# T Test And Chi Square Test Pdf

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- The Chi-square test of independence
- Chi Square
- Pearson's chi-squared test
- SPSS Tutorials: Chi-Square Test of Independence

*The chi-square independence test is a procedure for testing if two categorical variables are related in some population. Example: a scientist wants to know if education level and marital status are related for all people in some country. A good first step for these data is inspecting the contingency table of marital status by education.*

## The Chi-square test of independence

A chi-square test is a statistical test used to compare observed results with expected results. The purpose of this test is to determine if a difference between observed data and expected data is due to chance, or if it is due to a relationship between the variables you are studying.

Therefore, a chi-square test is an excellent choice to help us better understand and interpret the relationship between our two categorical variables.

To perform a chi-square exploring the statistical significance of the relationship between s2q10 and s1truan , select Analyze , Descriptive Statistics , and then Crosstabs. Find s2q10 in the variable list on the left, and move it to the Row s box. Find s1truan in the variable list on the left, and move it to the Column s box. Click Statistics , and select Chi-square. Click Continue and then OK to run the analysis. Your output should look like the table on the right.

Take a look at the column on the far right of this output table. This means that the relationship between Year 11 truancy and enrolment in full time education after secondary school is significant. Running a chi-square test cannot tell you anything about a causal relationship between truancy and later educational enrolment. Before we use s1q62a , we should check its frequencies to make sure the data is ready for bivariate analysis.

Go to Analyze , Descriptive Statistics , and then Frequencies. Move s1q62a into the Variable s box on the right side of the dialogue box. Click OK to run a frequency test. We should code this information as missing data before we run our chi square test, so that we are only performing the test on data relevant to our research question.

Luckily, doing this is very easy. This will open up a Find and Replace dialogue box. Just enter s1q62a into the text bar and click Find Next.

This will find the s1q62a row in the dataset. Click this cell to open it. Now you should see a dialogue box that lists all the numerical values of the categories of this variable. To recode these categories as missing data, all you need to do is move over one column to the Missing column. Click to open that cell. In the dialogue box that opens, select Discrete missing values and enter These are the numerical codes for the three categories that include missing data.

Click OK. You should now see that our three missing codes are saved in the Missing cell of the s1q62a row. To make sure that the missing data is no longer included in tests we run using this variable, run a frequency check on s1q62a. And, because we have cleaned up s1q62a , we are ready to run our chi square test.

Select Analyze , Descriptive Statistics , and then Crosstabs. Find s1q62a in the variable list on the left, and move it to the Column s box.

Your output should look like the table on the left. Take a look at the Asymptotic Significance of this chi square test. Using this information, what can we say about the relationship between paternal degree and full time enrolment in education after secondary school? Before you run the chi square, make sure to check the frequencies in s1q62b and make any corrections you think are necessary.

Is there a statistically significant relationship between maternal degree and full time education after secondary school? Remember that you are simply able to say now that paternal degree and Year 11 truancy both have relationships with respondent enrolment in full time education after secondary school. You cannot say, for example, that a paternal degree causes enrolment in full time education.

Univariate analysis Bivariate analysis Multivariate analysis. Crosstabs Chi square. Research Question 4: Full time education. Bivariate analysis. Chi square. PDF Reader.

## Chi Square

Our websites may use cookies to personalize and enhance your experience. By continuing without changing your cookie settings, you agree to this collection. For more information, please see our University Websites Privacy Notice. The t test is one type of inferential statistics. It is used to determine whether there is a significant difference between the means of two groups. With all inferential statistics, we assume the dependent variable fits a normal distribution. When we assume a normal distribution exists, we can identify the probability of a particular outcome.

Our tutorials reference a dataset called "sample" in many examples. If you'd like to download the sample dataset to work through the examples, choose one of the files below:. The Chi-Square Test of Independence determines whether there is an association between categorical variables i. It is a nonparametric test. This test utilizes a contingency table to analyze the data.

Key words: Chi-square test, goodness of fit, independence, homogeneity. contain Student-t tests and ANOVA test assuming that the data come from a normal.

## Pearson's chi-squared test

It is the most widely used of many chi-squared tests e. Its properties were first investigated by Karl Pearson in It tests a null hypothesis stating that the frequency distribution of certain events observed in a sample is consistent with a particular theoretical distribution.

This module will continue the discussion of hypothesis testing, where a specific statement or hypothesis is generated about a population parameter, and sample statistics are used to assess the likelihood that the hypothesis is true. The hypothesis is based on available information and the investigator's belief about the population parameters. The specific tests considered here are called chi-square tests and are appropriate when the outcome is discrete dichotomous, ordinal or categorical.

Literature Rumsey D. Statistical Essentials for Dummies. Hoboken: Wiley Publishing. Ismay C. Statistical Inference for Data Science.

*A chi-square test is a statistical test used to compare observed results with expected results. The purpose of this test is to determine if a difference between observed data and expected data is due to chance, or if it is due to a relationship between the variables you are studying.*

### SPSS Tutorials: Chi-Square Test of Independence

The chi-square test tests the null hypothesis that the categorical data has the given frequencies. Expected frequencies in each category. By default the categories are assumed to be equally likely. The p-value is computed using a chi-squared distribution with k - 1 - ddof degrees of freedom, where k is the number of observed frequencies.

The Chi-square goodness of fit test is a statistical hypothesis test used to determine whether a variable is likely to come from a specified distribution or not. It is often used to evaluate whether sample data is representative of the full population. The Chi-square goodness of fit test checks whether your sample data is likely to be from a specific theoretical distribution. We have a set of data values, and an idea about how the data values are distributed.

The Chi-square statistic is a non-parametric distribution free tool designed to analyze group differences when the dependent variable is measured at a nominal level. Like all non-parametric statistics, the Chi-square is robust with respect to the distribution of the data. Specifically, it does not require equality of variances among the study groups or homoscedasticity in the data. It permits evaluation of both dichotomous independent variables, and of multiple group studies. Unlike many other non-parametric and some parametric statistics, the calculations needed to compute the Chi-square provide considerable information about how each of the groups performed in the study.

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