Week_5_stat_signif_hyp_test

Week_5_stat_signif_hyp_test - SAN JOS STATE UNIVERSITY...

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SAN JOSÉ STATE UNIVERSITY College of Social Work S. W. 242 Spring 2008 Edward Cohen Week 5: February 22, 2008 Testing Hypotheses and Statistical Significance “Statistics means never having to say you’re certain!” Anon. Normal distribution Z score Skewed distributions Inferential analysis Sampling error Null hypothesis Two tailed hypothesis One-tailed hypothesis Alpha (or rejection) level Type I error Type II error I. Continuation from last week’s notes: A. Measures of Dispersion—Big Question: Why are large samples better than smaller ones? Consider the “Descriptives” data results from last week’s exercise (dataset from Ch. 6, Kirkpatrick & Feeney) Statistics 30 30 30 0 0 0 15.5000 1.5000 78.7333 15.5000 1.5000 82.5000 1.00 a 1.00 a 89.00 8.80341 .50855 14.22221 77.50000 .25862 202.27126 29.00 1.00 65.00 1.00 1.00 33.00 30.00 2.00 98.00 Valid Missing N Mean Median Mode Std. Deviation Variance Range Minimum Maximum STUDENT GENDER SCORE Multiple modes exist. The smallest value is shown a. 1. Range – (the largest value minus the smallest value + 1) Calculate the Score range from the data set: (Maximum-Minimum +1) = (98-33) +1 = 66 2. Variance – the average of the squared deviations from the mean 1
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3. Standard deviation -- the square root of the variance 2
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Calculate the variance and standard deviation for the Score variable (Ch. 6 Kirkpatrick & Feeney): Student Score Subtract mean Deviation from mean Squared deviation from mean 1 87 -78.33 8.67 75.17 2 53 -78.33 -25.33 641.61 3 92 -78.33 13.67 186.87 4 70 -78.33 -8.33 69.39 5 78 -78.33 -0.33 0.11 Do this with all 30 cases . . . . . . . . . . . . . . 30 . . . . Variance: Sum of all 30 squared deviations divided by n (or 30) 202.21 Standard Deviation: Square root of squared deviations 14.22 Fascinating! properties of the standard deviation: 1. The SD is in the same units as the original measure (Score points) 2. For the SD of Score, we say that “one standard deviation is equivalent to 14.22 score points” 3. Different samples of classes taking this test could possibly have the same mean, but different standard deviations. What does this say about means, in general? What does this say about sample size, in general? 4. A population can have a standard deviation. Since the population mean and SD are rarely known in social research, we infer it from samples. Then, the question is, does the sample mean represent the mean of the population from which the sample was chosen? What’s the role of the SD in answering this question? 5. One more highly interesting fact: the Weinbach/Grinnell book computes the variance with a denominator of n . SPSS (and many other statistics books) use n-1, a smaller denominator (larger Variance) hence a more “conservative” approximation of the variance in the population. There’s a theory behind this. Ask me sometime. OK, since you insist:
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This note was uploaded on 09/08/2010 for the course SCWK 242 at San Jose State University .

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Week_5_stat_signif_hyp_test - SAN JOS STATE UNIVERSITY...

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