Answer to Question #139274 in Statistics and Probability for Jeanina Muñoz

Question

The new memory enhancer X recently gained a reputation in the market as the most effective memory enhancer ever produced by XY Pharma. The recorded average memory level among people who had taken the enhancer was 95 with a standard deviation of 10. As a neuroscientist, you want to test the claim and conducted a study and measure the memory level of 50 participants. The average memory level of the participants came out to be 80. Compute the effect size using the formula in the example above.

Answer 1

The provided sample mean is $\bar{X}=80$ and the known population standard deviation is $\sigma=10,$ and the sample size is $n=50.$

The following effect size (Cohen's d) is computed as:

$$d=\dfrac{|\bar{X}-\mu|}{\sigma}=\dfrac{|80-95|}{10}=1.5$$

Interpretation: The effect size obtained is $d=1.5.$ According to guidelines specified by Cohen, this corresponds to a large effect size( $d>0.8$ ).