202notes3__Ttests

202notes3__Ttests - Chapter 9 The Significance of the...

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Chapter 9 The Significance of the Difference between Means The t-test for comparing the difference between two means Tests the hypothesis that the mean scores on some interval- or ratio-scaled variables will be significantly different for the two independent samples or groups How far apart do the two mean s have to be so that one can say the difference is not due to chance/sampling error Answer: resort to sampling distribution Null Hypothesis : difference between sample means Assume there is no difference in the means of the populations from which the 2 samples were drawn: i.e. assume the means of the 2 populations are the same Ho : υ 1 - υ 2 = 0 Slight difference between means will occur due to sampling error t = Mean 1 - Mean 2 ______ Variability of random means t = X1 - X2 = difference between means___________ S combined standard error of difference between means X1-X2 *If one surveys many different samples, there will be a whole array of differences between means: X1 - X2, X3 - X4, X5 - X6 and so forth 1. The differences between means are arrayed as a sampling distribution 2. The mean of the sampling distribution would be 0 3. The batch of differences would be normally distributed around the mean of the differences The distribution of differences in a normal distribution, therefore: 1. 68.23% of the differences would fall between -1 and +1 standard deviations from the mean 2. 95% of all the differences would fall between -1.96 and +1.96 standard deviations from the mean 3. 99% of the differences would fall between -2.58 and +2.58 standard deviations from the mean Probability statements concerning the normal curve would apply 1. p = .68 that any difference would fall between u diff + or - standard deviation 2. p = .95 that any difference would fall between u diff + or - 1.96 standard deviations 3. p = .05 that any difference would fall outside the same interval, u diff = or - 1.96 standard deviations The question we ask then is where in the sampling distribution of differences does our obtained difference (between the two means) lie? If it is near the mean, i/e. between -1.96 and +1.96, we say the difference is due to sample error. If the difference is large and falls outside the area of -1.96 and +1.96, we think the difference may not be do to sample error, i.e. it is a rare occurrence The procedure: calculate the z-score for the difference between the two means and find its location in the sampling distribution of differences *USE TABLE A. FIND THE X-SCORE, THEN LOOK TO THE RIGHT TO FIND
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This note was uploaded on 04/25/2011 for the course MKT 202 taught by Professor Hillman during the Spring '10 term at DePaul.

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202notes3__Ttests - Chapter 9 The Significance of the...

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