Chi Square Test

Quick reference

• 00:04 Hi I'm Ray Sheen.
• 00:05 Now sometimes we have many data sets with discreet data and
• 00:09 we wanna understand if there's a relationship between them.
• 00:13 The Chi Square Hypothesis Test will answer that question for us.
• 00:18 Starting with our hypothesis test decision tree, we go to normal data, discrete x and
• 00:23 y data, and more than two variables, which is the chi-square test.
• 00:27 The chi-square test is ideally suited for multiple attribute data hypothesis.
• 00:33 If you have two or more discreet variables in your sample,
• 00:36 it can determined if they are independent or if they are linked.
• 00:39 Some of you may be aware of other uses of the Chi Square Test in basic research,
• 00:43 such as checking for goodness of fit or homogeneity.
• 00:46 We will be focused on lean Six Sigma projects and multiple discrete attribute
• 00:50 testing, and it can use more than just true false or on off data.
• 00:54 It is excellent for counts.
• 00:56 If you're comparing two different samples,
• 00:57 the two sample test of proportions is best.
• 01:00 But if you're comparing two or
• 01:01 more variables within one sample, then use this test.
• 01:05 This test relies on the number of counts for each variable or
• 01:08 attribute characteristic to determine if the different attributes are truly
• 01:12 independent or if they are related to each other, or some other factor.
• 01:17 When using this test in Lean Six Sigma be careful to check your categories for
• 01:21 real, potential, root causes.
• 01:23 The Chi-Square test doesn't know if the categories make sense
• 01:26 to be tracked separately.
• 01:28 If you're trying to determine factors relating to people who have arthritis,
• 01:32 Chi-Square will likely show you that there is a relationship between people with
• 01:35 with gray hair and arthritis, but that does not mean gray hair causes arthritis.
• 01:40 Obviously, a much more relevant factor would be age,
• 01:43 which increases the likelihood of both gray hair and susceptibility to arthritis.
• 01:49 The null hypothesis for Chi-Square is always at the factors are all independent.
• 01:53 There is nothing connecting any of them.
• 01:55 The alternative hypothesis is that the factors are dependent.
• 01:58 There is a relationship between at least two of the factors.
• 02:02 Let's look at how to do this test with Excel.
• 02:05 It's a rather complex process that must be followed.
• 02:08 Excel uses the CHISQ.TEST function to compare two tables.
• 02:13 One table is the actual values and one is expected values.
• 02:17 The actual values we get from our data,
• 02:19 the expected value we have to create manually.
• 02:23 Both tables are structured in the same manner.
• 02:25 The columns are the event categories where we have the count data.
• 02:29 The rows are the categories we're using to create the different proportions.
• 02:34 The actual table is easy to populate.
• 02:37 Create your row and column categories and then count the instances for
• 02:40 each cell in the table.
• 02:41 The expected tables calculated based upon the percentage values for
• 02:46 each total row value and total column value from the actual table.
• 02:51 The value MSL is the row percentage times the column percentage times
• 02:55 the total count of all items.
• 02:57 Let's look at an example.
• 02:59 In this example, we want to determine the types of entertainment values people
• 03:03 attend is dependent upon their age.
• 03:06 The null hypothesis is that the attendance at the different venues and
• 03:09 the persons age are independent.
• 03:12 The alternative hypothesis is that the type of entertainment venue attended
• 03:15 does depend upon the age of individual.
• 03:18 This table is the actual's table.
• 03:20 The ages of divided into eight categories, and
• 03:23 there are seven different entertainment venues.
• 03:25 The total for each row and each column is added up and the total for
• 03:30 the entire table is added up in the lower right corner.
• 03:33 A total of 1181 data points in the table.
• 03:37 Now, the percentage for each row and each column are also
• 03:42 determined by dividing the row or column totals by 1181.
• 03:47 Now we build the expected table.
• 03:49 To do this for each cell, take the column percentage for that cell, multiply it
• 03:54 times the row percentage for that cell and then multiply that times the grand total.
• 04:00 So for our upper left cell, we take the column percentage for
• 04:03 movies of 19.31%, multiply it times the row percentage for
• 04:09 age 6 to 12 which is 5.42% and then multiply that
• 04:13 result times 1181 which is the total number of counts in the table.
• 04:19 This gives us a value of 12.36 for that cell.
• 04:24 Then continue that process for all of the other 55 cells in the table.
• 04:28 Now you are ready to use the CHISQ.TEST function.
• 04:31 The arguments for that function are the range in the two tables.
• 04:35 Be sure that you do not use the total and percentage rows and
• 04:38 columns in the actual table, just the rows and columns with data.
• 04:43 The answer from Excel is 1.59 times e to the -39, which means there are 38
• 04:50 0s to the right of the decimal point before we start to see any other numbers.
• 04:55 In Lean Six Sigma, we call that a P value of 0, so reject the null hypothesis.
• 05:00 The entertainment venue selected by an individual does depend upon their age.
• 05:06 Well the Chi Square Test is much easier to complete in Minitab.
• 05:09 The Minitab version of Chi Square Test uses the same actual table as Excel.
• 05:14 But Minitab will create the expected table for
• 05:16 you, you don't need to do that manually.
• 05:19 To do the test, go to the Stat pulldown menu, select Tables which is
• 05:23 near the bottom of the list, and then select Chi Square Test for association.
• 05:28 That will bring up this panel.
• 05:29 Assuming your data is in the table format, select Summarized Data in two-way table.
• 05:35 Then select the table columns that contain data.
• 05:38 Now select the column with your category labels.
• 05:41 In our example, it was the Ages column.
• 05:43 Minitab now creates expected table, runs the calculation, and
• 05:48 provides a P value just like with Excel.
• 05:50 The P value is 0, so reject the null hypothesis.
• 05:54 Age does influence entertainment venue selection.
• 05:57 The Chi Square takes some work to do that analysis in Excel.
• 06:02 It's definitely much easier in Minitab.
• 06:05 But whichever application you use,
• 06:07 this hypothesis test can bring order to confusion.

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