# Difference Between T Test And Z Test In Hypothesis Testing Pdf

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- Difference Between T-test and Z-test (With Table)
- Statistical Tests — When to use Which ?
- Difference Between T-test and Z-test
- Z-Test vs T-Test

By Madhuri Thakur. 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. On the other hand, Z-test, also a univariate test which is based on a standard normal distribution.

## Difference Between T-test and Z-test (With Table)

Sign in. For a person being from a non-statistical background the most confusing aspect of statistics, are always the fundamental statistical tests, and when to use which.

This blog post is an attempt to mark out the difference between the most common tests, the use of null value hypothesis in these tests and outlining the conditions under which a particular test should be used.

Before we venture on the difference be t ween different tests, we need to formulate a clear understanding of what a null hypothesis is. A null hypothesis, proposes that no significant difference exists in a set of given observations. For the purpose of these tests in general. Null : Given two sample means are equal. Alternate : Given two sample means are not equal. For rejecting a null hypothesis, a test statistic is calculated. This test-statistic is then compared with a critical value and if it is found to be greater than the critical value the hypothesis is rejected.

The critical values are the boundaries of the critical region. Critical value can tell us, what is the probability of two sample means belonging to the same distribution. Higher, the critical value means lower the probability of two samples belonging to same distribution. The general critical value for a two-tailed test is 1.

Critical values can be used to do hypothesis testing in following way. Calculate test statistic. Calculate critical values based on significance level alpha. Compare test statistic with critical values.

If the test statistic is lower than the critical value, accept the hypothesis or else reject the hypothesis. For checking out how to calculate a critical value in detail please do check.

Before we move forward with different statistical tests it is imperative to understand the difference between a sample and a population.

For our example above, it will be a small group of people selected randomly from some parts of the earth. To draw inferences from a sample by validating a hypothesis it is necessary that the sample is random. For instance, in our example above if we select people randomly from all regions Asia, America, Europe, Africa etc.

In such cases, a population is assumed to be of some type of a distribution. The most common forms of distributions are Binomial, Poisson and Discrete.

However, there are many other types which are mentioned in detail at. The determination of distribution type is necessary to determine the critical value and test to be chosen to validate any hypothesis. Now, when we are clear on population, sample, and distribution we can move forward to understand different kinds of test and the distribution types for which they are used.

As we know critical value is a point beyond which we reject the null hypothesis. P-value on the other hand is defined as the probability to the right of respective statistic Z, T or chi. The benefit of using p-value is that it calculates a probability estimate, we can test at any desired level of significance by comparing this probability directly with the significance level. For e. However, if we calculate p-value for 1. Important point to note here is that there is no double calculation required.

In a z-test, the sample is assumed to be normally distributed. Null : Sample mean is same as the population mean. Alternate : Sample mean is not same as the population mean. The statistics used for this hypothesis testing is called z-statistic, the score for which is calculated as.

A t-test is used to compare the mean of two given samples. Like a z-test, a t-test also assumes a normal distribution of the sample. A t-test is used when the population parameters mean and standard deviation are not known. There are three versions of t-test. Independent samples t-test which compares mean for two groups. Paired sample t-test which compares means from the same group at different times. One sample t-test which tests the mean of a single group against a known mean.

The statistic for this hypothesis testing is called t-statistic, the score for which is calculated as. There are multiple variations of t-test which are explained in detail here. ANOVA, also known as analysis of variance, is used to compare multiple three or more samples with a single test.

In addition, MANOVA can also detect the difference in co-relation between dependent variables given the groups of independent variables. Null : All pairs of samples are same i.

Alternate : At least one pair of samples is significantly different. The statistics used to measure the significance, in this case, is called F-statistics. The F value is calculated using the formula. Chi-square test is used to compare categorical variables. There are two type of chi-square test. Goodness of fit test, which determines if a sample matches the population. A chi-square fit test for two independent variables is used to compare two variables in a contingency table to check if the data fits.

A small chi-square value means that data fits. The hypothesis being tested for chi-square is. Null : Variable A and Variable B are independent. Alternate : Variable A and Variable B are not independent. The statistic used to measure significance, in this case, is called chi-square statistic. The formula used for calculating the statistic is. Note: As one can see from the above examples, in all the tests a statistic is being compared with a critical value to accept or reject a hypothesis.

However, the statistic and way to calculate it differ depending on the type of variable, the number of samples being analyzed and if the population parameters are known. Thus depending upon such factors a suitable test and null hypothesis is chosen. This is the most important point which I have noted, in my efforts to learn about these tests and find it instrumental in my understanding of these basic statistical concepts.

This post focuses heavily on normally distributed data. Z-test and t-test can be used for data which is non-normally distributed as well if the sample size is greater than 20, however there are other preferable methods to use in such a situation.

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## Statistical Tests — When to use Which ?

A Z -test is any statistical test for which the distribution of the test statistic under the null hypothesis can be approximated by a normal distribution. Z-test tests the mean of a distribution. For each significance level in the confidence interval , the Z -test has a single critical value for example, 1. Because of the central limit theorem , many test statistics are approximately normally distributed for large samples. Therefore, many statistical tests can be conveniently performed as approximate Z -tests if the sample size is large or the population variance is known. How to perform a Z test when T is a statistic that is approximately normally distributed under the null hypothesis is as follows:.

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T-test refers to a univariate hypothesis test based on t-statistic, wherein the mean is known, and population variance is approximated from the sample. On the other hand, Z-test is also a univariate test that is based on standard normal distribution. In simple terms, a hypothesis refers to a supposition which is to be accepted or rejected. There are two hypothesis testing procedures, i. Now, in the parametric test, there can be two types of test, t-test and z-test.

## Difference Between T-test and Z-test

Just about every statistics student I've ever tutored has asked me this question at some point. When I first started tutoring I'd explain that it depends on the problem, and start rambling on about the central limit theorem until their eyes glazed over. Then I realized, it's easier to understand if I just make a flowchart. So, here it is! When you're working on a statistics word problem, these are the things you need to look for.

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### Z-Test vs T-Test

T-test and z-test are terms common when it comes to the statistical testing of hypothesis in the comparison of two sample means. Notably, the two tests are parametric procedures of hypothesis testing since they are both their variables are measured on an interval scale. A hypothesis refers to a conjecture which is to be accepted or rejected after further observation, investigation, and scientific experimentation. The difference between T-test and Z-test is that a T-test is used to determine a statistically significant difference between two sample groups that are independent in nature, whereas Z-test is used to determine the difference between means of two populations when the variance is given. A T-test is best with the problems that have a limited sample size, whereas Z-test works best for the problems with large sample size. The t-test is a parameter applied to an identity to identify how the data averages differ from each other when the variance or standard deviation is not given. The t-test is based on Student t- statistic , having the mean being known and the variance of the population approximated from the sample.

Sign in. For a person being from a non-statistical background the most confusing aspect of statistics, are always the fundamental statistical tests, and when to use which. This blog post is an attempt to mark out the difference between the most common tests, the use of null value hypothesis in these tests and outlining the conditions under which a particular test should be used. Before we venture on the difference be t ween different tests, we need to formulate a clear understanding of what a null hypothesis is. A null hypothesis, proposes that no significant difference exists in a set of given observations. For the purpose of these tests in general. Null : Given two sample means are equal.

Simply put: AnalystNotes offers the best value and the best product available to help you pass your exams. Quantitative Methods 2 Reading Hypothesis Testing Subject 8. Why should I choose AnalystNotes? Find out more. Subject 8. Z-Test PDF Download When testing a hypothesis concerning the value of a population mean, either a t-test or a z-test can be conducted.

#### Content: T-test Vs Z-test

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Statistics for Analytics and Data Science: Hypothesis Testing and Z-Test vs. T-Test · Overview · Introduction · Table of Contents · Fundamentals of.