X mand another difficulty is that no two samples are the same How can weknow which best describes the populationWe need rules that relate samples to populations ID: 107637
Download Pdf The PPT/PDF document "For example: The probability of picking ..." is the property of its rightful owner. Permission is granted to download and print the materials on this web site for personal, non-commercial use only, and to display it on your personal computer provided you do not modify the materials and that you retain all copyright notices contained in the materials. By downloading content from our website, you accept the terms of this agreement.
For example: The probability of picking a black ball from jar A is one half; theprobability of picking a black ball from jar B is one tenth. [This is reasoning aboutprobability.]jar A:50 black,50 whitejar B:90 black,10 white [We would use Inferential statistics to answer questions such as: from which jaris one more likely to get a sample of four black balls?] X " mand another difficulty is that no two samples are the same. How can weknow which best describes the population?We need rules that relate samples to populationsÒThe Distribution of Sample MeansÓDefinition: the distribution of sample means is the collection of sample meansfor all the possible random samples of a particular size (n) that can beobtained from a population.It is not a distribution of scores, but a distribution of statistics. X = s/#n.This formula shows how it is that the accuracy of the estimate provided by asample increases as the sample size increases. (This formulaÑand a related oneweÕll introduce shortlyÑis something APA says one needs to know for thelicensing exam.)Now we can turn to....Hypothesis TestingDefinition:hypothesis testing is an inferential procedure that uses sample datato evaluate the credibility of a hypothesis about a population.Remember?null hypothesis (H0): the treatment has no effect.i.e., the experimental group and the control group are drawn from thesame population.This will seem confusing, since a good experiment assigns subjectsrandomly to the two groups. The point here is that the nullhypothesis asserts that it is still the case AFTER THETREATMENT that the two groups belong to the same population.If, on the other hand, the treatment did have an effectÑwhich ofcourse means that the null hypothesis is falseÑthen the two groupswould now come from different populations. Comprendas?i.e., X expt and X control will not differ by more than random error.i.e.,they will not differ by more than the Òstandard error.ÓHow do we know the standard error? Remember, itÕs the standard deviation ofthe distribution of sampling means. Actually, we donÕt know it directly. But wecan estimate it: our estimate replaces the population parameter s with thesample statistic, s:Remember we said that it can be shown that s X = s/#n.In the same way: s X X control / s X ! 1 (simply rearranging the formula)The left hand side of this equation is called Ò