Z Test & T Test: Similarities & Differences

A t-test is a statistical method used to see if two sets of data are significantly different. A z-test is a statistical test to help determine the probability that new data will be near the point for which a score was calculated. Learn about these two statistical calculations, their differences, and their similarities.
Z-Tests and T-Tests
Z-tests and t-tests are statistical methods involving data analysis that have applications in business, science, and many other disciplines. Let’s explore some of their differences and similarities as well as situations where one of these methods should be used over the other.
Z-tests are statistical calculations that can be used to compare population means to a sample’s. The z-score tells you how far, in standard deviations, a data point is from the mean or average of a data set. A z-test compares a sample to a defined population and is typically used for dealing with problems relating to large samples (n > 30). Z-tests can also be helpful when we want to test a hypothesis. Generally, they are most useful when the standard deviation is known.
Like z-tests, t-tests are calculations used to test a hypothesis, but they are most useful when we need to determine if there is a statistically significant difference between two independent sample groups. In other words, a t-test asks whether a difference between the means of two groups is unlikely to have occurred because of random chance. Usually, t-tests are most appropriate when dealing with problems with a limited sample size (n < 30).
Both z-tests and t-tests require data with a normal distribution, which means that the sample (or population) data is distributed evenly around the mean, just like in this figure:
normal curve
Let’s illustrate some of the differences between the two tests and explore a pair of situations when each of these two types of statistical methods would be appropriate.
Z-Test Example
A teacher wants to know how well students perform in her math class relative to students in other math classes in her school district. She administers a standardized test, which students in other classes had taken, with a mean (average) of 60 and standard deviation of 10. Her class has 40 students. Which statistical method should she use?
Well, based on the problem, let’s take a look at information that will help us determine the most appropriate method to choose:
The teacher wants to compare students in her math class (the sample) to students in other math classes throughout the district (the population).
The teacher will administer a standardized test with a given mean and standard deviation.
The sample is greater than 30.
Since the problem provides a mean, a standard deviation, and a sample size larger than 30, the teacher should use the z-test to determine how well the students in her math class perform relative to students in other math classes. To do this, she will compare the mean for her students against that of the standardized test.
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