Hi everybody,At my workplace blackbelts’ have a reunion every 3 or 4 months to take a review test and to review 6s tools.During todays session, while reviewin Hypothesis Testing, some of my fellow bb’s and I had a disagreement with the instructor, a very experienced master black belt.We could not change his position regarding a specific excercise which I will describe next. I would appreciate your feedback and comments, because I feel pretty sure we are correct and he is wrong.Situation:.
Real life situation.There are two point-of-purchase sellers, who work under the same selling policies. You have the suspect that one of them is giving far more discounts that the second one. To prove this, you test the two sellers by telling each one of them to “invoice” 10 different sales. (You give each specific sale to both).The question was to decide what to use: paired-t or 2 sample-tSeller A Seller BMean $1193.04 $1195.37Std Dev 2.64 2.37For me it was pretty obvious that a paired-t should be used, since the two sellers were proven under each specific sale. In this case the two sellers could be considered different.The master black belt’s argument was that since the standard deviation was very low, it meant that all the sales were around the same amount, and they could be taken as normally distributed. For that reason he decided to use a 2 sample-t.
The two-sample t-test is a hypothesis test for answering questions about the mean where the data are collected from two random samples of independent.
In this case the two sellers could be considered equal.Both methods gave a different result to the hypothesis test, and therefore my answer in the test is “wrong”.Since we do not know more information than the shown above, I feel a paired-t should be use.What do you think?Thanks in advance for your feedback,FNF. Hi,Here we have to think about the applicability of the tests i.e. Paired and Two Sample T-test.Two-sample t-test is used to determine if two population means are equal.The data may either be paired or not paired. Refer to Six Sigma Dictionary)For paired t test, the data is dependent, i.e.
There is a one-to-one correspondence between the values in the two samples.For example, same subject measured before & after a process change, or same subject measured at different times.For unpaired t test, the sample sizes for the two samples may or may not be equal.Hence in my opinion paired t-test is the right choice (Same sales given to both the parties). SK,I agreed with everything you said until you jumped to the conclusion that a paired t test is the right choice.
I thought you made a perfect argument that this should be a 2-sample t test.If the same invoices had been given to the same salesperson before and after a training session, then a paired t would be the obvious choice. But since they were given to two completely different salespeople, then the results are clearly independent.The given example would be like running two sets of samples through parallel machines in a manufacturing plant. You would never run a paired t test on that dataSP. Most of the battle in deciding to use a paired-t vs. 2-sample-t comes with determining how to design the study. A paired-t design should block a significant portion of the uncontrolled variation, in this case the unit-to-unit variation.
Naturally, paired-t tests are more difficult to execute because you have to choose the units to be tested and hold them constant between subjects. Fortunately this has already been done for you, so based on the example, I agree that the paired-t would work, but I say that with some trepidation. The paired-t should be able to detect smaller differences between sellers since the unit-to-unit variation is effectively blocked. However, in the POS world, other sources of variation like customer behavior and economic conditions due to time or geography could make this testing method impractical because the variation you see will include all of this in addition to the seller-to-seller variation.In general, the paired-t should be more informative than the 2-sample-t because you have (hopefully) blocked a significant portion of the unit-to-unit variation. Just be careful in assuming that all the variation that you see is due exclusively to the differences between subjects.
Essentially, a t-test allows us to compare the average values of the two data sets and determine if they came from the same population. In the above examples, if we were to take a sample of students from class A and another sample of students from class B, we would not expect them to have exactly the same mean and standard deviation.
Similarly, samples taken from the placebo-fed control group and those taken from the drug prescribed group should have a slightly different mean and standard deviation. A t-test is a type of inferential statistic used to determine if there is a significant difference between the means of two groups, which may be related in certain features. The t-test is one of many tests used for the purpose of hypothesis testing in statistics. Calculating a t-test requires three key data values. They include the difference between the mean values from each data set (called the mean difference), the standard deviation of each group, and the number of data values of each group. There are several different types of t-test that can be performed depending on the data and type of analysis required.Ambiguous Test Results. After the drug trial, the members of the placebo-fed control group reported an increase in average life expectancy of three years, while the members of the group who are prescribed the new drug report an increase in average life expectancy of four years.
![Two sample t-test calculator Two sample t-test calculator](/uploads/1/2/5/5/125503843/868966678.jpg)
Instant observation may indicate that the drug is indeed working as the results are better for the group using the drug. However, it is also possible that the observation may be due to a chance occurrence, especially a surprising piece of luck. A t-test is useful to conclude if the results are actually correct and applicable to the entire population. In a school, 100 students in class A scored an average of 85% with a standard deviation of 3%.
Another 100 students belonging to class B scored an average of 87% with a standard deviation of 4%. While the average of class B is better than that of class A, it may not be correct to jump to the conclusion that the overall performance of students in class B is better than that of students in class A. This is because, along with the mean, the standard deviation of class B is also higher than that of class A. It indicates that their extreme percentages, on lower and higher sides, were much more spread out compared to that of class A. A t-test can help to determine which class fared better. The first assumption made regarding t-tests concerns the scale of measurement.
The assumption for a t-test is that the scale of measurement applied to the data collected follows a continuous or ordinal scale, such as the scores for an IQ test. The second assumption made is that of a simple random sample, that the data is collected from a representative, randomly selected portion of the total population. The third assumption is the data, when plotted, results in a normal distribution, bell-shaped distribution curve. The fourth assumption is a reasonably large sample size is used. Larger sample size means the distribution of results should approach a normal bell-shaped curve.
The final assumption is the homogeneity of variance. Homogeneous, or equal, variance exists when the standard deviations of samples are approximately equal. The t-test produces two values as its output: t-value and degrees of freedom. The t-value is a ratio of the difference between the mean of the two sample sets and the difference that exists within the sample sets. While the numerator value (the difference between the mean of the two sample sets) is straightforward to calculate, the denominator (the difference that exists within the sample sets) can become a bit complicated depending upon the type of data values involved.
The denominator of the ratio is a measurement of the dispersion or variability. Higher values of the t-value, also called t-score, indicate that a large difference exists between the two sample sets.
The smaller the t-value, the more similarity exists between the two sample sets.