Introduction
A Z test is a type of hypothesis test, that can be conducted through SPSS help, a way for the researchers to figure out if the results of the test are valid or repeatable. For example, if the researchers found that the new drug cures cancer, then performing the Z test is appropriate to test the validity of the statement, whether it is true or not. The Z test is utilised when the data is approximately normally distributed. Hence, the assumption of normal distribution and random sampling is crucial for performing the Z test, which ensures the validity of the research and the test results.
Two proportion Z-tests
There are several tests in statistics through which the researchers can analyse the data and information by using SPSS and Microsoft Excel, such as the F test, Z test, Chi-Square test and T-test. The researchers can perform the Z test if the sample size is greater than 30, otherwise, the researchers have to choose the T-test, rather than the Z test. The sample size should be equal if possible and the data gathered by the researchers should be randomly selected from a population, where each item has an equal chance of being selected. Hence, random distribution is mandatory to be met in order to perform the Z test. The researchers are also concerned about a normally distributed data set, where a large sample size is being considered for further data analysis and evaluation. The data points should be independent of each other, in other words, one data point cannot affect another data point in the data set. For performing the Z test in the research, it is mandatory to develop a hypothesis, null and alternative so that defining the hypothesis can be possible. Choosing the alpha level is crucial along with finding the critical value of Z in the table. After calculating the Z test statistics, comparing the test statistics to the critical z value and deciding if it rejects or accepts the null hypothesis is also mandatory for the researchers to check h validity of the results. The formula for two statistics Z test is,
Where,
p^1 is the proportion of the first sample in the data set
p^2 is the proportion of the second sample in the data set
N1 is the number of data samples in the first maple
N2 is the number of the data samples in the second sample collected by the researchers
p^ is the mean of both the samples in the data set
Purpose and comparison of Z test with other tests
In statistics, one proportion test is performed to confirm claims or debunks, and a two-sample Z test for proportion is a method that is utilised to determine whether two samples are drawn from the same population. This test is widely used when the population proportion is unknown and there is not enough information to use Chi-squared distribution. The test uses the standard normal distribution for calculating the Z test statistics. Hence, the main purpose of conducting a two-proportion test is to determine whether two proportions are different from each other or not. While performing the two proportions Z test, it is computed from two independent samples and the null hypothesis is that the two proportions are equal. For performing the two-proportion Z test, the major conditions are such as,
- The two samples are random samples from the two populations
- The two proportions must be independent of each other
- The two populations must be normal or approximately normal or progressing in the two proportion Z test
If any of the above-mentioned conditions are not met, the researchers cannot use to proportion Z test in the study for further critical evaluation. The major steps of conducting a two-proportion Z test are such as:
- Calculating the standard error of the differences between the two population proportions is mandatory and it is the first step to progress in the Z test
- Next, the second step is to calculate the Z test statistics by taking the differences between the two populations and dividing them by the standard error of the differences.
