University:
York University
Course:
PSYC 2021 | Statistical Methods I
Academic year:

2024
Views:

390

Pages:

3
Author:

Nick T.

Measuring Variance and Standard Deviation (Sample) goal of inferential Statistics: -draw general conclusions about population. - based on limited information from a Sampie Sampies differ from the population - Samples have less variability - Computing the variance and standard deviation in the same way as for a population would give a biased estimate of the population values Population vs. Sample" population variance mean is known - deviations are computed from a known mean • Sample variance as estimate of population population mean is unknown - Using Sample mean restricts vourioubility Degrees of Freedom degrees of freedom the number of measurements in a Sample that are free to vary if we know the mean, then all but one value in a sample can be different (vary) • examples: the remaining valves are fixed (i.e., not free to vary) -x+١٥-٧ Example you can choose any valve for X or Y but not both Lets assume the values in a distribution are unknown (but there are 5 of them), if you had to guess at the values for the dotribution would be wird. - X+Y+Z=15 if we choose 4 for X then Y must be le However, if tell you the mean is 5 and the first tour values are 3,4,6, and then the final value must be what? By calculating the mean we loose on va from the shibution that can vary, le, ane Sagree of freedom you can choose any value for 2 but not all 3 Learning Check a Sample of 4 Scores has SS = 24. What is the variance a) the variance is lo b) the variance is 7 C) the variance is 8 d) the variance is 12 decide if each of the following statements is true or false T/F a Sample Systematically has less variability than a population the standard deviation is the distance T/F from the mean to the farthest point on the distribution curve More About Variance and Standard Deviation • means and Standard deviations are particularly useful in clarifying graphs of distributions • means and Standard deviations together provide extremely useful descriptive Statistics for Characterizing distributions Presenting the mean and Standard Deviation in a Graph • for botu populations and samples it is easy to represent mean and Standard deviation Transformations of Scale • adding a constant to each Score the mean is changed the standard deviation is unchanged • multiplying each score by a constant - the mean is changed Standard deviation is also changed the Standard deviation is multiplied by that constant Standard Deviation and Descriptive Statistics •a Standard deviation describes scores in terms of distance from the mean • describe an entire distribution with just two numbers (Mands) Variance and Inferential Statistics goal of inferential Statistics is to detect meaningful and significant patterns in research results Variability in the data influences how easy it is to see patterns - high variability obscures patterns that would be visible in low variability Sampies - Variability is sometimes called error variance Learning Check A population has M = 16 and o=2. each score is muttiplied by 10. what is the shape of the resulting distribution? a) M = 60 and 0=2 b) M = 6 and 0=20 C) M = 60 and 0=20 d) M = 6 and 0=5