{"id":145,"date":"2018-03-09T04:55:00","date_gmt":"2018-03-09T03:55:00","guid":{"rendered":"https:\/\/kindsonthegenius.com\/blog\/2018\/03\/09\/chi-square-goodness-of-fit-example-step-by-step-procedure\/"},"modified":"2020-08-22T20:23:54","modified_gmt":"2020-08-22T18:23:54","slug":"chi-square-goodness-of-fit-example-step-by-step-procedure","status":"publish","type":"post","link":"https:\/\/kindsonthegenius.com\/blog\/chi-square-goodness-of-fit-example-step-by-step-procedure\/","title":{"rendered":"Chi-Square Goodness of Fit Example – Step by Step Procedure"},"content":{"rendered":"
\n
Question<\/b>
256 musicians were polled to determine their zodaic sign. The results are given below
Aries 29
Torus 24
Gemini 22
Cancer 19
Leo 21
Virgo 18
Libra 19
Scorpio 20
Sagittarius 23
Capricorn 18
Aquarius 20
Pisces 23<\/p>\n

Test the hypothesis that the zodaic signs are evenly distributed accross the musicians.<\/p>\n

Solution Steps<\/b>
Get the excel sheet for this question <\/a>
The formular for chi-square is<\/p>\n

<\/div>\n
<\/a><\/div>\n

where
O = Observed values
E = Expected value <\/p>\n

Step 1: State the null and alternate hypothesis<\/b>
H0<\/sub>:<\/b> The values are evenly distributed
Ha<\/sub><\/b>: The values are not evenly distributed<\/p>\n

Acceptance criteria for the null value is for large p-Value. (we would calculate this)
Rejection criteria is when p-value is low.<\/p>\n

Step 2:Create the Table<\/b>
I have created the table in Excel as shown below<\/p>\n

<\/a><\/div>\n

Step 3: Calculate the Expected Value <\/b>
The expected value corresponds to the mean of the samples  and has been calculated as 21.33.<\/p>\n

Step 4: Calculate the Difference<\/b>
This is given by the formular Observed Value – Expected Value (O – E) for each of the observations.<\/p>\n

Step 5: Calculate the Squared Difference<\/b>
This is the square of the value calculated in Step 4. The values are shown in Table 3.<\/p>\n

<\/ins><\/p>\n

Step 6: Calculate the Component<\/b>
This is given by the chi-square formula<\/p>\n

<\/a><\/div>\n
<\/div>\n

Calculate this value for each of the squared values
At this point the excel sheet would look like the one below<\/p>\n

 <\/a><\/div>\n
Table 3<\/b>: Final Chi-Square Table <\/div>\n

Step 7: Calculate the Chi-Square Statitic<\/b>
You can easily find this value by taking the sum of the last column.
Chi-Square test statistic = 5.09<\/p>\n

Step 8: Find the p-Value <\/b>
You can find the p-value using the calculate chi-square statistic and the degrees of freedom<\/p>\n

Degrees of freedom is given by N-1
df = 12 – 1 = 11
where N is the number of observations in this case
See statistical tables here <\/a><\/p>\n

From the chi-square table we get a p-value of between 0.900<\/b> and 0.950.<\/b><\/p>\n

Step 9: State the Conclustion<\/b>
In chi-square, the null-hypotheis is accepted if the p-value is very large, say 90% to 100% and we reject the null hypothesis for small values of p-value.<\/p>\n

In this case, the p-value is between 90% and 95%. Therefore, we accept the null hypothesis.<\/p>\n

Get this excel file<\/a><\/div>\n<\/div>\n

<\/ins>
<\/ins><\/p>\n","protected":false},"excerpt":{"rendered":"

Question256 musicians were polled to determine their zodaic sign. The results are given belowAries 29Torus 24Gemini 22Cancer 19Leo 21Virgo 18Libra 19Scorpio 20Sagittarius 23Capricorn 18Aquarius 20Pisces … <\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_mi_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0},"categories":[223],"tags":[],"_links":{"self":[{"href":"https:\/\/kindsonthegenius.com\/blog\/wp-json\/wp\/v2\/posts\/145"}],"collection":[{"href":"https:\/\/kindsonthegenius.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/kindsonthegenius.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/kindsonthegenius.com\/blog\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/kindsonthegenius.com\/blog\/wp-json\/wp\/v2\/comments?post=145"}],"version-history":[{"count":1,"href":"https:\/\/kindsonthegenius.com\/blog\/wp-json\/wp\/v2\/posts\/145\/revisions"}],"predecessor-version":[{"id":1460,"href":"https:\/\/kindsonthegenius.com\/blog\/wp-json\/wp\/v2\/posts\/145\/revisions\/1460"}],"wp:attachment":[{"href":"https:\/\/kindsonthegenius.com\/blog\/wp-json\/wp\/v2\/media?parent=145"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/kindsonthegenius.com\/blog\/wp-json\/wp\/v2\/categories?post=145"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/kindsonthegenius.com\/blog\/wp-json\/wp\/v2\/tags?post=145"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}