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Chapter 14

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Sociology and Anthropology
SOAN 3120
Michelle Dumas

Significance Tests Just like in Chapter 11, P is found in relation to z. The z score (or z test score as it is called in chapter 14, since we’re looking at multiple samples rather than populations, as we were in chapter 11, or single samples in chapter 3) gives us a point on the x axis of a Normal curve. The table A gives us the proportion of the curve to the left of that point (a value from 0.001 to .9999) which we can use to find the P value (more on that in 14.22). Z test statistics are calculated using: Z= -µ σ(σ/) Note that the portion of the equation in the brackets is itself an equation of division, where the standard deviation of the population is divided by the square root of the number included in the sample. See example 14.9 on page 379 of the textbook to see how this equation is used. This is the equation we use for 14.40, where it gives us a value for z, which we then use to find the P value. Since we are doing hypothesis testing, we use the P value to reject the null hypothesis. If the p value is less than 0.05 (that is P<0.05) we can say that the data are statistically significant at the 5% level and reject the null hypothesis. If P<0.01, we can say that the data are statistically significant at the 1% level and reject the null hypothesis. If data are statistically significant, it means that the results did not occur ‘by chance’ and that it is likely a good representation of the population beyond those sampled. 14.22 Significance from a table. A test of H :oµ=1 against H : a≠1 has test statistic z=1.776. Is this test significant at the 5% level (α=0.05)? Is it significant at the 1% level? Z* at the 5% level is 1.960. The given value 1.776 is smaller than this value. Since it fails to meet the critical value, it is not significant at the 5% level. It necessarily is not significant at the 1% level (where the critical value is 2.576). To determine significance by comparing P values, a two sided P is necessary because the H is a two sided (µ≠1). The z score is given, so table A (pg 691) can be used to look at the proportion of the Normal curve being asked for. Z=1.77 (approximately, you could also use the value for 1.78 but the calculation will still be ‘off’ so to speak), the corresponding value is 0.9616. 1- 0.9616=0.0384. Because it is two sided, we need to multiply this value by two (to take into account both extremes of the curve. Figur
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