Chi Square

Quick reference

• 00:04 Hi, I'm Ray Sheen.
• 00:06 Sometimes we have many discrete data sets, and
• 00:08 we want to understand whether there's a relationship between them.
• 00:12 The Chi-Square hypothesis test will answer that question for us.
• 00:18 >> Start with our hypothesis test decision tree.
• 00:21 We go to the discrete X and Y data and
• 00:24 more than two variables which is the Chi-Square test.
• 00:29 The Chi-Square test is ideally suited for multiple attribute data hypotheses.
• 00:34 If you have two or more discrete variables in your sample,
• 00:37 it can be used to determine if they are independent or if they are linked.
• 00:42 Some of you may be aware of other uses of Chi-Square test and basic research,
• 00:46 such as checking for goodness of fit or homogeneity.
• 00:50 We will be focusing on the Lean Six Sigma projects, and
• 00:53 multiple discrete attribute testing.
• 00:56 And it can use more than just true false or on off data.
• 01:00 It's excellent for counts.
• 01:02 If you're only comparing two samples, the two sample tests or proportions is best.
• 01:07 But if you are comparing two or
• 01:08 more variables within one sample then use this test.
• 01:12 This test relies on the number of counts for each variable attribute characteristic
• 01:17 to determine if the different attributes are truly independent or
• 01:20 if they are related to each other or some other factor.
• 01:25 When using this test in Lean Six Sigma, be careful to choose your categories for
• 01:29 real potential root causes.
• 01:31 The Chi-Square test doesn't know if the categories make sense to be tracked
• 01:35 separately.
• 01:36 So if you're trying to determine factors relating to people who have arthritis,
• 01:41 Chi-Square will likely show that there is a relationship between people with gray
• 01:45 hair and arthritis.
• 01:47 But that does not mean that gray hair causes arthritis.
• 01:51 Obviously, much more relevant factor would be age which
• 01:54 increases the likelihood of both gray hair and susceptibility to arthritis.
• 01:59 The null hypothesis for the Chi-Square is always that the factors are all
• 02:03 independent, there is nothing connecting any of them.
• 02:07 The alternative hypothesis is that the factors are dependent.
• 02:11 There is a relationship between at least two of the factors.
• 02:14 Let me explain the Chi-Square statistic.
• 02:17 The Chi-Square test will use both the actual data and
• 02:21 a table of expected values which is referred to as a contingency table.
• 02:26 Two mirror image tables, at least in format, are created.
• 02:30 One table has the actual values, and the other table will have expected values,
• 02:34 if there were no relationships between the factors.
• 02:38 With these two tables, the chi-square statistic is calculated
• 02:42 by comparing the proportions from the actual data and the calculated data.
• 02:46 The formula is shown here.
• 02:49 The calculated Chi-Square value is then compared to the Chi-Square value from this
• 02:53 lookup table.
• 02:54 The lookup table is based upon the selected alpha, and
• 02:57 the number of degrees of freedom.
• 03:00 Let's look at how to do this with Excel.
• 03:02 It's a rather complex process that must be followed.
• 03:06 Excel uses the CHISQ TEST function to compare tables of actual values and
• 03:11 the one of expected values.
• 03:14 The actual value we can get from our data.
• 03:17 The expected value we have to create manually.
• 03:20 Both tables are structured in the same manner.
• 03:23 The columns are the event categories where we have the count data.
• 03:27 The rows are the categories that we are using to create the different proportions.
• 03:32 The actual table is easy to populate.
• 03:35 Create your rows and column categories and
• 03:37 then count the instances for each cell in the table.
• 03:41 The expected table is calculated by using the percentage values for
• 03:45 each total row and total column from the actual table.
• 03:49 The value of a cell in the expected table is the row percentage from the actual
• 03:53 table times the column percentage from the actual table times the total count of all
• 03:58 the items in the actual table.
• 04:01 Let's look at an example.
• 04:03 In this example we want to determine if the types of entertainment venues
• 04:06 people attend, is dependent upon their age.
• 04:09 The null hypothesis is that attendance at the different venues and
• 04:13 a person's age are independent.
• 04:15 The alternative hypothesis is that the type of entertainment venue attended does
• 04:20 depend upon the age of the individual.
• 04:23 This table is the actual table.
• 04:25 Their ages are divided into eight categories and
• 04:28 there are seven different entertainment venues.
• 04:31 The total for each row and each column is added up.
• 04:34 And the total for the entire table is added up in the lower right corner.
• 04:39 A total of 1181 data points are in this table.
• 04:42 Now the percentage for each row and
• 04:44 each column is also determined by dividing the row or column total by 1,181.
• 04:51 Next we will build the expected table.
• 04:53 To do this for each cell, take the column percentage for that cell,
• 04:57 multiply it times the role percentage for that cell, and
• 05:00 then multiply it times the grand total.
• 05:03 So in our upper left cell, we take the column percentage for
• 05:07 movies of 19.31%, multiply it times the row percentage for
• 05:13 age 6-12, which is 5.42%, and then multiply that result times 1,181.
• 05:19 Which is the total number of counts in the table.
• 05:23 This gives us a value of 12.36 for that cell.
• 05:27 Then continue with this process for all of the other 55 cells in the table.
• 05:33 Now you are ready to use the Chi-Square test function.
• 05:36 The argument for that functions are the range of the two tables.
• 05:40 Be sure that you do not use the total and percentage rows and
• 05:43 columns in the actual tables, just the rows and columns with data.
• 05:48 The answer from Excel is 1.59 times E to the minus 30 nights which means there
• 05:53 are 38 zeros to the right of the decimal point before we start to see any numbers.
• 06:00 In Lean Six Sigma, we call that P value 0.
• 06:03 So reject the null hypothesis.
• 06:06 The entertainment venues selected by individuals does depend upon their age.
• 06:10 Well, the Chi-Square test function is much easier to complete in Minitab.
• 06:15 The mini tap version of Chi-Square test uses the same actual table as Excel.
• 06:20 But Minitab will create the expected table for you so you don't need to do that.
• 06:25 To do this test, go to the stat pulldown menu, select tables, which is
• 06:30 near the bottom of the list and then select Chi-Square test for association.
• 06:34 That will bring up this panel.
• 06:37 Assuming your data is in the table format, select summarize data into a table.
• 06:43 Then select the table columns that contain the data.
• 06:47 Now select the columns with your category label.
• 06:50 In our example, it was the Age column.
• 06:53 Minitab now creates the expected value, runs the calculation, and
• 06:57 provides a P-value.
• 06:59 Just like with Excel, the P-value is 0, so reject the null hypothesis.
• 07:03 Age does influence the entertainment venue selection.
• 07:07 >> Chi-Square takes some work to do the analysis in Excel,
• 07:10 but it is much easier in Minitab.
• 07:13 Now whichever approach you use,
• 07:15 this hypothesis test can help us to bring order from confusion.

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