Type I errors
The conduct of multiple t-tests causes an increased risk for Type I errors. If only one t-test is conducted on study data, the risk of Type I error does not increase. The Bonferroni procedure and the more stringent Tukey’s honestly significant difference (HSD), Student Newman-Keuls, or Scheffé test can be calculated to reduce the risk of a Type I error (Plichta & Kelvin, 2013; Zar, 2010).
7. The Bonferroni procedure is calculated by alpha ÷ number of t-tests conducted on study variables’ data. Note that researchers do not always report all t-tests conducted, especially if they were not statistically significant. The t-tests conducted on demographic data are not of concern. Canbulat et al. reported the results of four t-tests conducted to examine differences between the intervention and control groups for the dependent variables procedural self-reported pain with WBFS, procedural self-reported pain with VAS, parent-reported anxiety levels, and observer-reported anxiety levels. The Bonferroni calculation for this study: 0.05 (alpha) ÷ number of t-tests conducted = 0.05 ÷ 4 = 0.0125. The new α set for the study is 0.0125.
9. The intervention and control groups were examined for differences related to the demographic variables gender, age, and BMI and the dependent variable preprocedural anxiety that might have affected the procedural pain and anxiety posttest levels in the children 7 to 12 years old. These nonsignificant results indicate the intervention and control groups were similar or equivalent for these variables at the beginning of the study. Thus, Canbulat et al. (2015) can conclude the significant differences found between the two groups for procedural pain and anxiety levels were probably due to the effects of the intervention rather than sampling error or initial group differences.
10. No, the independent samples t-test would not have been appropriate to analyze the differences in gender between the Buzzy intervention and control groups. The demographic variable gender is measured at the nominal level or categories of females and males. Thus, the χ2 test is the appropriate statistic for analyzing gender data (see Exercise 19). In contrast, the t-test is appropriate for analyzing data for the demographic variables age and BMI measured at the ratio level.
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1. What do degrees of freedom (df) mean? Canbulat et al. (2015) did not provide the dfs in their study. Why is it important to know the df for a t ratio? Using the df formula, calculate the df for this study.
2. What are the means and standard deviations (SDs) for age for the Buzzy intervention and control groups? What statistical analysis is conducted to determine the difference in means for age for the two groups? Was this an appropriate analysis technique? Provide a rationale for your answer.
6. What is the null hypothesis for procedural self-reported pain measured with the Wong Baker Faces Scale (WBFS) for the two groups? Was this null hypothesis accepted or rejected in this study? Provide a rationale for your answer.
9. In your opinion, is it an expected or unexpected finding that both t values on Table 2 were found to be statistically significant. Provide a rationale for your answer.
The paired or dependent samples t-test is a parametric statistical procedure calculated to determine differences between two sets of repeated measures data from one group of people. The scores used in the analysis might be obtained from the same subjects under different conditions, such as the one group pretest–posttest design. With this type of design, a single group of subjects experiences the pretest, treatment, and posttest. Subjects are referred to as serving as their own control during the pretest, which is then compared with the posttest scores following the treatment. Paired scores also result from a one-group repeated measures design, where one group of participants is exposed to different levels of an intervention. For example, one group of participants might be exposed to two different doses of a medication and the outcomes for each participant for each dose of medication are measured, resulting in paired scores. The one group design is considered a weak quasi-experimental design because it is difficult to determine the effects of a treatment without a comparison to a separate control group (Shadish, Cook, & Campbell, 2002).
A less common type of paired groups is when the groups are matched as part of the design to ensure similarities between the two groups and thus reduce the effect of extraneous variables (Grove, Burns, & Gray, 2013; Shadish et al., 2002). For example, two groups might be matched on demographic variables such as gender, age, and severity of illness to reduce the extraneous effects of these variables on the study results. The assumptions for the paired samples t-test are as follows: