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. 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.
In statistical tests, statistical significance is determined by citing an alpha level, or the probability of rejecting the null hypothesis when the null hypothesis is true.
For this example, alpha, or significance level, is set to 0. The sample mean 75 , the sample standard deviation 9. Assume the average height of students in the school is 69 inches:. The calculated t-value can be used to test the original hypotheses and determine statistical significance.
When to perform a statistical test Choosing a parametric test: regression, comparison, or correlation Choosing a nonparametric test Flowchart: choosing a statistical test Frequently asked questions about statistical tests.
Statistical tests work by calculating a test statistic — a number that describes how much the relationship between variables in your test differs from the null hypothesis of no relationship. It then calculates a p -value probability value. The p -value estimates how likely it is that you would see the difference described by the test statistic if the null hypothesis of no relationship were true. If the value of the test statistic is more extreme than the statistic calculated from the null hypothesis, then you can infer a statistically significant relationship between the predictor and outcome variables.
If the value of the test statistic is less extreme than the one calculated from the null hypothesis, then you can infer no statistically significant relationship between the predictor and outcome variables. You can perform statistical tests on data that have been collected in a statistically valid manner — either through an experiment , or through observations made using probability sampling methods.
For a statistical test to be valid , your sample size needs to be large enough to approximate the true distribution of the population being studied. If your data do not meet the assumptions of normality or homogeneity of variance, you may be able to perform a nonparametric statistical test , which allows you to make comparisons without any assumptions about the data distribution.
If your data do not meet the assumption of independence of observations, you may be able to use a test that accounts for structure in your data repeated-measures tests or tests that include blocking variables.
The types of variables you have usually determine what type of statistical test you can use. Quantitative variables represent amounts of things e. Types of quantitative variables include:. Categorical variables represent groupings of things e. Types of categorical variables include:. Choose the test that fits the types of predictor and outcome variables you have collected if you are doing an experiment , these are the independent and dependent variables.
Consult the tables below to see which test best matches your variables. Scribbr Plagiarism Checker. Parametric tests usually have stricter requirements than nonparametric tests, and are able to make stronger inferences from the data. They can only be conducted with data that adheres to the common assumptions of statistical tests. The most common types of parametric test include regression tests, comparison tests, and correlation tests.
Regression tests look for cause-and-effect relationships. They can be used to estimate the effect of one or more continuous variables on another variable.
Comparison tests look for differences among group means. They can be used to test the effect of a categorical variable on the mean value of some other characteristic. T-tests are used when comparing the means of precisely two groups e. Correlation tests check whether variables are related without hypothesizing a cause-and-effect relationship.
These can be used to test whether two variables you want to use in for example a multiple regression test are autocorrelated. This flowchart helps you choose among parametric tests.
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