1. Research Methods in Politics Chapter 14 1 Research Methods in Politics 14 Understanding Inferential Statistics

2. Research Methods in Politics Chapter 142 Teaching and Learning Objectives 1. to understand what is meant by inferential statistics 2. to learn how the normal distribution enables generalisations to be drawn from the descriptive statistics of representative samples 3. to learn how to calculate the confidence limits which can be attached to opinion polls 4. to understand the meaning of the null hypothesis and how it can be applied to sample data.

3. Research Methods in Politics Chapter 143 The Normal Distribution additional characteristics additional characteristics –95% of events or terms lie within 1.96 standard deviations (SDs) of the mean –probability that 95 out of every 100 terms in a normal distribution will lie within 1.96 SDs of mean –99 terms in 2.97 SDs

4. Research Methods in Politics Chapter 144 Central Limit Theorem arithmetic means of large samples will follow a normal distribution arithmetic means of large samples will follow a normal distribution sampling error sampling error standard error of sampling mean SE standard error of sampling mean SE formula, SE = sd/n formula, SE = sd/n At 95% probability, population mean X will lie within 1.96 standard errors of the ample mean, x At 95% probability, population mean X will lie within 1.96 standard errors of the ample mean, x X = x ± 1.96 SE X = x ± 1.96 SE

5. Research Methods in Politics Chapter 145 Example a random sample of 100 Labour party members that reveals an average weekly net disposable income of £84.12 with a standard deviation of £21.07. So we can say that: a random sample of 100 Labour party members that reveals an average weekly net disposable income of £84.12 with a standard deviation of £21.07. So we can say that: x = 84.12 sd = 21.07 n = 100 The standard error, SE = sd/n = 21.07/100 = 21.07/ ± 10 The standard error, SE = sd/n = 21.07/100 = 21.07/ ± 10 = ± 2.107 You can calculate the income of the population of all Labour party members at a probability of 95% by substituting in the formula: X = x ± 1.96 SE = 84.12 ± (1.96)(2.107) = 84.12 ± 4.12972 You can calculate the income of the population of all Labour party members at a probability of 95% by substituting in the formula: X = x ± 1.96 SE = 84.12 ± (1.96)(2.107) = 84.12 ± 4.12972 = 79.9902 to 88.24972 You can infer that 95 0f every 100 members will have an income of £80.00 and £88.25. These are lower and upper confidence intervals. The variance is the confidence interval or margin of error You can infer that 95 0f every 100 members will have an income of £80.00 and £88.25. These are lower and upper confidence intervals. The variance is the confidence interval or margin of error

6. Research Methods in Politics Chapter 146 Standard Error of the Proportion standard error of the proportion, Se p standard error of the proportion, Se p formula, Se p = {p (1-p)/n} formula, Se p = {p (1-p)/n} –where p is proportion of sample sharing characteristic –value of p is standardised, e.g., for, say, 40% is 0.4 to calculate proportion of population from proportion of sample use formula: to calculate proportion of population from proportion of sample use formula: –P = p ± 1.96 Se p at 95% probability

7. Research Methods in Politics Chapter 147 Null Hypothesis practical application of Poppers falsifiability practical application of Poppers falsifiability concept of no difference: differences between the control and experimental samples is entirely due to chance concept of no difference: differences between the control and experimental samples is entirely due to chance findings cannot be accepted until null hypothesis has been disproved findings cannot be accepted until null hypothesis has been disproved –null Hypothesis H 0 –experimental or research hypothesis H 1 where only one variable studied - univariate statistics – null hypothesis is that the sample has not been drawn randomly from the population where only one variable studied - univariate statistics – null hypothesis is that the sample has not been drawn randomly from the population

8. Research Methods in Politics Chapter 148 Significance likelihood that any similarity between sample and population means etc occurred entirely by chance likelihood that any similarity between sample and population means etc occurred entirely by chance t-tests t-tests t-distribution tables t-distribution tables degrees of freedom, df degrees of freedom, df

9. Research Methods in Politics Chapter 149 Questions for Discussion, Workshop Tasks or Assignments 1. Work your way through each of the worked examples given in the textbook at your own pace to test and improve your understanding of the procedures 2. Discuss what is meant by confidence level, confidence interval and confidence limits. Where and why should they be used? 3. Using MS Excel, develop your own table for calculating the confidence limits of opinion polls. In column A enter sizes of sample from 10, 20, 30,...100, 200, 300,.... 3,000, 4,000, 5,000, 6,000,.. 10,000, 15,000, 20,000... 100,000. You can use the Autofil routine to simplify this process. In row 1, enter the percentages of the sample sharing the same characteristic or attitude from 01, 02, 03,04, 05,... 99%. Write your own formula for calculating the confidence limits at 95% confidence levels, i.e. values of 1.96(p(p-1)/n. Copy your formula across the spreadsheet and save.