Question

Create 2 data sets. One with 5 observations and the other with 15 observations. Illustrate how variance is sensitive to an extreme score. Also show how sample size mediates the effect of an extreme score.

Answer 1

take 2 data sets

DATA SET 1:- 1,2,3,4,30

DATA SET 2:-   1,2,3,4,5,6,7,8,9,10,11,12,13,14,30

FOR DATA SET 1:

Sample Standard Deviation, s	12.349089035228
Variance (Sample Standard), s2	152.5
Population Standard Deviation, ?	11.045361017187
Variance (Population Standard), ?2	122

FOR DATA SET 2

Sample Standard Deviation, s	7.0710678118655
Variance (Sample Standard), s2	50
Population Standard Deviation, ?	6.8313005106397
Variance (Population Standard), ?2	46.666666666667

(a) lets say data set is 1,2,3,4,5

its results are

Sample Standard Deviation, s	1.5811388300842
Variance (Sample Standard), s2	2.5
Population Standard Deviation, ?	1.4142135623731
Variance (Population Standard), ?2	2

now compare the results of above data set with data set 1. Due to the presence of value 30,there is a huge gap in the standard deviation from 2.5 to 152.5.

Thus, it measures spread around the mean. Because of its close links with the mean, standard deviation can be greatly affected if the mean gives a poor measure of central tendency. Standard deviation is also influenced by outliers onevalue could contribute largely to the results of the standard deviation.as standard deviation varies,So variance also varies.

(b) now compare data set 1 and data set 2

as the sample size increases from 5 to 15, the variance decreased from 152.5 to 50

If your effect size is small then you will need a large sample size in order to detect the difference otherwise the effect will be masked by the randomness in your samples. Essentially, any difference will be well within the associated confidence intervals and you won’t be able to detect it.larger sample sizes give more reliable results with greater precision and power, but they also cost more time and money.