Q1: For the chi-square test, independent t-test, ANOVA, repeated measures ANOVA, and correlation, describe the inferential statistics and what levels of measurement are needed.
Chi-square test: This inferential statistic can be used both as a baseline measure in determining the success of the randomization procedure in the sample assignment and in analyzing the sample attrition level during the study implementation between the baseline point and the study endpoint, which, in the Jemmott, Jemmott, and Fong (1998) study, experienced a small (below 10%) attrition over the period of 3 to 12 months. The level of measurement for the independent and dependent values may be nominal and/or ordinal (Fitzgerald & Fitzgerald, 2014). The Chi-square test represents the extent of difference between the table of observed frequencies and that of the expected frequencies under the assumption that the null hypothesis is true (Weiers, 2014).
Independent (or independent-samples) t-test: This inferential statistic compares the means between two unrelated (independent) samples on the same continuous, dependent variable (Weiers, 2014). Like the Chi-square test, it can also be used to analyze the level of attrition in the sample population during the study period, as what happened in Jemmott, Jemmott, and Fong (1998), which experienced a little (below 10%) attrition within the period of 3 to 12 months. The level of measurement for its independent variable is largely nominal; while its dependent variable can be either interval or ratio (Fitzgerald & Fitzgerald, 2014). As such, it assumes that no significant outliers affect variables; that the dependent variable is roughly of normal distribution; and that the variances are homogeneous (Weiers, 2014).
Analysis of variances (ANOVA): Analysis of variances, whether one-way, two-way or randomized block, is a procedure (or a set of techniques) that compares the means of two or more independent samples simultaneously. It measures both variation between the sample groups and the variation within the groups (Weiers. 2014). The former reflects the variation effect of the factor levels; while the latter indicates the random errors acquired in the sampling process. The level of measurement of its independent variable is nominal, which can be in 3 or more group categories; while its dependent variable either interval or ratio (Fitzgerald & Fitzgerald, 2014). Moreover, it can test the overall strength of the relationship between the dependent variable and the independent variables performed in correlation (regression) analysis (Weiers, 2014).
Repeated measures ANOVA: This inferential statistic, one of the set of ANOVA techniques, is a series of analyses of variances used to determine the success of the randomization procedure during the sample assignment to groups (Jemmott, Jemmott, & Fong, 1998). Its level of measurement is similar to that of the ANOVA (Fitzgerald & Fitzgerald, 2014). Moreover, like that with any ANOVA, it tests the equality of the means. It is most appropriately used when all units in the randomly assigned sample population are measured under different conditions.
Correlation: Correlation analysis measures the strength of the linear relationship between two variables, both independent and dependent (Weiers, 2014). As a correlational statistic, logistic regression analyses were used in Jemmott, Jemmott, and Fong (1998) to measure dependent behaviors with dichotomous variables providing control for baseline outcomes. The level of measurement for both the independent and dependent variables can be either interval or ratio. However, the independent variables can be dummy variables (Fitzgerald & Fitzgerald, 2014). Correlational analysis has two important strength measures: the coefficient of correlation and the coefficient of determination (Weiers, 2014).
Q2: For SPSS output #1, what is the inferential statistic performed and determine whether or not the analysis was statistically significant. Given the research study objective, why was this test chosen?
The study used the inferential statistic two-tail t-test at p <0.05 with an analysis giving out a statistically significant outcome of p 0.000, being equivalent to p <0.05. The test was chosen because (1) the population is assumed to approximately follow the normal distribution and (2) the mean of the samples (baseline and at 3 month f/u) needs to be compared for significant difference to test the null hypothesis that the mean 3-month fasting glucose sample equals the mean baseline fasting glucose sample.
However, the statistic used was incorrect because t-test is appropriate only in samples with small size (below 30). The study, conversely, has N=50; thus, a large sample size. In effect, using t-test for a large sample size tends to flatten the distribution curve instead of keeping it at normal distribution, violating reason #1. Thus, the more appropriate statistic should be the two-tail z-test (Weiers, 2014).
Q3: For SPSS output #2, what is the inferential statistic performed and determine whether or not the analysis was statistically significant? Given the research study objective, why was this last test chosen?
The inferential statistic performed is correlation analysis. Its two-tailed significance is however more than the minimum significance of p <0.05; thus, the two variables (baseline fasting glucose and participate age) are not statistically significant. The test was chosen in order to understand whether the relationship between the independent variable (participate age) is positively correlated with the dependent variable (baseline fasting glucose); or whether any change in participate age will have a consequent change in the baseline fasting glucose.
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