Variance & Standard Deviation
Variance & Standard Deviation Psyc-21621
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This 2 page Class Notes was uploaded by Amy Turk on Wednesday April 27, 2016. The Class Notes belongs to Psyc-21621 at Kent State University taught by Dr. Gordon in Spring 2016. Since its upload, it has received 8 views. For similar materials see Quantitative Methods Psych I in Psychlogy at Kent State University.
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Date Created: 04/27/16
PSYCH STATS POWERPOINT 5 ● the standard deviation tells us the typical, or standard, distance from the mean ● describes how spread out scores are in a distribution ● if the standard deviation is small, there’s not a lot of variability ○ if the standard deviation is big, there’s a lot of variability ● samples tend to be less variable than the population ○ when you’re pulling a subgroup from a larger group, it may not always be representative ○ sample stats can be biased ■ when the statistic is smaller than the parameter, it underestimates the population ■ when a statistic is bigger than the parameter, it over estimates the population ● the (n-1) in the equation corrects for bias in a sample data set ● variance: average of the squared deviation scores ● what influences variability? ○ extreme scores ■ range is most affected ■ variance and SD affected by squaring ○ sample size ■ range is directly related ■ SD is relatively unaffected ○ stability in samples ■ range varies heavily from sample to sample ■ variance and SD are stable ● degrees of freedom: ○ to adjust for bias, when finding the SD for a sample, we divide the SS by (n-1) ○ (n-1) allows values to be larger ■ larger SD = more variability ● samples underestimate variability, so (n-1) tries to make it bigger ● degrees of freedom: the number of scores that are free to vary ○ ex. I have a sample of 5 scores with a mean of 7 ■ the sum of the scores have to equal 35 ■ the first 4 scores are said to be free to vary because they can assume any value. The last score, however, cannot. ■ knowing the sample mean places a restriction on sample variability ● to calculate a z-score, you need the mean and the SD ○ will tell us exactly where the score is located relative to the mean and all other scores ○ standardization: so we can directly compare them to each other, even if they are from a different metric ● z-score: a standardized scored based on the population mean and population SD ○ indicates location of raw score ○ sign indicates positive relation to mean ■ mean has a z-score of zero ○ value indicates the distance from the mean ■ negative one indicates 1 SD below the mean ● step 1: subtract mean from the raw score ● step 2: divide by SD ● you need the raw score, mean, and standard deviation ● the value tells you how far away the score is from the mean ● we can also use the formula to figure out the raw score ○ X = M + z(S) ○ the sign is dependent on the z-score ● finding the standard deviation: ○ s = (x-m)/z ● 3 main uses of z-scores: ○ location of score ○ comparison across different measures ○ easy method of changing scale of measure ● you can take every score in a distribution and turn it into a z-score ● standardized distribution: group of scores that have been transformed to create predetermined values for the mean and SD ○ allows for comparisons across dissimilar distributions ● not changing the shape, just changing the metric ● mean = 0 ● SD = 1
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