Differences Between Z-Test and T-Test
Z Test is the statistical hypothesis which is used in order to determine that whether the two samples means calculated are different in case the standard deviation is available and sample is large whereas the T test is used in order to determine a how averages of different data sets differs from each other in case standard deviation or the variance is not known.
Z-tests and t-tests are the two statistical methods that involve data analysis, which has applications in science, business, and many other disciplines. The t-test can be referred to as a univariate hypothesis test based on t-statistic, wherein the mean, i.e., the average is known, and population variance, i.e., the standard deviation, is approximated from the sample. On the other hand, Z-test, also a univariate test which is based on a standard normal distributionStandard Normal DistributionThe standard normal distribution is a symmetric probability distribution about the average or the mean, depicting that the data near the average or the mean are occurring more frequently than the data far from the average or the norm. Thus, the score is termed “Z-score”..
#1 – Z-Test
Z-test FormulaZ-test FormulaZ-test formula is applied hypothesis testing for data with a large sample size. It denotes the value acquired by dividing the population standard deviation from the difference between the sample mean, and the population mean., as mentioned earlier, are the statistical calculations that can be used to compare population averages to a sample’s. The z-test will tell you how far, in standard deviationsStandard DeviationsStandard deviation (SD) is a popular statistical tool represented by the Greek letter 'σ' to measure the variation or dispersion of a set of data values relative to its mean (average), thus interpreting the data's reliability. terms, a data point is from the average of a data set. A z-test will compare a sample to a defined population that is typically used for dealing with problems relating to large samples (i.e., n > 30). Mostly, they are very useful when the standard deviation is known.
#2 – T-Test
T-testsT-testsA T-test is a method to identify whether the means of two groups differ from one another significantly. It is an inferential statistics approach that facilitates the hypothesis testing. are also calculations that can be used to test a hypothesis, but they are very useful when we need to determine if there is a statistically significant comparison between the 2 independent sample groups. In other words, a t-test asks whether the comparison between the averages of 2 groups is unlikely to have occurred due to random chance. Usually, t-tests are more appropriate when dealing with problems with a limited sample sizeSample SizeThe sample size formula depicts the relevant population range on which an experiment or survey is conducted. It is measured using the population size, the critical value of normal distribution at the required confidence level, sample proportion and margin of error. (i.e., n < 30).
Z-Test vs. T-Test Infographics
Here we provide you with the top 5 differences between the z-test vs. t-test you must know.
- One of the essential conditions for conducting a t-test is that population standard deviation or the variance is unknown. Conversely, the population variance formulaPopulation Variance FormulaPopulation variance can be calculated using this formula: σ2 = ∑ni=1 (xi – μ)2 / N, where, σ2 is population variance, x1, x2, x3,…..xn are the observations, N is the number of observations and µ is the mean of the data set., as stated above, should be assumed to be known or be known in the case of a z-test.
- The t-test, as mentioned earlier, is based on student’s t-distributionT-distributionThe formula to calculate T distribution is T=x¯−μ/s√N. Where x̄ is the sample mean, μ is the population mean, s is the standard deviation, N is the size of the given sample.. On the contrary, the z-test depends upon the assumption that the distribution of sample means will be normal. Both the normal distribution and student’s t-distribution appears the same, as both are bell-shapedBell-shapedBell Curve graph portrays a normal distribution which is a type of continuous probability. It gets its name from the shape of the graph which resembles to a bell. and symmetrical. However, they differ in one of the cases that in at-distribution, there is lesser space in the center and more in their tails.
- Z-test is used as given in the above table when the sample size is large, which is n > 30, and the t-test is appropriate when the size of the sample is not big, which is small, i.e., that n < 30.
Z-Test vs. T-Test Comparative Table
|Basic Definition||Z-test is a kind of hypothesis test which ascertains if the averages of the 2 datasets are different from each other when standard deviation or variance is given.||The t-test can be referred to as a kind of parametric test that is applied to an identity, how the averages of 2 sets of data differ from each other when the standard deviation or variance is not given.|
|Population Variance||The Population variance or standard deviation is known here.||The Population variance or standard deviation is unknown here.|
|Sample Size||The Sample size is large.||Here the Sample Size is small.|
|Based upon (a type of distribution)||Based on Normal distributionNormal DistributionNormal Distribution is a bell-shaped frequency distribution curve which helps describe all the possible values a random variable can take within a given range with most of the distribution area is in the middle and few are in the tails, at the extremes. This distribution has two key parameters: the mean (µ) and the standard deviation (σ) which plays a key role in assets return calculation and in risk management strategy..||Based on Student-t distribution.|
By and to the larger extent, both these tests are almost similar, but the comparison comes only to their conditions for their application, meaning that the t-test is more appropriate and applicable when the size of the sample is not more than thirty units. However, if it is greater than thirty units, one should use a z-test. Similarly, there are also other conditions, which will make it clear that which test is to be performed in a situation.
Well, there are also different tests like the f test, two-tailed vs. single-tailed, etc., statisticians must be careful while applying them after analyzing the situation and then deciding which one to use. Below is a sample chart for what we discussed above.
This article has been a guide to Z-Test vs. T-Test. Here we discuss the top 5 differences between these hypothesis testing along with infographics and a comparative table. You may also have a look at the following articles –
- What is Hypothesis Testing?
- Formula of F-Test
- Logical Test in Excel (AND, OR, IF)
- How to do F-Test in Excel?