Question

22. Wegesin and Stern (2004) found greater consistency (less variability) in the memory performance scores for younger women than for older women. The following data represent memory scores obtained for two women, one older and one younger, over a series of memory trials. a. Calculate the variance of the scores for each woman. b. Are the scores for the younger woman more consistent (less variable)?

Answer 1

For younger women,

Mean score $= \frac{8+6+6+7+8+7+8+8}{8} = 7.25$

Variance of score

$= \frac{1}{8}[(8 - 7.25)^2 +(6 - 7.25)^2+(6- 7.25)^2+(7 - 7.25)^2+(8 - 7.25)^2+(7 - 7.25)^2+(8 - 7.25)^2+(8 - 7.25)^2]$

$= \frac{1}{8}[0.5625+1.5625+1.5625+0.0625+0.5625+0.0625+0.5625+0.5625]$

$= 0.6875$

For older women,

Mean score $=\frac{7+5+8+5+7+6+8+5}{8} = 6.375$

Variance of score

$=\frac{1}{8}[(7- 6.375)^2 + (5- 6.375)^2 + (8- 6.375)^2 + (5- 6.375)^2 + (7- 6.375)^2 + (6- 6.375)^2 + (8- 6.375)^2 + (5- 6.375)^2 ]$

$=\frac{1}{8}[0.390625+1.89063+2.64063+1.89063+0.390625+0.140625+2.64063 +1.89063 ]$

$= 1.48438$

b) Since

score variance for younger women < score variance for older women,

So, scores for younger women is less consistent.