The outcome of the t-test produces the t-value. This calculated t-value is then compared against a value obtained from a critical value table called the T-Distribution Table. This comparison helps to determine the effect of chance alone on the difference, and whether the difference is outside that chance range.
The t-test questions whether the difference between the groups represents a true difference in the study or if it is possibly a meaningless random difference. The T-Distribution Table is available in one-tail and two-tails formats. The former is used for assessing cases which have a fixed value or range with a clear direction positive or negative.
For instance, what is the probability of output value remaining below -3, or getting more than seven when rolling a pair of dice? The calculations can be performed with standard software programs that support the necessary statistical functions, like those found in MS Excel.
The t-test produces two values as its output: t-value and degrees of freedom. The t-value is a ratio of the difference between the mean of the two sample sets and the variation that exists within the sample sets. While the numerator value the difference between the mean of the two sample sets is straightforward to calculate, the denominator the variation that exists within the sample sets can become a bit complicated depending upon the type of data values involved.
The denominator of the ratio is a measurement of the dispersion or variability. Higher values of the t-value, also called t-score, indicate that a large difference exists between the two sample sets. The smaller the t-value, the more similarity exists between the two sample sets.
Degrees of freedom refers to the values in a study that has the freedom to vary and are essential for assessing the importance and the validity of the null hypothesis. Computation of these values usually depends upon the number of data records available in the sample set.
The correlated t-test is performed when the samples typically consist of matched pairs of similar units, or when there are cases of repeated measures. For example, there may be instances of the same patients being tested repeatedly—before and after receiving a particular treatment.
In such cases, each patient is being used as a control sample against themselves. This method also applies to cases where the samples are related in some manner or have matching characteristics, like a comparative analysis involving children, parents or siblings. Correlated or paired t-tests are of a dependent type, as these involve cases where the two sets of samples are related. The formula for computing the t-value and degrees of freedom for a paired t-test is:.
The remaining two types belong to the independent t-tests. They include cases like a group of patients being split into two sets of 50 patients each. One of the groups becomes the control group and is given a placebo, while the other group receives the prescribed treatment. This constitutes two independent sample groups which are unpaired with each other. The equal variance t-test is used when the number of samples in each group is the same, or the variance of the two data sets is similar.
The following formula is used for calculating t-value and degrees of freedom for equal variance t-test:. The unequal variance t-test is used when the number of samples in each group is different, and the variance of the two data sets is also different. This test is also called the Welch's t-test. The following formula is used for calculating t-value and degrees of freedom for an unequal variance t-test:. The following flowchart can be used to determine which t-test should be used based on the characteristics of the sample sets.
The key items to be considered include whether the sample records are similar, the number of data records in each sample set, and the variance of each sample set. Assume that we are taking a diagonal measurement of paintings received in an art gallery.
One group of samples includes 10 paintings, while the other includes 20 paintings. The data sets, with the corresponding mean and variance values, are as follows:. Though the mean of Set 2 is higher than that of Set 1, we cannot conclude that the population corresponding to Set 2 has a higher mean than the population corresponding to Set 1.
Is the difference from We establish the problem by assuming the null hypothesis that the mean is the same between the two sample sets and conduct a t-test to test if the hypothesis is plausible. The t-value is Since the minus sign can be ignored when comparing the two t-values, the computed value is 2. The degrees of freedom value is One can specify a level of probability alpha level, level of significance, p as a criterion for acceptance.
A t -test asks the question,. Obtain two random samples of at least 30, preferably 50, from each group. Report results in text or table format see below. Note: We acknowledge that the average scores are different. With a t -test we are deciding if that difference is significant is it due to sampling error or something else? For a science CRCT score, we take several samples and compare the different means.
After a few calculations, we could determine something like. We can be fairly certain that the difference in scores will be between In text, the basic format is to report: population N , mean M and standard deviation SD for both samples, t value, degrees freedom df , significance p , and confidence interval CI. Therefore, we reject the null hypothesis that there is no difference in reading scores between teaching teams 1 and 2.
Therefore, we fail to reject the null hypothesis that there is no difference in science scores between females and males. Table 1. Note: On the Web site, this appears blocked and should not be. See the. This resource was created by Dr. Patrick Biddix Ph. Research Rundowns. Significance Testing t-tests.
What is Statistical Significance? The traditional way to test this question involves: Step 1. Develop a research question. Alternate Step 4. We find no relationship between A and B. Table of contents When to use a t-test What type of t-test should I use? Performing a t-test Interpreting test results Presenting the results of a t-test Frequently asked questions about t-tests.
A t-test can only be used when comparing the means of two groups a. If you want to compare more than two groups, or if you want to do multiple pairwise comparisons, use an ANOVA test or a post-hoc test. The t-test is a parametric test of difference, meaning that it makes the same assumptions about your data as other parametric tests.
The t-test assumes your data:. If your data do not fit these assumptions, you can try a nonparametric alternative to the t-test, such as the Wilcoxon Signed-Rank test for data with unequal variances. When choosing a t-test, you will need to consider two things: whether the groups being compared come from a single population or two different populations, and whether you want to test the difference in a specific direction.
Scribbr Plagiarism Checker. The t-test estimates the true difference between two group means using the ratio of the difference in group means over the pooled standard error of both groups.
You can calculate it manually using a formula, or use statistical analysis software. In this formula, t is the t-value, x 1 and x 2 are the means of the two groups being compared, s 2 is the pooled standard error of the two groups, and n 1 and n 2 are the number of observations in each of the groups.
A larger t -value shows that the difference between group means is greater than the pooled standard error, indicating a more significant difference between the groups. You can compare your calculated t -value against the values in a critical value chart to determine whether your t -value is greater than what would be expected by chance.
If so, you can reject the null hypothesis and conclude that the two groups are in fact different. This built-in function will take your raw data and calculate the t -value.
It will then compare it to the critical value, and calculate a p -value. This way you can quickly see whether your groups are statistically different. In your comparison of flower petal lengths, you decide to perform your t-test using R. The code looks like this:. Sample data set. If you perform the t-test for your flower hypothesis in R, you will receive the following output:.
When reporting your t-test results, the most important values to include are the t -value , the p -value , and the degrees of freedom for the test. These will communicate to your audience whether the difference between the two groups is statistically significant a.
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