regardless of the number of tests conducted. One could reduce the risk of type I error by decreasing the significance level to say 1%; however, this only increases the risk of making a type II error -- failing to reject the null hypothesis when it indeed is false.

Part Two: Analysis of Animal Research Case Study

The case study is based on the question of whether or not researchers ought to be allowed to use animals in research (Lane, n.d.). One faction believes that the use of animals in research is essential; another, however, believes that the practice is unethical and ought to be stopped. Experts believe that the choice of whether or not the use of animals in research is essential is dependent largely on gender. The study sought to determine whether there were any differences between how men and women felt about the controversial subject (Lane, n.d.).

RQ1: is there a gender difference with respect to the belief that animal research is necessary?

The corresponding null and alternative hypotheses are:

H0: µA= µB

There is no significant gender difference with respect to the belief that animal research is necessary (A represents the females' group and B represents the men's group)

H1: µA ? µB

There are observable and significant gender differences with respect to the belief that animal research is necessary.

Variables: the research question can be restated simply as 'how does gender influence the belief that animal research is necessary?' In this case, the variables can be easily identified -- gender is the independent variable whereas the essentiality of animal research is the dependent variable. The independent variable, gender, was defined in terms of individuals' sex, and comprised of two categories; 1) female and 2) male, which implies that it was measured as a discrete, nominal variable. The dependent variable, on the other hand, was defined in terms of the extent to which one believed that it was necessary to use animals in research. The variable was measured as a continuous, interval variable -- participants were supposed to indicate their degree of agreement or disagreement with the belief that animal research was necessary on a 7-point scale with scores from 1 to 7. The higher an individual's score, the greater their belief that animal research is necessary. The actual score for each participant was then recorded alongside their gender (group) and independent sample t-tests conducted.

Data Analysis: the independent sample t-test was used to test the hypotheses. There was no statistically significant difference between the two groups at the 95% confidence level -- team 1 (M=5), team 2 (M=4), t (32) =1.84, p>0.05. The t-statistic indicates that the groups have different means with respect to the belief that animal research is necessary. However, the difference between the two means is not significant at the 0.05 level, implying that the null hypothesis is true. If, however, the confidence level is adjusted to 0.1, then p< 0.1, which would basically imply that the difference in beliefs between the two groups is significant, and that hence, the null hypothesis is not true. At the 0.1 confidence level, therefore, the null hypothesis would be rejected. The t-test was selected for this question because the independent variable has only two categories; if there were three or more groups or categories, ANOVA would have been used.