What is tTest?A ttest is a type of inferential statistic used to determine the significant difference between the means of two groups, which may be related to certain features. A ttest is used as a hypothesis testing tool, which allows testing an assumption applicable to a population. A ttest looks at the tstatistic, the tdistribution values, and the degrees of freedom to determine the statistical significance. A ttest allows us to compare the two data sets' average values and determine if they came from the same population. For example, if we take a sample of students from class A and another sample of students from class B, we don't get the same mean and standard deviation. Similarly, samples taken from the placebofed control group and those taken from the drug prescribed group should have a slightly different mean and standard deviation. Mathematically, the ttest takes a sample from each of the two sets and establishes the problem statement by assuming a null hypothesis that the two means are equal. Based on the applicable formulas, certain values are calculated and compared against the standard values, and the assumed null hypothesis is accepted or rejected. If the null hypothesis qualifies for rejection, it indicates that data readings are strong and not due to chance. The ttest is just one of many tests used for this purpose. Statisticians must additionally use tests other than the ttest to examine more variables and tests with larger sample sizes. Statisticians use a ztest for a large sample size. Other testing options include the chisquare test and the ftest. TTest Assumptions
When to Use a TTest?A ttest is only used when comparing the means of two groups' also known as a pairwise comparison. If you want to compare more than two groups or make multiple pairwise comparisons, use an ANOVA test or a posthoc test. The ttest is a parametric test of difference, which means it makes the same assumptions about your data as other parametric tests.
If your data do not fit these assumptions, you can try a nonparametric alternative of the ttest, such as the Wilcoxon SignedRank test for data with unequal variances. Types of TTestsThere are three types of ttests we can perform based on the data, such as: 1. OneSample ttest In a onesample ttest, we compare the average of one group against the set average. This set average can be any theoretical value, or it can be the population mean. In a nutshell, here's the formula to calculate or perform a onesample ttest: Where,
Note: As mentioned earlier in the assumptions, a large sample size should be taken for the data to approach a normal distribution. Although ttest is essential for small samples as their distributions are nonnormal.2. Unpaired or Independent ttest The unpaired ttest is used to compare the means of two different groups of samples. For example, we want to compare the male employees' average height to their average height. Of course, the number of males and females should be equal for this comparison. This is where an unpaired or independent ttest is used. Here's the formula to calculate the tstatistic for a twosample ttest: Where,
Here, the degree of freedom is n_{A} + n_{B}  2. We will follow the same logic we saw in a onesample ttest to check if one group's average is significantly different from another group. That's right  we will compare the calculated tstatistic with the tcritical value. 3. Paired ttest The paired sample ttest is quite intriguing. Here, we measure one group at two different times. We compare different means for a group at two different times or under two different conditions. A certain manager realized that the productivity level of his employees was trending significantly downwards. This manager decided to conduct a training program for all his employees to increase their productivity levels. The formula to calculate the tstatistic for a paired ttest is: Where,
Calculating TTestsCalculating a ttest requires three key data values. They include the difference between the mean values from each data set called the mean difference, the standard deviation of each group, and the number of data values of each group. The outcome of the ttest produces the tvalue. This calculated tvalue is then compared against a value obtained from a critical value table called the TDistribution Table. This comparison helps determine the effect of chance alone on the difference and whether it is outside that chance range. The ttest questions whether the difference between the groups represents a true difference in the study or possibly a meaningless random difference.
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