Essay on Independent Samples T-Test

The two-sample t-test, also known as Independent Samples t Test is a parametric test used to find out if a difference in means between two independent groups exists (Beatty, 2016). Comparison of means of two independent groups helps researchers to establish whether a statistical evidence exists that the group means are significantly different. For this type of analysis to be conducted, the data must meet certain requirements. First, the dependent variable must be continuous, either at interval or ratio level while the independent variable must be categorical (usually two groups). Secondly, there must exist independence of observations. That is, there should be no association between the participants in each of the groups. Thirdly, the dependent variable should be normally distributed for each of the groups because non-normal distributions are associated with decreased power of the test. Lastly, there must be homogeneity of variances in all groups so as to obtained a reliable p-value (McKenzie, Powell, & Usher, 2005).

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Table 1 below shows data obtained following the assessment of oxygen levels in patients by a drug company. The patients oxygen levels were measured after the patients were administered a test medication. To determine whether there is a difference in oxygenation levels between group 1, which was given the medication, and group 2, which did not receive the medication, a two-tailed two-Sample t-test analysis assuming equal variances was conducted in excel. In this statistical analysis, the p-value was set at .05. Table 2 below shows the results obtained from this analysis.

A 2-sample Students t-test is used to test the null hypothesis that there exist no differences between the population means of the two groups being examined. This type of t-test is based on the assumption that the variances of the data found in the two groups are equal. In this analysis, the null hypothesis was: There is no statistically significant between patients oxygenation levels in group 1 and group 2.

In Table 2 below, it can be seen that the calculated absolute value of t (also known as tStat is .898. When a comparison of tStat value and t Critical two-tail value is made, it is realized that t Critical two-tail value is smaller (0.38). These values are based on a value of 0.05 (two-sided) and 16 df. Because |tcalc| > tcrit (.898 > .38), the null hypothesis is rejected at the 95% confidence level [100% (1 - a)]. Thus, patients oxygenation levels mean in group 1 and group 2 are statistically different at the 95% level of confidence.

The p-value of .38 obtained is useful in deciding whether a difference between the means of group 1 and group 2 exist. The p-value shows the probability that the difference between the means of the two groups is at least as large as what has been seen, given the assumption that both means are equal. Because the p-value obtained is smaller, it is a strong indicator that the two groups have different means.

Table 1

Group 1 Group 2

2 1

3 2

3 2

4 3

4 4

7 4

8 5

9 5

6

8

Table 1: Group 1 and group 2 patients oxygen levels data

Table 2

Group 1 Group 2

Mean 5 4

Variance 6.88 4.44

Observations 8 10

Pooled Variance 5.5

Hypothesized Mean Difference 0

df 16

t Stat 0.898

P(T<=t) two-tail 0.38

t Critical two-tail 2.12

Table 2: t-test: two-sample assuming equal variances results

References

Beatty, C. F. (2016). Community Oral Health Practice for the Dental Hygienist. Elsevier Health Sciences.

McKenzie, G., Powell, J., & Usher, R. (2005). Understanding Social Research: Perspectives on Methodology and Practice. Routledge.