PSY201H1 Chapter Notes - Chapter 4: Statistic, Standard Deviation, Statistical Parameter
Problem with Sample Variability
A sample statistic is said to be biased if, on average, it consistently overestimates or underestimates the
corresponding population parameter.
- Samples consistently tend to be less variable than their populations
Extreme scores in a population tend to make the population variability relatively large
- HOWEVER, these extreme values are unlikely to be obtained when you are selecting a sample
- Thus the sample variability is relatively small.
- This means that the sample variability gives a biased estimate of population
variability.
- This bias is in the direction of underestimating the population value
rather than being right on the mark
The bias in sample variability is consistent & predictable thus it can be corrected.
- The purpose of adjustments is to make the resulting value for sample variance an accurate and
unbiased representative of the population variance.
Formulas for Sample Variance and Standard Deviation
- There is a change in notation in which M is used for the sample mean.
Formulas for sample variance and standard deviation divide SS by n-1, unlike population formulas which
divide by N.
- This adjustment is necessary to correct for the bias in sample variability
- This is to increase the value you will obtain.
For a sample:
- Sample variance = estimated population variance
- Sample standard deviation = estimated population standard deviation
Sample Variability and Degrees of Freedom
Population
Document Summary
A sample statistic is said to be biased if, on average, it consistently overestimates or underestimates the corresponding population parameter. Samples consistently tend to be less variable than their populations. Extreme scores in a population tend to make the population variability relatively large. However, these extreme values are unlikely to be obtained when you are selecting a sample. Thus the sample variability is relatively small. This means that the sample variability gives a biased estimate of population variability. This bias is in the direction of underestimating the population value rather than being right on the mark. The bias in sample variability is consistent & predictable thus it can be corrected. The purpose of adjustments is to make the resulting value for sample variance an accurate and unbiased representative of the population variance. There is a change in notation in which m is used for the sample mean.
