Statistical Technique in Review The paired or dependent samples t -test is a par

Question

Statistical Technique in Review

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:

1. The distribution of scores is normal or approximately normal.

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

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

4. The differences between the paired scores are independent.

Research Article

Source

Lindseth, G. N., Coolahan, S. E., Petros, T. V., & Lindseth, P. D. (2014). Neurobehavioral effects of aspartame consumption.Research in Nursing & Health, 37(3), 185–193.

Introduction

Despite the widespread use of the artificial sweetener aspartame in drinks and food, there are concern and controversy about the mixed research evidence on its neurobehavioral 172effects. Thus Lindseth and colleagues (2014) conducted a one-group repeated measures design to determine the neurobehavioral effects of consuming both low- and high-aspartame diets in a sample of 28 college students. “The participants served as their own controls....A random assignment of the diets was used to avoid an error of variance for possible systematic effects of order” (Lindseth et al., 2014, p. 187). “Healthy adults who consumed a study-prepared high-aspartame diet (25 mg/kg body weight/day) for 8 days and a low-aspartame diet (10 mg/kg body weight/day) for 8 days, with a 2-week washout between the diets, were examined for within-subject differences in cognition, depression, mood, and headache. Measures included weight of foods consumed containing aspartame, mood and depression scales, and cognitive tests for working memory and spatial orientation. When consuming high-aspartame diets, participants had more irritable mood, exhibited more depression, and performed worse on spatial orientation tests. Aspartame consumption did not influence working memory. Given that the higher intake level tested here was well below the maximum acceptable daily intake level of 40–50 mg/kg body weight/day, careful consideration is warranted when consuming food products that may affect neurobehavioral health” (Lindseth et al., 2014, p. 185).

Relevant Study Results

“The mean age of the study participants was 20.8 years (SD = 2.5). The average number of years of education was 13.4 (SD = 1.0), and the mean body mass index was 24.1 (SD = 3.5)....Based on Vandenberg MRT scores, spatial orientation scores were significantly better for participants after their low-aspartame intake period than after their high intake period (Table 2). Two participants had clinically significant cognitive impairment after consuming high-aspartame diets....Participants were significantly more depressed after they consumed the high-aspartame diet compared to when they consumed the low-aspartame diet (Table 2)....Only one participant reported a headache; no difference in headache incidence between high- and low-aspartame intake periods could be established” (Lindseth et al., 2014, p. 190).

TABLE 2

WITHIN-SUBJECT DIFFERENCES IN NEUROBEHAVIOR SCORES AFTER HIGH AND LOW ASPARTAME INTAKE (N = 28)

*p < .05.

**p < .01.

M = Mean; SD = Standard deviation; N.S. = Nonsignificant.

Lindseth, G. N., Coolahan, S. E., Petros, T. V., & Lindseth, P. D. (2014). Neurobehavioral effects of aspartame consumption. Research in Nursing & Health, 37(3), p. 190

1. 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?

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

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

Variable M SD Paired t-Test p Spatial orientation High-aspartame 14.1 4.2 2.4 .03* Low-aspartame 16.6 4.3 Working memory High-aspartame 730.0 152.7 1.5 N.S. Low-aspartame 761.1 201.6 Mood (irritability) High-aspartame 33.4 9.0 3.4 .002** Low-aspartame 30.5 7.3 Depression High-aspartame 36.8 7.0 3.8 .001** Low-aspartame 34.4 6.2

Explanation / Answer

Answers:

1. Assumptions for conducting a paired or dependent samples t-test in a study:

a) All the samples to be iid (identical independent distribution)

b) samples exhibit Normality

c) Homoskedasticity (equal variances) between samples

Out of these assumptions we can see that i.i.d exists in the samples. Normality can be questioned due to small sample size (n<30). We can check for Normality & Homoskedasticity using statistical tests.

2. From the result of depression for High & low-aspartame, we can conclude that there exists a significant difference between High & low-aspartame samples since p-value<0.05 so we reject H0.

3. The smallest t-value in table-2 is 1.5 which is for ‘Working memory’ test.

Yes. This t-value is insignificant since based on this the p-value is 0.145 (=T.DIST.2T(1.5,27) in excel).

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