A single-sample t-test is a hypothesis test that compares a sample from which the data was collected to a population where the mean is known but the standard deviation is unknown. It is used when the statistician wants to know if a sample comes from a given population yet the full population information is unknown. It is used only for sample mean tests. The hypothesis takes different forms depending on whether it is directional or non-directional.
The one sample t-test is used when data is collected on a single sample that is drawn from a given population. In this case, there is a group of subjects where data is collected from them and the sample statistics are compared to the population mean. The population parameters indicate what is expected if the sample is drawn from it. A substantial difference in the sample statistics beyond the expected from the sampling error indicates that the sample was drawn from another population. The one sample t-test allows comparison of the mean which is calculated from a set of scores to a known population mean.
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There are two hypotheses in a single sample t-test. The alternate hypothesis assumes that there are differences in the assumed mean and the values to be compared. The null hypothesis, on the other hand, assumes that no differences exist. The goal of a single sample t-test is to establish whether the null hypothesis should be rejected.
The one sample t-test can be used to estimate the standard deviation of the population using sample data. It requires that such data be numeric as well as continuous because it is based on the normal distribution. A psychologist can use single sample t-test to determine the statistical differences in a sample mean and a hypothesized value of the population mean. It can also be used to determine the statistical differences in the sample mean and the midpoints of the test variables. It also gives the statistical differences in the sample mean of a variable and chance by first determining the chance level of a test variable. It also establishes the statistical differences in a change score and zero.
