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. Investing Essentials. Fundamental Analysis. Your Privacy Rights. To change or withdraw your consent choices for Investopedia.
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Key Takeaways Statistical significance is a determination that a relationship between two or more variables is caused by something other than chance. Statistical significance is used to provide evidence concerning the plausibility of the null hypothesis, which hypothesizes that there is nothing more than random chance at work in the data.
Statistical hypothesis testing is used to determine whether the result of a data set is statistically significant. How Is Statistical Significance Determined? Part I reviews the basics of significance testing as related to the null hypothesis and p values.
Part II shows you how to conduct a t -test, using an online calculator. Part III deal s with interpreting t -test results. Part IV is about reporting t -test results in both text and table formats and concludes with a guide to interpreting confidence intervals.
The lower the significance level, the more confident you can be in replicating your results. Significance levels most commonly used in educational research are the. If it helps, think of. These numbers and signs more on that later come from Significance Testing, which begins with the Null Hypothesis.
We start by revisiting familiar territory, the scientific method. The traditional way to test this question involves:. Step 2. Find previous research to support, refute, or suggest ways of testing the question.
Step 3. Construct a hypothesis by revising your research question:. Step 4. Test the null hypothesis. This way, you leave yourself room without having the burden of proof on your study from the beginning. This is called a sampling error , something you must contend with in any test that does not include the entire population of interest.
Redman notes that there are two main contributors to sampling error: the size of the sample and the variation in the underlying population. Sample size may be intuitive enough.
Think about flipping a coin five times versus flipping it times. Of course, showing the campaign to more people costs more, so you have to balance the need for a larger sample size with your budget. Variation is a little trickier to understand, but Redman insists that developing a sense for it is critical for all managers who use data.
Consider the images below. Each expresses a different possible distribution of customer purchases under Campaign A. In the chart on the left with less variation , most people spend roughly the same amount of dollars. Compare that to the chart on the right with more variation. Here, people vary more widely in how much they spend.
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