# Understanding Independent Samples t-Test

EXERCISE 16
Understanding Independent Samples t-Test

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.

Degrees of freedom “are the number of independent pieces of information that are free to vary in order to estimate another piece of information” (Grove & Cipher, 2017, p.297). Knowing the df for a t ratio is important in comparing the distribution of critical values from a study.

Formula: df = (# of subjects in sample 1 + # of subjects in sample 2)-2.

Buzzy (88) + Control (88)-2= 174

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.

The means and standard deviations (SDs) for age are

Buzzy Control

(Mean ± SD) 8.25 ± 1.51 8.61 ± 1.69

The t-test was the analysis use to determine the difference in means for age between the two groups and it was appropriate because it uses the ratio level.

What are the t value and p value for age? What do these results mean?

The t value and the p value for age are -1.498 and 0.136 respectively. These results mean that there is no significant difference between the 2 groups tested since the p=0.136, which is greater than the set level of significance (α) that was set at 0.05 “the two groups need to be similar for demographic variables to decrease the potential for error and increase the likelihood that the results are an accurate reflection of reality” (Grove & Cipher, 2017, p.166).

What are the assumptions for conducting the independent samples t-test?

Grove & Cipher (2017, p.161-162) mentioned the following assumptions for conducting independent samples t-test as follows:

The raw scores in the population are normally distributed

The dependent variable(s) is (are) measured at the interval or ratio levels.

The two groups examined have equal variance

All scores or observations collected within each group are independent

Are the groups in this study independent or dependent? Provide a rationale for your answer.

They are independent as mentioned above as one of the assumptions that “all scores or observations collected within each group are independent or not related to other study scores or observations” (p.162).

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.

According to the t-value and the p-value reported from procedural self-reported pain with WBFS as -6.498 and 0.000 respectively, and from this study there is no difference between the Buzzy and the Control groups hence the null hypothesis was rejected.

Should a Bonferroni procedure be conducted in this study? Provide a rationale for your answer.

“The Bonferroni procedure is a simple calculation in which the alpha is divided by the number of t-tests conducted on different aspects of the study data” (Grove & Cipher, 2017, p.161). Yes the Bonferroni procedure should be conducted to reduce the risk of a Type 1 error due to multiple t-tests.

What variable has a result of t = −6.135, p = 0.000? What does this result mean?

The variable that has a result of t = −6.135, p = 0.000 is Procedural Child Anxiety as reported by the parent. The t value is statistically significant as indicated by the p=0.000, which is less than the set alpha level of 0.05 from the study, which means there is a significant difference between the two groups (Grove & Cipher, 2017, p.166).

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.

Yes I think it is an expected finding because the tables show that the different interventions brought different experiences during peripheral IV cannulation, just as differences are expected when testing for effectiveness of interferences.

Describe one potential clinical benefit for pediatric patients to receive the Buzzy intervention that combined cold and vibration during IV insertion.

From the study, the potential clinical benefit for pediatric patients receiving the Buzzy intervention is to decrease pain and anxiety during peripheral IV insertion. Another benefit would be as a result of decreased pain and anxiety which will lead to building trusting relationships between the patients and the caregivers.

EXERCISE 17
Understanding Paired or Dependent Samples t-Test

What are the assumptions for conducting a paired or dependent samples t-test in a study? Which of these assumptions do you think were met by the Lindseth et al. (2014) study?

Grove & & Cipher (2017) listed the following as assumptions on p. 171 for the paired samples t-test as follows:

The distribution of scores is normal or approximately normal

The dependent variable(s) is (are) measured at interval or ratio levels

Repeated measures data are collected from one group of subjects, resulting in paired scores.

The differences between the paired scores are independent.

All these assumptions were met by the Lindseth et al. (2014) study.

In the introduction, Lindseth et al. (2014) described a “2-week washout between diets.” What does this mean? Why is this important?

A “2-week washout between diets” means the changing of participants from one diet to another without them having knowledge of which diet they might be on. Its importance is that the random assignment of the diets helps “to avoid an error of variance for possible systemic effects of order” (Grove & & Cipher, 2017, p. 172)

What is the paired t-test value for mood (irritability) between the participants’ consumption of high- versus low-aspartame diets? Is the result statistically significant? Provide a rationale for your answer.

The paired t-test value is 3.4 and yes the result is significant because the provided p=0.002 which is less than the * p < .05 as indicated at the bottom of Table 2.

State the null hypothesis for mood (irritability) that was tested in this study. Was this hypothesis accepted or rejected? Provide a rationale for your answer.

The null hypothesis for mood (irritability) is that there was no significant difference in the group that consumed a low-aspartame diet as compared to those who consumed a high-aspartame diet. The significance found was only p=0.002 which was less than the set ** p < 0.01, hence rejected.

Which t value in Table 2 represents the greatest relative or standardized difference between the high- and low-aspartame diets? Is this t value statistically significant? Provide a rationale for your answer.

The greatest t value is 3.8. Statistically it is significant as shown by the p=0.001 and the set ** p < 0.01

Discuss why the larger t values are more likely to be statistically significant.

Grove & & Cipher (2017) state that “when interpreting the results of t-tests, the larger the calculated t ratio, in absolute value, the greater the difference between the two groups” (p.161). The p value is what determines how strong or weak the significance of a test is influencing the status of whether to be accepted or rejected.

Discuss the meaning of the results regarding depression for this study. What is the clinical importance of this result?

The narrative part of the study shows that the consumption of high-aspartame diet led to more depression, and the t-value is 3.8 which was significant hence important because Grove & & Cipher (2017) points out that “given the higher intake level tested here was well below the maximum acceptable daily intake level of 40-50mg/kg body weight/day, careful consideration is warranted when consuming food products that may affect neurobehavioral health” (p.172).

What is the smallest, paired t-test value in Table 2? Why do you think the smaller t values are not statistically significant?

The smallest paired t-test is 1.5 under working memory. Smaller t values indicate that the differences between the tested groups were very minimal if any.

Discuss the statistical and clinical importance of these study results about the consumption of aspartame. Document your answer with a relevant source.

The importance of these study results is that they showed how differently the groups were affected by the consumption of aspartame by comparing two diets as indicated by Grove & & Cipher (2017) “given the higher intake level tested here was well below the maximum acceptable daily intake level of 40-50mg/kg body weight/day, careful consideration is warranted when consuming food products that may affect neurobehavioral health” (p.172).

Are these study findings related to the consumption of high- and low-aspartame diets ready for implementation in practice? Provide a rationale for your answer.

Well, I don’t think these diets are ready for implementation even though it is informative because the size of the sample study was small (N=28) which increases the risk of creating Type II error. Grove & & Cipher (2017) states that;

Longitudinal studies to examine the effects of aspartame over more than 8 days are needed. Future research needs to examine the length of washout period needed between the different levels of aspartame diets. Researchers also need to examine the measurement methods to ensure they have strong validity and reliability” (p.176)

References

Grove, S. K., & Cipher, D. J. (2017). Statistics for nursing research: A workbook for evidence-based practice (2nd ed.). St. Louis, MI.