The main question I have about the statistics after reading the ad is where are the statistics? There is no analysis and yet the conclusions made by the company was that the shoes provide an “obvious vertical lift” which could be clearly seen based on the data. But you can’t conclude they are actually different unless you analyze the data statistically.
Placing four players into five groups is a good way to approach the data collection althoughit doesn’t say anything about sampling and assignment and larger sample sizes would have improved the design. In addition, using a more diversified sample would have given more information. Given these are basketball players they are used to pushing themselves to jump their highest. So while these shoes may give a slight advantage it would be difficult to determine if the difference is statistically significant given there may be range restriction.
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A summary of the main problems I see with this analysis is seen in the bulleted list below:
• No random sampling or random assignment used
• Sample size not large enough
• Possible range restriction issues
• Only used basketball players so even if inferential statistics were used you couldn’t generalize the results to the general population.
• No report of demographics so don’t know if any of these types of factors could have played a role in the outcomes.
The calculation of means for the purpose of comparison was a good step but you can’t eyeball them and tell if there is a meaningful difference. You need a statistical test, specifically an ANOVA. The type of ANOVA would be a one way balanced ANOVA since there is only one outcome variable and the same number of players in each group. The ANOVA would determine whether there differences between any of the groups in the study. However, it wouldn’t determine which groups differed significantly from the other groups. For that you would need to use post hoc tests to test each group against the others, like The Tukey test or the Scheffe test.
