Research Methods in Politics 14

1
Research Methods in Politics14

• Understanding Inferential Statistics

2
Teaching and Learning Objectives

• to understand what is meant by inferential
  statistics
• to learn how the normal distribution enables
  generalisations to be drawn from the descriptive
  statistics of representative samples
• to learn how to calculate the confidence limits
  which can be attached to opinion polls
• to understand the meaning of the null hypothesis
  and how it can be applied to sample data.

3
The Normal Distribution

• 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
Central Limit Theorem

• arithmetic means of large samples will follow a
  normal distribution
• sampling error
• standard error of sampling mean SE
• formula, SE sd/vn
• At 95 probability, population mean X will lie
  within 1.96 standard errors of the ample mean, x
• X x 1.96 SE

5
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
• x 84.12
• sd 21.07
• n 100
• The standard error, SE sd/vn 21.07/v100
  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
• 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

6
Standard Error of the Proportion

• standard error of the proportion, Sep
• formula, Sep v 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
• P p 1.96 Sep at 95 probability

7
Null Hypothesis

• practical application of Poppers falsifiability
• 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
• null Hypothesis H0
• experimental or research hypothesis H1
• where only one variable studied - univariate
  statistics null hypothesis is that the sample
  has not been drawn randomly from the population

8
Significance

• likelihood that any similarity between sample and
  population means etc occurred entirely by chance
• t-tests
• t-distribution tables
• degrees of freedom, df

9
Questions for Discussion, Workshop Tasks or
Assignments

• 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
• Discuss what is meant by confidence level,
  confidence interval and confidence limits. Where
  and why should they be used?
• 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(vp(p-1)/n.
  Copy your formula across the spreadsheet and save.