Which t test to do

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. Comparing this value against the computed value of 2. Therefore, it is safe to reject the null hypothesis that there is no difference between means. The population set has intrinsic differences, and they are not by chance.

Financial Ratios. Tools for Fundamental Analysis. Portfolio Management. 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. He worked at the Guiness Brewery in Dublin and published under the name Student. The test was called Studen t Test later shortened to t test.

I have created an Excel Spreadsheet that does a very nice job of calculating t values and other pertinent information. UConn A-Z. A PowerPoint presentation on t tests has been created for your use. Other factors being equal, the greater the difference between the two means, the greater the likelihood that a statistically significant mean difference exists. If the means of the two groups are far apart, we can be fairly confident that there is a real difference between them.

How much overlap is there between the groups? Originally for Statistics , by Phil Spector. One of the most common tests in statistics is the t-test, used to determine whether the means of two groups are equal to each other.

The assumption for the test is that both groups are sampled from normal distributions with equal variances. The null hypothesis is that the two means are equal, and the alternative is that they are not. There is also a widely used modification of the t-test, known as Welch's t-test that adjusts the number of degrees of freedom when the variances are thought not to be equal to each other. Before we can explore the test much further, we need to find an easy way to calculate the t-statistic.

The function t. Let's test it out on a simple example, using data simulated from a normal distribution. Before we can use this function in a simulation, we need to find out how to extract the t-statistic or some other quantity of interest from the output of the t. For this function, the R help page has a detailed list of what the object returned by the function contains. A general method for a situation like this is to use the class and names functions to find where the quantity of interest is.

In addition, for some hypothesis tests, you may need to pass the object from the hypothesis test to the summary function and examine its contents. For t. The value we want is named " statistic ". To extract it, we can use the dollar sign notation, or double square brackets:.

Of course, just one value doesn't let us do very much - we need to generate many such statistics before we can look at their properties. In R, the replicate function makes this very simple. The first argument to replicate is the number of samples you want, and the second argument is an expression not a function name or definition! To generate t-statistics from testing two groups of 10 standard random normal numbers, we can use:.

The null hypothesis H 0 is that the true difference between these group means is zero. The alternate hypothesis H a is that the true difference is different from zero. In your test of whether petal length differs by species: Your observations come from two separate populations separate species , so you perform a two-sample t-test. Receive feedback on language, structure and layout Professional editors proofread and edit your paper by focusing on: Academic style Vague sentences Grammar Style consistency See an example.

From the output table, we can see that the difference in means for our sample data is Our p -value of 2. What is a t-test? What does a t-test measure? Which t-test should I use? What is the difference between a one-sample t-test and a paired t-test?

Can I use a t-test to measure the difference among several groups? Is this article helpful? Rebecca Bevans Rebecca is working on her PhD in soil ecology and spends her free time writing. She's very happy to be able to nerd out about statistics with all of you.

Other students also liked. Statistical tests: which one should you use? Your choice of statistical test depends on the types of variables you're dealing with and whether your data meets certain assumptions. A step-by-step guide to hypothesis testing Hypothesis testing is a formal procedure for investigating our ideas about the world.