How To Find Chi Square Test Statistic On Statcrunch

You lot can use this chi-square figurer as part of a statistical analysis test to determine if there is a significant difference betwixt observed and expected frequencies.

To utilize the calculator, simply input the true and expected values (on separate lines) and click on the "Summate" button to generate the results.

What is a Chi-square Test?

A chi-square test is a pop statistical analysis tool that is employed to identify the extent to which an observed frequency differs from the expected frequency.

Let'south expect at an case.

Let's say you are a higher professor. The 100 students you teach consummate a test that is graded on a scale ranging from 2 (lowest possible grade) through to 5 (highest possible grade). In advance of the test, you lot expect 25% of the students to achieve a 5, 45% to achieve a 4, twenty% to attain a iii, and 10% to get a ii.

Afterwards the test, you grade the papers. You can and then employ the chi-square exam to determine the extent to which your predicted grades differed from the bodily grades.

How to Calculate a Chi-square

The chi-square value is adamant using the formula beneath:

X^two = (observed value - expected value)² / expected value

Returning to our example, before the test, you had anticipated that 25% of the students in the class would attain a score of 5. As such, you expected 25 of the 100 students would attain a form v. Even so, in reality, thirty students achieved a score of 5. As such, the chi-foursquare calculation is as follows:

X² = (xxx - 25)² / 25 = (v)ⁱⁱ / 25 = 25 / 25 = 1

An In-depth Example of the Chi-square Estimator

Allow's take a more in-depth look at the paper grading instance.

The class distribution for the 100 students you tested were as follows: 30 received a v, 25 received a 4, 40 received a 3, and 5 received a 2.

a.) Nosotros tin can now determine how many students were expected to receive each form per the forecast distribution.
Course ii: 0.x * 100 = 10
Grade iii: 0.twenty * 100 = 20
Grade iv: 0.45 * 100 = 45
Grade 5: 0.25 * 100 = 25
b.) Nosotros tin utilize this data to decide the chi-square value for each grade.
Grade two: Ten² = (5 - 10)² / ten = 2.five
Class 3: 10² = (40 - 20)² / twenty = twenty
Grade iv: X² = (25 - 45)² / 45 = 8.89
Grade 5: X^two = (xxx - 25)² / 25 = 1
c.) Finally, we tin sum the chi-square values: Ten^two = two.5 + twenty + viii.89 + ane = 32.39