III. Methodology
3.3 Data Analysis
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3.3 Data Analysis
The statistical software package, STATA, was used for the data analysis.
In order to ensure the internal consistency of the perceived benefits and barriers scales, Cronbach’s alpha, α, was tested on both scales. Cronbach’s alpha tests can be used to measure the reliability of multiple-scale Likert question surveys. The test ensures that the questionnaire is accurately measuring the perceived benefits and barriers to exercise. The formula for Cronbach’s alpha is:
𝛼 = 𝑘
𝑘 − 1(1 −∑𝑆𝑖2 𝑆𝑇2 )
k is the number of items on the scale. 𝑆𝑖2 is the variance of the ith item, and 𝑆𝑇2 is the variance of the total score formed by summing all of the items (Bland & Altman, 1997). Both the perceived benefits and perceived barriers scales can be interpreted as reliable. According to Bland & Altman (1997), an alpha between 0.7 to 0.8 can be seen as satisfactory, although for clinical applications the alpha should be above 0.9 or 0.95. The internal consistency (alpha) for the perceived benefits scale was 0.82, while the alpha for the perceived barriers scales was 0.8. Therefore, the scales can be deemed as reliable.
For this study, it is expected that adults who exercise more than 3 times per week – categorized as having High activity levels – should perceive higher benefits and lower barriers to exercise, compared to those who exercise less than 3 times per week – categorized as having Low activity levels. To further ensure the validity of the study, a simple linear regression was run on perceptions of the overall benefits and barriers to exercise relative to participants activity levels. The formula is as follows:
𝑦 = 𝛼 + 𝛽𝑥+ 𝜖
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Table 2: Regression analysis summary for High activity levels on Perceptions of Benefits to Exercise
One asterisk indicates a significance level of 5%, two asterisks indicate a significance level of 1%, three asterisks indicate a significance level of 0.1% (* p < 0.05, ** p < 0.01, *** p < 0.001)
Table 3: Regression analysis summary for High activity levels on Perceptions of Barriers to Exercise
Coefficient Standard Error T - Value
One asterisk indicates a significance level of 5%, two asterisks indicate a significance level of 1%, three asterisks indicate a significance level of 0.1% (* p < 0.05, ** p < 0.01, *** p < 0.001)
As the results of the regression in Table 2 shows, participants who reported to exercise 3 times or more per week perceived the benefits of exercise significantly higher than participants exercising less than 3 times per week. Highly active participants were likely to score an average 0.39 higher on the likert scale than Low activity level participants for the perceived benefits of exercise. As well as this, participants categorized as having High activity levels perceived the barriers to exercise significantly lower than participants who exercised less
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than 3 times per week. Highly active participants were likely to score an average 0.52 lower on the likert scale than Low activity level participants for the perceived barriers of exercise.
In order to compare and observe significant differences between the two independent groups, non-Taiwanese and Taiwanese adults, with regards to perceived benefits, perceived barriers and early influences to exercise, two-sample independent t-tests were run on individual perceived benefit items, individual perceived barrier items, individual early influences items, as well as overall means scores for the benefits scale and overall mean scores for the barriers scale. In order to obtain the t-value, the formula for the two-sample t-test is:
𝑡 = 𝑥̅1− 𝑥̅2
√𝑠2(1 𝑛1+ 1
𝑛2)
Where 𝑥̅1is the mean of non-Taiwanese adults and 𝑥̅2 is the mean of Taiwanese adults. The denominator is the standard error of difference, which is the combined standard error of the non-Taiwanese and Taiwanese adults (Mendenhall and Beaver, 2012, p. 397).
As well as the two-sample t-tests, Wilcoxon rank-sum tests, equivalent to the Mann Whitney U-Test, were run on individual items as well as the overall benefits and barriers scales, in order to observe differences in the ranked positions of answers between non-Taiwanese and Taiwanese adults. The Wilcoxon rank-sum test is an alternative nonparametric test to the t-test.
The Wilcoxon rank-sum test is used when the data is ordinal and the distribution is non-normal.
As the data is Likert scale data (with 1 equating to Strongly Disagree up to 5 equating to Strongly Agree) it can be treated as ranked ordinal data. The distribution of answers on our Likert scale were non-normal for most items. The Wilcoxon rank-sum test calculates the rank of each value on the Likert scale. The null hypothesis of the test is that the two samples (non-Taiwanese and (non-Taiwanese adults) should have the same median. The test statistic for the the Wilcoxon rank-sum test is the z-statistic. The formula is as follows:
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𝑧 =𝑇1−𝑛1(𝑛1+ 𝑛2+ 1) 2
√𝑛1𝑛2(𝑛1+ 𝑛2+ 1) 12
Where n is the sample size for non-Taiwanese adults or Taiwanese adults, and 𝑇1 is the sum of the ranks for sample 1; non-Taiwanese adults (Mendenhall and Beaver, 2012, p. 639).
Although the Wilcoxon rank-sum test is recommended for when the distribution is non-normal and the data is ordinal, De Winter and Dodou (2010) stated either test can work in cases with two independent samples and five-point Likert data, as both tests will have nearly equivalent type I error rates and power. In the case of this study, any statistically significant differences between non-Taiwanese and Taiwanese adults observed by the two-sample t-test when measuring for differences in means of the benefits, barriers or early influences to exercise were also perceived to be significantly different when using the Wilcoxon rank-sum test.
Similarly, when there were no significant differences observed from the two-sample t-test, no significant differences occurred from the Wilcoxon rank-sum tests.