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What is chi-square? And Chi-square Assignments?

Chi-square is a parametric statistical test used for categorical data. It is the sum of products of all possible pairs, illustrating the relationship between two variables and their frequencies. If you are looking for Chi-square Assignments help, we can help! We got expert tutors waiting for you.

Uses of Chi-Square in Hypothesis Testing

1. For goodness-of-fit testing (e.g., the null hypothesis is that the populations are equally distributed among categories).
2. Test of independence in contingency tables, referred to as chi-square test for association , especially in comparing two nominal variables.
3. As a multivariate test of independence , such as analysis of variance or linear regression, for categorical data.
4. As a test of goodness-of-fit for multinomial distributions .
5. As an extension to the Kolmogorov–Smirnov test in comparing two cumulative distribution functions .
6. For hypothesis testing when one must control the Type I and Type II error rates, but must also control the familywise error , such as simultaneous testing of two correlated hypotheses.  Chi-square tests in this case are known as Fisher’s exact test and Wilcoxon rank sum test .
7. As a measure of nonparametric correlation for continuous data (Tetenbaum & Lahiri, 1987).
8. As a measure of independence in contingency tables for ordinal data (Agresti, 1990).
9. To test multidimensional scaling results using SPSS . Cohen’s Kappa approximate 2 x 2 – chi-square but is easier to compute and gives similar results (Hartigan & Hartigan, 2002), though see  Donoho and Elad (1992).
10. As a measure of goodness-of-fit for bivariate distributions when the expected value is not zero, obtained by inverting chi-square distributed with one degree of freedom under the null hypothesis (Agresti & Finlay, 1986).

What does Chi-Square tell us about categorical data?

It tests whether the frequencies in each cell of the table add up to a sample proportion.  A good way to think about it is that it tells us if the observed frequencies are consistent with what was expected, based on an assumed distribution for each of your variables.  For example, in order to test our null hypothesis, we need to compare the observed frequencies with expected frequencies.

The most common probability distribution used in testing for independence (as mentioned above) is the  binomial distribution and Chi-square is a function of binomials, so we will be using that.  In this post, we will talk about how to do some basic chi-square tests in SPSS using a simulated example.

First, you need to set up the data file with variables for each of the categorical predictors and one variable that is a count variable (the number of events/categories).  For example, if I wanted to look at the effect of teaching methods on cognitive development in children, I would include teaching method as a categorical variable (shown below) and count the number of times each method was used.

Set you data correct when using Chi-square

The next thing you need to do is set up another data file with variables for each of your continuous predictors, along with one other categorical predictor that tells you when the event occurred (for example, if you are looking at the effect of teaching method on student cognitive development and grade level, you would have a variable for the teaching method, another for the grade of students).  The code below shows how to set up this second data file:

For this example, I programmed grades as 1 = K – 2 (kindergarten – second grade), 2 = 3 – 4, 3 = 5 – 6, 4 = 7 – 8.  I did the same thing for age (third continuous variable).

Now that I have my data set up, let’s look at how to do some of the basic chi-square tests.

OKAY…so now what?

For each test, you need to first generate your expected values and then compute your chi-square statistic.  You can get your expected values by counting the frequencies in the table above (for example, for age).

How does one use SPSS to run these tests?

The process is a little different depending on whether you are using categorical or continuous data.  Since I use SPSS for my examples, let’s look at the chi-square test with categorical data as an example.  I have seen several sources that use different approaches–the simplest way I could think of to do it is to first create your expected value and then run a basic chi-square test on the table.  Let’s go ahead and do that using SPSS.

The first step in chi-square tests with categorical data is to set up your expected value, which you can do by running a frequency count for each cell (the code below shows how I did this in SPSS). You can then run the chi-square test for independence by going to SPSS->Analyze ->Chi Square and filling in the information below:

NOTE: The formula is shown above, but I actually used “count” as my chi-square variable.  Doing this will allow you to use frequencies rather than raw numbers, which will be easier to deal with in SPSS.  You could also use “expected values” instead, but you would need to compute your expected values and enter them into the formula above. If you are looking for p-values, you can get those by selecting chi-square distribution (goodness of fit) as your test statistic (instead of calculating the chi-square statistic in SPSS, as I did above).  You will need to change your degrees of freedom slightly (df = k – 1, where k = number of columns -1) because you are using frequencies instead of raw numbers.

Also note that if you are looking at two categorical variables, you can do a test for independence by using SPSS to create your expected value and then running 2 separate chi-square tests (the code below shows how I did this in SPSS).  The formula is the same as before, except that you have two columns of frequencies.  You could also use “expected values”

Chi-square homework help

The easiest way to do chi-square homework is to get the expected value from your textbook or instructor (if they don’t provide it, you will need to run a frequency count in SPSS).  Just plug those numbers into the formulas above and calculate your statistic and p-values.

Some of our tutors have experience with chi-square, but if you are trying to figure it out on your own, the process is very similar to using SPSS for other analyses.  To learn more about chi-square analysis with SPSS check out this post .

What software does KA use?

KA uses Mathlab or SageMath to do all of our calculations.  You can learn more about them in this post .

How do you calculate degrees of freedom? What do the letters stand for?

I generally define “degrees of freedom” as the number of outcomes that are not restricted by your null hypothesis.  In a one-sample t-test with 14 observations, the null hypothesis is typically that there is no effect.  In this case, the degrees of freedom are 14-1 = 13 because we cannot count the outcome where everyone has a mean score of 0 (this would not be allowed under our null hypothesis).

We use letters to represent things in statistics all the time…so why not here?

It is mostly used in descriptive statistics to determine whether an observed distribution differs significantly from that which would be expected if the null hypothesis were true. chi-square was invented by Karl Pearson.

chi-square is used to determine if there is a correlation between two continuous variables AND/OR whether the difference between two categorical data sets are significant.

If you do not understand chi-square, please contact our editors at : https://researchanalyticsediting.wordpress.com

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Selected References

1. Student’s t-distribution , TechTarget,  Retrieved from: http://searchcio.techtarget.com/definition/t-distribution 2.   Chi-square test of goodness of fit , Math Is Fun, Retrieved from: http://www.mathsisfun.com