Wednesday, October 3 Variability

nominal ordinal interval

nominal ordinal interval Range Interquartile Range Variance Standard Deviation

Range

Interquartile Range

X _

Population Sample X µ _ The population mean is µ. The sample mean is X. _

Population Sample X µ _ The population mean is µ. The sample mean is X. The population standard deviation is , the sample sd is s. _  s

SS Variance of a population,  2 (sigma squared). It is the sum of squares divided (SS) by N N 22 =

SS Variance of a population,  2 (sigma squared). It is the sum of squares divided (SS) by N N 22 =  (X –  ) 2

SS The Standard Deviation of a population,  It is the square root of the variance. N  = This enables the variability to be expressed in the same unit of measurement as the individual scores and the mean.

Population Sample X µ _ The population mean is µ. The sample mean is X. _

Population Sample X µ _ The population mean is µ. The sample mean is X. The population standard deviation is , the sample sd is s. _  s

Population Sample A X A µ _ Sample B X B Sample E X E Sample D X D Sample C X C _ _ _ _ In reality, the sample mean is just one of many possible sample means drawn from the population, and is rarely equal to µ.

Population Sample A X A µ _ Sample B X B Sample E X E Sample D X D Sample C X C _ _ _ _ In reality, the sample mean is just one of many possible sample means drawn from the population, and is rarely equal to µ.  sasa sbsb scsc sdsd sese

Sampling error = Statistic - Parameter Sampling error for the mean = X - µ _ Sampling error for the standard deviation = s - 

Unbiased and Biased Estimates An unbiased estimate is one for which the mean sampling error is 0. An unbiased statistic tends to be neither larger nor smaller, on the average, than the parameter it estimates. The mean X is an unbiased estimate of µ. The estimates for the variance s 2 and standard deviation s have denominators of N-1 (rather than N) in order to be unbiased. _

SS N 22 =

(N - 1) s2s2 =

SS (N - 1) s2s2 =  (X – X ) 2 _

SS (N - 1) s =

Conceptual formula VS Computational formula

What is a measure of variability good for?