![]() ![]() ρ> 0(< 0), the variance of the mean difference is smaller (larger) than that in the case of independent samples. For the matched-pair data, if two observations within the same pair are positively (negatively) correlated, i.e. One of the differences is their variances, which can be easily seen from (1) and (3). From the above we know that the formulas to calculate the sample mean difference are always the same, which equals the sample mean of the treatment group minus the sample mean of the control group. ![]() To simplify our discussion, we assume n 0 = n 1 = n. We discuss the difference between independent samples and matched-pair samples based on the sample mean difference. The conclusion and discussion are reported in Section 5.Ģ.3 The difference between independent samples and matched-pair samples In section 4, we present three examples to explain the calculation process of the independent t-test in independent samples, and paired t-test in the time related samples and the matched samples, respectively. We discuss the differences and similarities of these two t-tests in Sections 3. Section 2 illustrates the data structure for two-independent samples and the matched pair samples. We take a close look at the differences and similarities between independent t-test and paired t-test. This paper aims to clarify some confusion surrounding use of t-tests in data analysis. ![]() ![]() When the objects in one sample are all measured twice (as is common in “before and after” comparisons), when the objects are related somehow (for example, if twins, siblings, or spouses are being compared), or when the objects are deliberately matched by the experimenters and have similar characteristics, dependence occurs. On the other hand, if the observations in the first sample are coupled with some particular observations in the other sample, the samples are considered to be paired. In this case, two-sample t-test should be applied to compare the mean values of two samples. Two samples could be considered independent if the selection of the individuals or objects that make up one sample does not influence the selection of the individuals or subjects in the other sample in any way. In some cases, the independence can be easily identified from the data generating procedure. If not, what’s the reason for correlation? According to Kirkwood: ‘When comparing two populations, it is important to pay attention to whether the data sample from the populations are two independent samples or are, in fact, one sample of related pairs (paired samples)’. The reason for this confusion revolves around whether we should regard two samples as independent (marginally) or not. Although this fact is well documented in statistical literature, confusion exists with regard to the use of these two test methods, resulting in their inappropriate use. If the data is normally distributed, the two-sample t-test (for two independent groups) and the paired t-test (for matched samples) are probably the most widely used methods in statistics for the comparison of differences between two samples. If the outcome data are continuous variables (such as blood pressure), the researchers may want to know whether there is a significant difference in the mean values between the two groups. The statistical methods used in the data analysis depend on the type of outcome. In clinical research, we usually compare the results of two treatment groups (experimental and control). ![]()
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