Chi- square Goodness-Of-Fit Test

Introduction

The Chi-Square test is used in statistics, science and other professions where data is analyzed. Let's pretend that I want to compare the driving habits of males and females. I predict that consistent seatbelt use is not related to gender. 

 The goodness-of-fit test is a one sample test. it is used to compare the observed or actual frequencies with expected or theoretical frequencies. These test are non parametric tests and are widely used in research.

Task

 

  1. To  test Goodness-Of-Fit Test  of two  or more variables.
  2.  To distinguish the use  of the goodness-to-fit test from test of associations.
  3.  To apply enumeration test in a given research data.
Process

 Example: In 200 tosses of a coin, 115 heads and 85 tails were observed. Test the hypothesis that the coins is fair using a 0.5 level of significance.

 Step 1. Hypotheses

  • Ho: O=E
  • Ha: O≠E

  • where:

                Ho- Null Hypothresis

                Ha- Alternative Hypothesis

Step 2. Level of Significance

                    α=. 05

 Step 3. Reject Ho if the computed value is greater than the critical value.

 

Step 4.  Test Statistics- Goodness-of Fit chi test.

           

where:

x2= Chi-Square goodness of fit test

O= observed value

E= expected value

               DF = k - 1 

where:

df= degrees of freedom

              Worksheet Computation

   O      

    E    

   (O-E)2

     

 

  115

 100

    225

     2.25

   85

 100

   225

     2.25

  200

  200

   450

     4.50

 

 Step 5.  The computed valued of 4.50 is greater than the critical value of 3.84, we reject the null hypothesis, thus a significant difference exists.

 

Step 6. Conclusion

  •  The coin is not fair at 0.05 level of significance.

 

 

Evaluation
  1.  A die is rolled 60 times. What is the probability that outcomes turn up 1, 2, 3, 4, 5, and 6 assuming that the expected frequencies are 10 each of the faces of the die.
  2.  Explain when and how to use enumeration tests including their limitations.( chi-square goodness-of-fit).
Conclusion

 The chi-square goodness-of-fit test is used to compare the observed from the theoretical frequencies. These test are considered nonparametric because the data are assumed to be normally ditributed.

In addition, when the frequency is small in one of the categories in a contingency table, the Yate's Correction shall be used to avoid erroneous findings and conclusion. when the category are more than two, collapse the table to reduce the categories particularly when such data are measured on Likert Scale. 

Credits
Teacher Page

Standard

Subject: Statistics

 Grade level: Grade 7

Name: Jenny Mae Tuliao

             Rachelle Ibus

             Choan Viernes