Like the normal distribution, the t- distribution is symmetric. If you think about folding it in half at the mean, each side will be the same. Like a standard normal distribution or z-distribution , the t- distribution has a mean of zero.
The normal distribution assumes that the population standard deviation is known. The t- distribution does not make this assumption. The t- distribution is defined by the degrees of freedom. These are related to the sample size. The t- distribution is most useful for small sample sizes, when the population standard deviation is not known, or both.
As the sample size increases, the t- distribution becomes more similar to a normal distribution. All of the distributions have a smooth shape. All are symmetric. All have a mean of zero.
Tails for hypotheses tests and the t -distribution When you perform a t -test, you check if your test statistic is a more extreme value than expected from the t- distribution. How to use a t- table Most people use software to perform the calculations needed for t -tests. Identify if the table is for two-tailed or one-tailed tests. Then, decide if you have a one-tailed or a two-tailed test.
The columns for a t- table identify different alpha levels. If you have a table for a one-tailed test, you can still use it for a two-tailed test. Identify the degrees of freedom for your data. The standard deviation of the population is estimated by dividing the standard deviation of the sample by the square root of the population size.
On the other hand, the z-test is the hypothesis test that ascertains if the averages of two sets of data differ from each other being given the variance or standard deviation.
The z-test is a univariate test that is based on the standard normal distribution. While the two statistical methods are commonly involved in the analysis of data, they largely differ from their application, formulae structure, and assumptions amongst other differences. The following are the key differences between the t-test and the z-test of the hypothesis. Both the t-test and z-test employ the use of distributions to compare values and reach conclusions in the testing of the hypothesis.
However, the two tests use different distribution types. Notably, the t-test is based on the Student t-distribution. On the other hand, the z-test is based on Normal distribution. While using both the t-test and z-test in the testing of the hypothesis, the population variance plays a major role in obtaining both the t-score and z-score.
While the population variance in the z-test is known, the population variance in the t-test is unknown. However, with the t-score calculation dependent on the population variance, we can always estimate the population variance given the standard deviation or variance of the sample mean and sample size. Notably, the population standard deviation is estimated from dividing the sample population standard deviation by the square root of the sample size.
While sample sizes differ from analysis to another, there is a suitable test of hypothesis for any sample size. Notably, the z-test is used in hypothesis testing when the sample size is large. On the other hand, the t-test is used in hypothesis testing when the sample size is small.
While conducting either the t-test or z-test, some assumptions are held by statisticians. Notably, in a t-test, all data points are assumed, not dependent. Sample values to be used in the test of a hypothesis are to be taken as well as recorded accurately.
We assume that ability measured by these three items is the same and it is normally distributed,. The score for each student in a class is used to calculate the mean of marks which is equal to 50 and a standard deviation of We can interpret that student score is 0 distance in units of standard deviations from the mean, so the student has scored average.
We can interpret that the student has scored above average — a distance of 1 standard deviation above the mean. Both Z score vs T score is part of hypothesis testing under the normal distribution. If you have a set of measurement scores on different measures using Z-scores, you can tell how the scores are placed in their distributions.
Then you can compare them. Standardization of scores is an extensively used procedure in the field of research and planning as they help in the comparison of various test scores. Standardizing scores, before combining them is helps a researcher to get better and comparable results.
This has been a guide to the top difference between Z score vs T score. Here we also discuss the Z score vs T score key differences with infographics and comparison table.
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