Why You Need Chi Square Analysis (+ Free Calculator)

November 18, 2016

Cross tabulation reports (called cross tabs) go a long way in helping to compare and analyze two questions and identify trends and patterns within your data… but determining statistical relevance is another matter. That’s where our Chi Square calculator comes in handy.

Chi Square is an especially powerful statistical method of assessing the goodness of fit (correlation) between observed values and the ones expected theoretically.

It allows you to test out a number of hypothesizes with the aim of finding out if what you see is true, is really true, and for testing for the “goodness of fit” between the observed and expected data after several investigations.


Ready to Calculate? Jump Right to the Calculator:

Chi-Square Calculator

Select a significance level:





To use the calculator:

  1. Fill in the group and category information.
  2. Fill in your values. These must be numbers.
  3. Choose a significance level
  4. Submit the table
  5. The table will output totals for the rows and columns, as well as the Chi-squared result. It will tell you if your result is statistically significant or not.

You can also find our Chi Square Calculator and an extended explanation of the process here.

Why Top Researchers Use Chi Square for Data Analysis

While the Chi Square equation is complex, there are a number of reasons why it’s the preferred method of many data analysts:

  • It is easier to compute
  • Can be used with data that has been measured on a categorical scale
  • Researchers should use it especially to see whether there are differences between two or more groups of participants.
  • Chi Square accepts weaker, less accurate data as inputs thus having less status in the pantheon of the statistical tests. It can be applied in surveys, business, decision making, quality control, medical and biological control.
  • It can be used in a wide variety of research contexts since it is not limiting in the data it accepts.
  • Chi Square is easy to calculate and interpret since you can get the correlating confirmation reports with ease.
  • It can also be used in analysis of nominal data


How Chi Square Works

Chi Square always tests for null hypothesis where there is no significant difference between the expected and observed results. The calculator above uses the following formula. (This is also the formula that you would use if you needed to calculate statistical association by hand.)


Chi Calculator

*The following information is not required to use our calculator, but is rather an in depth look at conducting a Chi Square Test by hand and the statistical process that comes with the resulting data.

To conduct a Chi Square test, observed frequencies are entered, the sum of the elements within rows and columns (such as those in our calculator) are then computed (call this T). The Chi-Square test of experiment is used to test for null hypothesis in that the frequencies (entered) within the cells is what is expected, given T. The Chi-Square test of “goodness of fit” is then used to test the hypothesis that the total sample is distributed evenly among all levels of the relevant factor. The expected value within each cell, if the null condition is true, is the product of the row and column total is divided by the overall sample for the test of independence and the sample divided by the number of levels of the single factor for the test of “goodness of fit.”

This means that the sum of the squared difference between the observed (O in the equation) data and the expected (E) over the expected data in all the possible categories. It should be noted that to determine Chi Square, first you need to determine the number expected in each category and the number observed. Chi-square requires that only numerical values should be used and not percentiles and or ratio. There are points to note when testing your hypothesis and calculating Chi Square:

  • Determination of the expected numbers for each observational class is crucial.
  • Ensure you complete all the calculations using the Chi-Square formula and also consider rounding off the answer to two significant digits.
  • Chi Square table should be used to determine the significance of the values. With it, you can; determine the degree of freedom (df) and locate the value in the required column, locate the value closest to the Chi-Square (£2) on the df row and determine the p-value by moving up the column.
  • Lastly, you need to state your conclusions regarding your hypothesis. Conclusions will be drawn when p is within the range of acceptable deviation. The extent of the deviation will depend on the conclusion that things other than chance were in place causing the observed to differ from the expected. It should be noted that sometimes when the expected value is <5, calculating Chi Square might be a problem.

Chi Square tests where the sampling distribution of the test statistics in a Chi Square distribution is obtained when the null hypothesis is true. The chi-square test is basically used in comparing the distribution of plain text and the decrypted cipher text in cryptanalysis. It has been, therefore, seen in solving cryptographic issues.

Chi Square tests can be constructed through sample variants and also from the sum of squared errors. Chi Square assumes normal independence in data distribution due to the central limit theorem. It is important to gather the data by conducting proper experimentation and stating the hypothesis being tested and also predict the results.

Measure Correlation With Chi Square

Data has become an important and trusted phenomenon for many business lives and the researchers. But having large volumes of data can be a challenge when it comes to data management and analysis.

Chi Square is one way to ensure that you’re getting accurate analysis from your data.

For more info, check out Alchemer’s help documentation on how our software gets the most out of Chi Square.

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