One Proportion Test

One Proportion Test

One proportion test

Statistics are very complicated, hence people depends on the data analysis and thus performs tests. There are multiple parameters that you can test. Like, for z-test (paired-sample-test), it is a test for the mean. The one proportion test is commonly done to confirm or debunk claims. Test for the population proportion is denoted as p. The only thing you need to do is take a random sample of components and use one proportion test to determine that the actual proportion backs up the claim. For example, you want to know the proportion of males within a total population of adults. Here test of proportion helps you assess whether the sample represents the true proportion from the entire population or not. There are a few things that needed to be defined first before conducting the proportion test.

Benefits of One Proportion Test:

It is said that these are the tests that are very useful if you are willing to check whether your sample is the same in the context of the population you are sampling or not. No doubt One proportion test is very used as it has many elements that make things easy for the researcher. It is seen that this test lets you know information regarding your population. E.g., how gender is distributed. This is the test that also allows you to check all the known parameters which are against it. It is very essential to know all the benefits of using a test so that you can also avail all of them while using it to make your research more meaningful. Many students access the SPSS proportion test tutorial to get familiar with all the areas of the test.

How to perform a test of proportion?

It is considered that a test of proportion will assess whether a sample from a population has the capability to represent the true proportion of the whole population or not. There are specific steps that are to be followed while conducting this test that needs to be followed. It is very essential to do the Statistical analysis of the data that is being gathered for the study. The steps to perform a test of proportion with the help of the critical value are mentioned below:

  • Firstly, mention related to the null hypothesis and the alternative hypothesis which is going to play a major role in the whole analysis. The Test of significance is very important to know.
  • After that, you have to calculate the statistics.
  • Then determine the region that is said to be critical.
  • Now make a decision that is suitable for your research in terms of getting the desired outcome. Determine if the statistic of the test falls in the critical region or not. If it is falling then, you can reject the null hypothesis, and if in case it does not then do not reject the null hypothesis. It is a fact that Hypothesis testing helps in identifying many areas of the variables and data.

It is advised to everyone that they should know the entire procedure of doing the test so that it can be done smoothly. It should be done on a priority basis. There are many sources available that can help you in knowing it.

There are two ways to perform a test of proportion;-

Critical value Approach

    1. State the null hypothesis H0 and the alternative hypothesis HA.
    2. Calculate the test statistic:
One Proportion Test
    1. where p0 is the null hypothesized proportion i.e. when H0:p=p0
    2. Determine the critical region.
    3. And lastly, determine if the test statistic falls in the critical region. As, If it does fall in it, reject the null hypothesis. If it does not, do not reject the null hypothesis.

p-value Approach

    1. State the null hypothesis H0 and the alternative hypothesis HA.
    2. Set the level of significance α
    3. Calculate the test statistic:
    4. Calculate the p-value.
    5. Decide by checking whether to reject the null hypothesis by comparing p-value to α. Also, If the p-value < α then reject H0; otherwise do not reject.

What is a one-proportion Z-test?

This test is performed to compare an observed proportion to a theoretical one when there are only two categories. Based on the sample size, normal approximation or binomial enumeration is done. If the sample size is large, the normal approximation provides an accurate result. If the sample size is less, then binomial enumeration gives the correct results. The binomial enumeration and normal approximation can be approximated when both mean (np) and variance( n(1-p)) values are greater than 10.

Compute one proportion z-test in R

R functions: binom.test() & prop.test()

  • The R functions binom.test() and prop.test() can be used to perform one-proportion test:
    1. binom.test(): compute exact binomial test. Recommended when the sample size is small
    2. prop.test(): can be used when the sample size is large ( N > 30). It uses a normal approximation to binomial

The syntax of the two functions are the same. The simplified format is as follow:

binom.test(x, n, p = 0.5, alternative = "two.sided")

prop.test(x, n, p = NULL, alternative = "two.sided",

correct = TRUE)

    1. x: the number of successes
    2. n: the total number of trials
    3. p: the probability to test against.
    4. correct: a logical indicating whether Yates’ continuity correction should be applied where possible.

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