3003PSY Survey Design And Analysis In Psychology - Significance Testing PDF

3003PSY Survey Design and Analysis in Psychology MULTIPLE REGRESSION: SIGNIFICANCE TESTING SIGNIFICANCE TESTING WHAT IS R? SIGNIFICANCE TESTING  TESTING THE SIGNIFICANCE OF R u Let's take the simpler case of a correlation (which is the basis for regression remember) urdescribes the...

3003PSY Survey Design and Analysis in Psychology MULTIPLE REGRESSION: SIGNIFICANCE TESTING SIGNIFICANCE TESTING WHAT IS R? SIGNIFICANCE TESTING  TESTING THE SIGNIFICANCE OF R u Let's take the simpler case of a correlation (which is the basis for regression remember) urdescribes the linear relationship between two variables in a sample u usuallywant to make inferences about the relationship in the population  TESTING THE SIGNIFICANCE OF R u is r large enough to conclude that there is a linear relationship between the variables in the population? or u is the correlation in the sample due to sampling error?  u r = rho u population correlation coefficient u H0 : r=0 TESTING THE H1 : r ¹ 0 SIGNIFICANCE u H0 : there is no linear relationship OF R between X and Y in the population H1: there is a linear relationship between X and Y in the population  uTake a random sample and calculate the correlation uWe would do this repeatedly for an infinite number of samples u The correlation does not always give r =0 u The value of the correlation will vary TESTING THE from one random sample to another SIGNIFICANCE random sample uAs a result we cannot be certain that the OF R correlation we get from a sample reflects whether the correlation in the population = 0 or is < 0 or > 0 u We can calculate a probability (likelihood) that the sample was taken from a population where r = 0 u This is same process as when we looked at the sampling distribution of means  TESTING THE SIGNIFICANCE OF R When correlation in the population is zero (i.e., Null hyp is true) for a large enough sample, r will be normally distributed around zero. Is our sample correlation 34% 34% significantly greater than (or significantly less than) zero?? 2% 14% 2% Is r large enough to conclude that 14% there is a non-zero correlation in -4 -3 -2 -1 0 1 2 3 4 2nd 16th 50th 84th 98th the population? Is the correlation in the sample due to sampling error? HAIR & IQ CORRELATION TESTING THE SIGNIFICANCE OF B TESTING THE SIGNIFICANCE OF B TESTING THE SIGNIFICANCE OF B  SUMMARY u Just as with our other analyses like the t test we check for significance of our overall R and for our b weights uThe correlation in the population is referred to as r (Rho) uWe use the same concept of sampling distributions as we used with means to test whether the correlation or the b weight in our sample is significantly different from zero uIn addition to testing whether there is a significant association between our predictors as a group (aka a linear combination; the regression equation) by looking at R we also test the significance of each predictor while controlling for all other predictors by looking at the significance of the b weights.