Why t test

But because your sample was too small, or because extraneous variation in your study was not properly accounted for, your study wasn't able to demonstrate statistical significance. You're on safer ground saying something like " Our study did not find evidence of a statistically significant difference. Now, if you're still with me, you might be asking, but why is it called a t -test? And where does the p-value come from?

You haven't explained any of that! Note: To find out more about how the p-values are calculated for a t-test, see this follow-up post.

Minitab Blog. What Is a t-test? Minitab Blog Editor 10 June, A t-test is one of the most frequently used procedures in statistics. Anatomy of a t-test A t-test is commonly used to determine whether the mean of a population significantly differs from a specific value called the hypothesized mean or from the mean of another population. The t-Value: The Ratio of Signal to Noise As the above formula shows, the t-value simply compares the strength of the signal the difference to the amount of noise the variation in the data.

Statistically Significant Messages So how is the t-test like telling a teenager to clean up the mess in the kitchen? Similarly, if your t-test results don't achieve statistical significance, it could be for any of the following reasons: The difference signal isn't large enough. In other words, a t test is used when we wish to compare two means the scores must be measured on an interval or ratio measurement scale.

We would use a t test if we wished to compare the reading achievement of boys and girls. With a t test, we have one independent variable and one dependent variable. The independent variable gender in this case can only have two levels male and female. The dependent variable would be reading achievement. The test statistic that a t test produces is a t -value. Conceptually, t -values are an extension of z -scores. In a way, the t -value represents how many standard units the means of the two groups are apart.

With a t tes t, the researcher wants to state with some degree of confidence that the obtained difference between the means of the sample groups is too great to be a chance event and that some difference also exists in the population from which the sample was drawn. If our t test produces a t -value that results in a probability of. We could say that it is unlikely that our results occurred by chance and the difference we found in the sample probably exists in the populations from which it was drawn.

This is concerned with the difference between the average scores of a single sample of individuals who are assessed at two different times such as before treatment and after treatment. It can also compare average scores of samples of individuals who are paired in some way such as siblings, mothers, daughters, persons who are matched in terms of a particular characteristics.

Note: The F-Max test can be substituted for the Levene test. The t test Excel spreadsheet that I created for our class uses the F -Max. A bit of history… William Sealy Gosset first published a t-test. Develop and improve products. List of Partners vendors. A t-test is a type of inferential statistic used to determine if there is a significant difference between the means of two groups, which may be related in certain features. It is mostly used when the data sets, like the data set recorded as the outcome from flipping a coin times, would follow a normal distribution and may have unknown variances.

A t-test is used as a hypothesis testing tool, which allows testing of an assumption applicable to a population. A t-test looks at the t-statistic, the t-distribution values, and the degrees of freedom to determine the statistical significance. To conduct a test with three or more means, one must use an analysis of variance. Essentially, a t-test allows us to compare the average values of the two data sets and determine if they came from the same population.

In the above examples, if we were to take a sample of students from class A and another sample of students from class B, we would not expect them to have exactly the same mean and standard deviation.

Similarly, samples taken from the placebo-fed control group and those taken from the drug prescribed group should have a slightly different mean and standard deviation. Mathematically, the t-test 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 accordingly.

If the null hypothesis qualifies to be rejected, it indicates that data readings are strong and are probably not due to chance. The t-test is just one of many tests used for this purpose. Statisticians must additionally use tests other than the t-test to examine more variables and tests with larger sample sizes. For a large sample size, statisticians use a z-test. Other testing options include the chi-square test and the f-test. There are three types of t-tests, and they are categorized as dependent and independent t-tests.

Consider that a drug manufacturer wants to test a newly invented medicine. It follows the standard procedure of trying the drug on one group of patients and giving a placebo to another group, called the control group. The placebo given to the control group is a substance of no intended therapeutic value and serves as a benchmark to measure how the other group, which is given the actual drug, responds. After the drug trial, the members of the placebo-fed control group reported an increase in average life expectancy of three years, while the members of the group who are prescribed the new drug report an increase in average life expectancy of four years.

Instant observation may indicate that the drug is indeed working as the results are better for the group using the drug. However, it is also possible that the observation may be due to a chance occurrence, especially a surprising piece of luck.

A t-test is useful to conclude if the results are actually correct and applicable to the entire population. While the average of class B is better than that of class A, it may not be correct to jump to the conclusion that the overall performance of students in class B is better than that of students in class A. This is because there is natural variability in the test scores in both classes, so the difference could be due to chance alone. A t-test can help to determine whether one class fared better than the other.

Calculating a t-test 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 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.

Revised on December 14, A t-test is a statistical test that is used to compare the means of two groups. It is often used in hypothesis testing to determine whether a process or treatment actually has an effect on the population of interest, or whether two groups are different from one another. You want to know whether the mean petal length of iris flowers differs according to their species. You find two different species of irises growing in a garden and measure 25 petals of each species.

You can test the difference between these two groups using a t-test. 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.

See an example. 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.