Testing whether one mean is higher than another

In summary, the conversation discusses a problem in class involving the quantity of items sold and promotion levels. The hypothesis is that the average quantity sold during a promotion is significantly higher than when there is no promotion. The professor suggests using a regression approach to test this hypothesis, but there are concerns about categorizing the data and the potential for unequal population variances. Alternatively, the conversation considers using a linear regression and checking the p-value for the slope, but there may be limitations with this approach depending on the data.
  • #1
Tom McCurdy
1,020
1
There was a problem that was talked about in class where we had the amount of quantity sold in one column and the promotion level in another column. The promotion took values between 0 and 0.88 with a number of values being zero.

The problem discussed was to test the following hypothesis
The average quantity sold by Bob when there is a promotion (p>0) is significantly higher than when there is no promotion.

My professor claimed the problem should be solved using regression. He had the independent column as the promotion value and the dependent column as the quantity sold. Then his plan was to use the regression results in excel to test whether or not the slope was equal to zero.

Now the biggest mistake I see right away is that he would need to categorize it into a discrete system where you have group 1) promotion, and group 2) no promotion. The second problem I see is then what arbitrary value do you give the group 1) of promotion


Now it's been awhile since I have taken a statistics class but from what I remember when you are doing hypothesis testing for two sample means and you have
[tex] H_0 : \mu_{promo} = \mu_{no-promo} [/tex]
[tex] H_1 : \mu_{promo} > \mu_{no-promo} [/tex]

Now the sample sizes are different
the promo category had 201 samples
the non promo category had 17 samples

Now you would need to decide if you could consider the population variances to be equal.
If they were equal you would test the means in one fashion, and if they weren't equal you had to test the means in another fashion... which was a substantial amount of work.

Is my professor right... can you just bypass this all by simply putting the numbers into two categories and doing a linear regression and checking the p-value for their slope?
 
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  • #2
For the professor's approach, which is essentially a graphics approach, but with Excel doing the calculations, it's not clear to me how you would plot the points representing the different samples. For the 17 samples where there was no promotion, you would have points scattered along the vertical axis.

If by "promotion" you mean something like "10% price drop" and "20% price drop," the graph would have many points scattered along vertical lines at the locations on the horizontal axis for the various price drops. I suppose you could find the line of best fit (i.e., use a regression line), but you'd want to take the calculated slope of the line with a grain of salt if the correlation coefficient R was large.
 

1. What is the purpose of testing whether one mean is higher than another?

The purpose of this test is to determine if there is a statistically significant difference between the means of two populations. This can be useful in comparing the effectiveness of different treatments or interventions, or in determining if there is a significant difference between two groups.

2. How is this test performed?

This test is typically performed using a t-test, which calculates the probability of obtaining the observed difference in means if there is truly no difference between the populations. This probability is compared to a predetermined significance level, usually set at 0.05, to determine if the difference is statistically significant.

3. What assumptions are made when performing this test?

The main assumptions made when performing this test are that the data is normally distributed and that the two populations have equal variances. If these assumptions are not met, alternative tests such as the Wilcoxon rank-sum test may be used.

4. Can this test be used for more than two populations?

Yes, this test can be extended to compare the means of more than two populations using analysis of variance (ANOVA). However, ANOVA assumes that the populations have equal variances and that the data is normally distributed.

5. What are the potential limitations of this test?

One potential limitation of this test is that it only compares the means of two populations and does not take into account any other factors that may be influencing the outcome. Additionally, if the sample sizes are small, the test may not accurately reflect the true difference between the populations.

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