One Sample Tests

Quick reference

• 00:04 Hi, I'm Ray Sheen.
• 00:05 The next set of tests are used to understand to what degree you can use
• 00:10 a dataset, is it representative or not?
• 00:14 I'll start again with the hypothesis test decision tree.
• 00:18 We are working with normal, discrete, and continuous data.
• 00:22 These are the tests that are used when there is only one dataset for analysis.
• 00:27 Let's take a minute to talk about testing with only one dataset sample.
• 00:32 These tests are normally done to demonstrate that the dataset is part of
• 00:37 a larger population, or is not from that same population.
• 00:40 But the analysis team does not have access to the larger population data.
• 00:45 They only have access to some descriptive statistics that represent that data.
• 00:50 So to conduct one sample test,
• 00:52 we need to have the descriptive statistics from the larger data population.
• 00:56 That might be historic statistics, such as the demonstrated process
• 01:01 performance when the new system was first installed.
• 01:04 It could be tied to industry comparison data.
• 01:07 For instance, if you're working in a call center, you would want to compare
• 01:11 your process performance to the industry average data for other call centers.
• 01:15 Sometimes it's not even based upon an actual population, but rather the data is
• 01:20 being compared against a target or goal that was embedded in the project charter.
• 01:26 Once you have the target value, now you can test to see if the mean of your
• 01:30 dataset matches the target mean or if the variance matches the target variance.
• 01:36 Let's think about this in the historical context,
• 01:38 since that's the way I've traditionally used this test.
• 01:42 You could check your mean against the historic mean to see if there's been
• 01:46 a shift in the process performance, either better or worst.
• 01:49 A shift in that performance would imply a special cause.
• 01:53 Or you could test your variance against the historic target variance to determine
• 01:58 if your standard deviation was smaller or larger.
• 02:01 A change in variance implies a change in the common cause factors that
• 02:06 are part of the routine process performance.
• 02:09 If you start with the one sample T test,
• 02:12 the test is somewhat similar to the one sample test of proportions.
• 02:16 Only instead of a target proportion, the target is a value for the mean.
• 02:21 The one sample T test checks the sample to see
• 02:24 if the mean is statistically different from the target value.
• 02:28 This is often used to test to see if there's a real difference in a product or
• 02:32 process after an improvement has been incorporated.
• 02:35 The target value being the original performance before the improvement.
• 02:39 Of course, we're working with normal data.
• 02:42 Otherwise, the mean value is not a meaningful number.
• 02:45 The hypothesis statements are very straightforward.
• 02:48 The null hypothesis is that the sample mean is equal to the target mean,
• 02:52 there's nothing unusual or special in the sample.
• 02:55 The alternative hypothesis is that the sample mean is not equal.
• 02:59 It could be specifically stated that it is greater than or less than the target.
• 03:04 The T statistic is a simple calculation,
• 03:07 the difference between the target and the actual value.
• 03:10 This is divided by the standard deviation over the square root of the number of
• 03:15 items in the sample.
• 03:16 So let's take a look at the calculation.
• 03:19 Excel does not provide a one sample T-test function.
• 03:22 So if you're working with Excel, calculate the T statistic using the formula from
• 03:28 the previous slide, then compare the value to the t value in the table shown here.
• 03:33 Enter the table using the alpha value and the number of degrees of freedom.
• 03:38 Minitab has a function, start with the Stat pulldown menu,
• 03:42 then select Basic Statistics, and select 1- Sample T, and
• 03:46 enter the column with your sample data.
• 03:49 Then check the box for hypothesis test,
• 03:52 and enter the target value in the field labeled Hypothesis mean.
• 03:56 The default is to check if the mean is not equal.
• 03:59 If you want to specifically check for greater than or less than, then select
• 04:04 the option button and change the field, just as we have done with other tests.
• 04:09 Next, we will consider the one sample variance test.
• 04:13 This test is very similar to the one sample T test only checks the sample to
• 04:18 see if the variance is statistically different from the target value.
• 04:22 This is often used to test if there's a change in the process environment and
• 04:26 process management.
• 04:28 It could be to see if there were any degradation over time, or
• 04:32 it could be used in the improve phase to see if the improvements reduce the common
• 04:37 cause variation, the target value being the original performance.
• 04:41 Of course, we're working with normal data, otherwise,
• 04:44 standard deviation would not be a useful measure in this test.
• 04:48 The hypothesis statement could use variance or standard deviation,
• 04:52 I've seen it both ways, although the purists would say that variance is better.
• 04:57 The null hypothesis is that the sample variance is equal to the target variance,
• 05:01 nothing has changed to affect the process variability.
• 05:05 The alternative hypothesis is that the sample variance is not equal.
• 05:09 It could be specifically stated that it is greater than or less than the target.
• 05:14 Excel does not provide a 1-Sample variance test function.
• 05:18 If working with Excel, use the formula for Chi-Squared variance.
• 05:22 This is the sample deviation squared,
• 05:24 multiplied by the number of items in the sample -1.
• 05:28 That is then divided by the variance of the target population.
• 05:32 Minitab has a 1-Sample variance test.
• 05:35 Start with the Stat pull down menu, then select Basic statistics, and
• 05:40 select 1-Variance.
• 05:41 Enter the column with your sample data, then check the box for hypothesis test.
• 05:46 You then select to either provide a target variance or a target standard deviation.
• 05:51 The default is to check to see if they are equal.
• 05:54 If you want to check for greater than or less than you must select the option
• 05:58 button and then change the field, just as we've done with the other tests.
• 06:03 Whether you're checking the mean or variance on just one sample of data,
• 06:08 these tests can tell you if something is different.
• 06:11 Either different from a historical perspective or
• 06:14 hopefully different in a better way after you've implemented your improvement.

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