Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download Lecture 4 Slides (Variability)
Document related concepts
Transcript
Wednesday, October 3 Variability nominal ordinal interval nominal ordinal Range Interquartile Range interval Variance Standard Deviation 610 600 590 580 570 560 DIS2 550 540 .4 T .6 .8 1.0 1.2 1.4 1.6 610 600 590 580 Range 570 560 DIS2 550 540 .4 T .6 .8 1.0 1.2 1.4 1.6 610 610 600 600 590 590 580 580 Interquartile Range DIS2 Range 570 570 560 560 550 550 540 540 .4 T .6 .8 1.0 N =1.2 23 1.4 DIS2 1.6 610 600 590 _ X 580 570 560 DIS2 550 540 .4 T .6 .8 1.0 1.2 1.4 1.6 Population µ Sample _ X _ The population mean is µ. The sample mean is X. Population µ Sample _ X s _ The population mean is µ. The sample mean is X. The population standard deviation is , the sample sd is s. Variance of a population, 2 (sigma squared). It is the sum of squares divided (SS) by N 2 SS = N Variance of a population, 2 (sigma squared). It is the sum of squares divided (SS) by N 2 2 SS = N (X – ) The Standard Deviation of a population, It is the square root of the variance. SS = N This enables the variability to be expressed in the same unit of measurement as the individual scores and the mean. Population µ Sample _ X _ The population mean is µ. The sample mean is X. Population µ Sample _ X s _ The population mean is µ. The sample mean is X. The population standard deviation is , the sample sd is s. Sample _ C XC Sample _ D XD Population Sample _ B µ Sample _ E XE XB Sample _ A XA In reality, the sample mean is just one of many possible sample means drawn from the population, and is rarely equal to µ. Sample _ C XC sc Sample _ D XD sd Population Sample _ B µ Sample _ E XE se XB sb Sample _ A XA sa In reality, the sample mean is just one of many possible sample means drawn from the population, and is rarely equal to µ. 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 s2 and standard deviation s have denominators of N-1 (rather than N) in order to be unbiased. 2 SS = N SS s2 = (N - 1) _2 (X – X ) SS s2 = (N - 1) s SS = (N - 1) Conceptual formula VS Computational formula What is a measure of variability good for?
