Repeated Measures ANOVA and Dependent Samples T Test Week 3 Assignment

Repeated Measures ANOVA and Dependent Samples t-Test: Week 3 Assignment

Week 3 Assignment: Repeated Measures ANOVA and Dependent Samples t-test

My research questions in week one sought to assess the impact of community youth sporting programs on adolescents' well-being, discipline and academic performance. None of the questions used then lends itself effectively to the repeated measures ANOVA or the dependent samples t-test; however, we could adjust RQ4 to make it qualify for the same. Originally, RQ4 read, "Are there any significant differences between the levels of discipline of students who engage in youth sporting activities and those that do not?"

To make it appropriate for the repeated measures ANOVA, we modified it as follows:

"Is there a difference in students' discipline levels before, after a three-month, and after a six-month period of engagement in community sporting activities?"

In this case, we would be interested in finding out how students' discipline levels vary based on the length of their engagement in sporting activities; we, for instance, would expect students who engage longer or more in sporting programs to be more disciplined than those who engage less. This question lends itself effectively to the repeated measures ANOVA because it compares the means of three related groups on the same dependent variable (Sukal, 2013). The first group consists of participants before engagement in community sporting activities, the second is of the same participants after a three-month engagement period (mid-way into the treatment) and the third is of the same participants after a six-month period. A dependent t-test would not be effective in this case because such a test is used when there are only two groups -- if, for instance, we were interested in comparing discipline levels of adolescents before and after completion of the program only, then the dependent t-test would be more appropriate. Of importance is that differently from the one-way ANOVA, the repeated measures ANOVA measures the same participants multiple times (in our case three times) on the same dependent variable (Lane, n.d.).

Variables: we are seeking to measure differences in students' discipline levels at three different time points -- before engagement, after three months and after six months engagement. This makes 'discipline level' our dependent variable and 'time' our independent variable. We will define the dependent variable in terms of one's ability to self-regulate their performance, impulses, emotions and thoughts. The Brief Self-Control Scale Questionnaire Survey will be used to measure participants' abilities in these four domains. The BSCS consists of 13 questions, to which participants respond by selecting their most preferred option from a 5-point Likert scale. The questions range from 'I am good at resisting temptation' to 'I am lazy, and so on; and the response list includes the following five options: a) very much like me, b) mostly like me, c) somewhat like me, d) a little like me, and d) not like me at all. We will assign a numerical value to each response -- 2, 1, 0, -1 and -2 respectively, and a participant's discipline level will be obtained by summing up the total value responses for the 13 questions. This would make the variable a continuous, interval variable. We could select 20 adolescents from a selected neighborhood who currently do not take part in any youth sporting programs, and then get them to voluntarily engage in the same say every weekend for the six-month period. We could then measure and record their discipline levels before the treatment program, after three months, and after the six-month completion period.

The independent variable, on the other hand, could be categorized into three related time groups; t0 (before engagement), t1 (after three months), and t2 (after six months), which would make the variable a categorical, ordinal variable. The order t0, t1 and t2 matters more than the quantitative difference between groups; as such, we cannot interchange the order of the category identifiers, say bring t2 before t0 and t1 and still have the scale make sense. Participants' discipline levels at times t0, t1 and t2 could then be recorded and subjected to the repeated measures ANOVA test.

Variable Qualification: in order for repeated measures ANOVA to be conducted, the dependent variable ought to be measured at the continuous level, that is as either a ratio or an interval variable (Sukal, 2013). Our dependent variable, level of discipline, satisfies this condition -- it is measured as a continuous, interval variable as described in the preceding section. Moreover, the independent variable should consist of at least two related groups -- ours consists of three such groups, t0, t1 and t2. Towards this end, we can rightly conclude that our variables perfectly fit the qualifications for the repeated measures ANOVA test (Sukal, 2013).

Hypothesis: the null and alternative hypotheses guiding the study are as follows:

H0: µ1 = µ2 = µ3

Participants' level of discipline is the same at all three time points

HA: µ1 ? µ2? µ3

The level of discipline is significantly different at one or more time points

Possible Errors: both type1 and type 2 errors are a possibility in this case depending on the significance level chosen. The conventional significance level is p

Discussion 2: Case Study

RQ: "Does higher dosage lead to higher cognitive performance?"

Hypotheses:

H0: µ1 = µ2 = µ3= µ4

Cognitive performance is the same at all four dosage levels

HA: µ1 ? µ2? µ3? µ4

Cognitive performance is significantly different at one or more dosage levels

Variables: it is evident, from the research question, that cognitive performance is the dependent variable and 'dosage' the independent variable. The dependent variable is measured as a continuous, interval variable because a score of zero (represented by zero stars) would not necessarily mean zero cognitive ability. The dependent variable, on the other hand, was measured as a categorical, ordinal variable -- it consisted of four ordered categories/levels (placebo, 0.15mg/kg, 0.3mg/kg, and 0.6mg/kg). The order of the categories was more significant than the quantitative differences between the values, and as such, there was no way one could interchange the order of the same without causing the scale to lose meaning.