Test of Proportions

Quick reference

• 00:05 Hi, I'm Ray Sheen.
• 00:06 You know, we've discussed hypothesis testing when
• 00:09 both the response variable and the independent variable are continuous.
• 00:12 Now it's time to look at the case when both are discreet,
• 00:15 and we'll start with a look at the test of proportions.
• 00:20 So let's look at our hypothesis testing decision tree.
• 00:24 We're still working with normal data, but
• 00:26 now we're considering the case when the data is discreet, both x and y values.
• 00:31 That means that we're working with counts instead of measurements.
• 00:34 And in this lesson we'll discuss one sample test of proportion and
• 00:38 the two sample test of proportions.
• 00:41 Before we go into how to run the test,
• 00:43 let's first explain what a test of proportions does.
• 00:47 Test of proportions is used with discrete or attribute data, so
• 00:50 the data will be counts of occurrences or true, false and on, off types of data.
• 00:56 The tests proportions will compare the percentage of items in the sample that
• 00:59 contain a particular attribute to another percentage, either from another sample or
• 01:04 from a baseline value.
• 01:05 The question is to determine if the proportion or percentage are the same, or
• 01:10 more precisely, if there are differences in the proportion, and
• 01:14 are the differences statistically significant?
• 01:16 This test is not testing means or standard deviation,
• 01:20 it is testing the percentage of counts in the category of interest.
• 01:24 The one sample test will compare the proportion to a target value.
• 01:27 It has been set based upon historic measurements or
• 01:30 the known value of another large population.
• 01:33 The null hypothesis will be that the sample proportion equals the target value,
• 01:37 nothing unusual is in the sample.
• 01:40 The alternative hypothesis will normally be that the sample proportion value
• 01:44 is larger or smaller than the target value.
• 01:47 The two Sample Test of Proportion does a similar comparison, except that the target
• 01:51 value is replaced with the proportional value found in a second data sample.
• 01:56 This test is normally used to determine if two samples are different or
• 01:59 are they from the same population.
• 02:01 It's very common to use this test with complaint or defect data and a before and
• 02:05 after comparison.
• 02:07 The two samples being before an improvement is introduced and
• 02:10 after an improvement is introduced.
• 02:12 The null hypothesis is always at the proportion of the two samples are equal,
• 02:16 which means that the subtracting one from the other results in 0.
• 02:20 The alternative hypothesis is that the proportions are not equal.
• 02:23 These set hypothesis are used in the analysis phase
• 02:26 to discover the differences that will lead to an understanding of the problem.
• 02:30 In doing the before and after type of comparison that is normally done in
• 02:33 the improve phase, we often want to show that the improve proportion is higher or
• 02:39 lower proportion than the original proportion.
• 02:41 In that case, the Null Hypothesis is normally that the two proportions
• 02:45 are equal, and the alternative hypothesis is that the new proportion is higher
• 02:49 than or lower than the base line proportion, and of course
• 02:53 the test is to determine if those differences are statistically significant.
• 02:57 Let's consider how we do the one sample test of proportions.
• 03:01 For our example, we'll consider the percentage of applications to college for
• 03:05 the current college year that have been accepted.
• 03:07 Historically the college has excepted 52% of applicants.
• 03:11 This year it was 57%.
• 03:12 Is the change significant?
• 03:15 The null hypothesis would be that this year's
• 03:17 percentage of applicants that were accepted is equal to the historic average.
• 03:22 The alternative hypothesis would be that this year's percentage
• 03:24 is higher than the historical average.
• 03:27 Excel does not perform this test, but in Minitab we select the stat pull down menu,
• 03:33 then select the Basic Statistics, and next select 1 Proportion.
• 03:38 That will bring up this panel.
• 03:39 Now select the column where your data's located.
• 03:42 We need to have a raw data so that Minitab has account on this sample size.
• 03:47 Recall that the sample size will impact the confidence interval.
• 03:51 Enter your target statistic in the window labelled hypothesis proportion.
• 03:55 If you select the option button, you can designate whether you want to test for
• 03:59 the relationship of either greater than or less than.
• 04:02 Then click okay, and the results will be found in the session window of Minitab,
• 04:06 with a P value that you can use to decide whether to reject the null hypothesis or
• 04:11 fail to reject the null hypothesis.
• 04:13 Now let's look at the two sample test of proportions.
• 04:16 We're comparing the proportions of an attribute between two samples of data.
• 04:20 In this illustration, the comparison is on the rate of on time
• 04:24 submittals of tax returns between 2016 and 2017.
• 04:28 Excel dos not provide this as a standalone function,
• 04:31 but we could still do this analysis on Excel, it just takes a few steps.
• 04:36 So there are several functions of Excel that,
• 04:37 when we string them together, can do the analysis.
• 04:41 One caution, make sure your data is in integer form,
• 04:44 because Excel will be doing calculations with it.
• 04:47 Start with the standard VAR or variance function for each data set.
• 04:51 Be sure to record those values for future use.
• 04:54 Next, go to the Data Analysis pull-down menu and select the z-test,
• 04:59 two samples for mean function and to the data range and
• 05:04 the previously calculated variances for each sample in the form that is displayed.
• 05:09 Also enter any difference that there's one you're expecting.
• 05:12 I normally set this one to zero.
• 05:14 Excel will give you a p value for both the greater than and
• 05:17 less than relationships Minitab is simpler.
• 05:21 Select Stat, then Basic Stats and then 2 proportion.
• 05:25 Select the format of your data, either all data in one column within the adjacent
• 05:30 column that specified which sample is associated with the data value, or
• 05:34 the data in two different columns where the sample is the column title.
• 05:39 Then select the appropriate data column and finally go to option button to change
• 05:42 the confidence level or to specify relationship.
• 05:46 The default is to check that they're equal, but
• 05:48 you can change that to make one greater than or less than the other.
• 05:51 The result is found in the session window with an associated p value.
• 05:55 Excel and Minitab will give slightly different results for p values.
• 05:59 But I find the differences are out of the third significant digit and are unlikely
• 06:03 to impact the decision of whether or not to reject the null hypothesis.
• 06:09 The one sample and two sample test of proportions are quick and easy tests that
• 06:13 help us understand the characteristics of a dataset made up of discreet data.

Lesson notes are only available for subscribers.