Questions: One sample has M=18 and a second sample has M=14. If the pooled variance for the two samples is 16, what is the value of Cohen's d? 0.25 0.50 1.00 Cannot be determined with the information given

Solution Steps

To calculate Cohen's \( d \), we need the means of the two samples and the pooled standard deviation. The formula for Cohen's \( d \) is:

\[ d = \frac{M_1 - M_2}{s_p} \]

where \( M_1 \) and \( M_2 \) are the means of the two samples, and \( s_p \) is the pooled standard deviation. Given the pooled variance, we can find the pooled standard deviation by taking the square root of the pooled variance.

We have two sample means:

• \( M_1 = 18 \)
• \( M_2 = 14 \)

The pooled variance is given as:

• \( \text{pooled variance} = 16 \)

The pooled standard deviation \( s_p \) is calculated as follows: \[ s_p = \sqrt{\text{pooled variance}} = \sqrt{16} = 4.0 \]

Cohen's \( d \) is calculated using the formula: \[ d = \frac{M_1 - M_2}{s_p} \] Substituting the values: \[ d = \frac{18 - 14}{4.0} = \frac{4}{4.0} = 1.0 \]

Final Answer