Using statistics in the analysis of quantitative data A good way to use this material for detailed study is to print the whole file then to run the slide show, while reading the text from the printed version. This will allow you to use the links and animations that are included in some of the slides. Suggested Print settings for use in the print dialogue box: Print Range: All Print what: Notes Pages (from the drop down box) Then tick:Black & White, Scale to fit paper

Types of data Data typeExample Nominal or Categorical Eye colour Ordinal Job seniority Interval: parametric non-parametric Language comprehension test score; IQ Ratio parametric non-parametric Age

Uses of statistics Use of statistics Inferential or Non- inferential Describing a sampleNon-inferential Looking for relationships between variable in a sample Non-inferential Estimating parameters in a population Inferential Testing hypothesesUsually used inferentially but can be used non- inferentially

SPSS task Entering data

Describing a sample

SPSS calculation of mean

Finding the spread of scores in a sample

Standard Deviation

Finding how scores are distributed

Distribution of attitude scores

Properties of the Normal Distribution

Checking normality

An overall test for normality

Describing ordinal data - Frequencies

Median and Mode for ordinal data

Describing ordinal data Bar charts (no gaps)

Describing nominal data - Frequencies

Nominal data - Mode

Describing nominal data – Bar Chart

Describing nominal data – Pie Chart

Exploring relationships between data

Correlation

Review of meaning and importance of linearity s/GlosMod/Flash/e_gm_fla_covariance.ht mhttp:// s/GlosMod/Flash/e_gm_fla_covariance.ht m

Extreme groups – a warning

Correlation - effect of measurement error motivation Test result Actual points

Correlation - effect of measurement error motivation Test result Actual points Measured points

Correlation - effect of measurement error motivation Test result

Correlation & Regression

Spearman Correlation Ordinal data

Chi squared test of association Nominal data

Chi squared showing an association

Calculating chi-squared from cell values contingency.html

Item analysis, reliability and validity

Cronbach’s Alpha

Estimating population values

Terminology Population (described by parameters) Sample (described by statistics)

Estimating population values

Sampling Samples that allow statistical generalisation random systematic stratified random cluster multi-stage Samples that don’t allow statistical generalisation quota convenience snowball

Sampling Samples that allow statistical generalisation random systematic stratified random cluster multi-stage Samples that don’t allow statistical generalisation quota convenience snowball

Making it practicable whilst retaining validity

Calculating required sample sizes and related web pageshttp://

Statistics and parameters Statistics of sample Mean = m Standard Deviation = s Correlation = r Parameters of population Mean = μ Standard deviation = σ correlation = ρ

Statistics and parameters Statistics of sample m s r Parameters of population Best estimate is… μ = m σ = ρ = r (for large samples >30)

95% confidence limits for the population mean - large samples

Calculation of confidence intervals Mean tmlhttp://glass.ed.asu.edu/stats/analysis/mci.h tml Correlation mlhttp://glass.ed.asu.edu/stats/analysis/rci.ht ml Standard deviation Walpole R (1982) Introduction to statistics 3rd Edition p277-8;482

Confidence interval for  2 Walpole R. (1982) Introduction to Statistics 3 rd Edn New York: Macmillan pp277-8

As long as the population is at least ten times as large as the sample, the size of the population has almost no influence on the accuracy of sample estimates. The margin of error for a sample size of 1000 is about 3% whether the number of people in the population is 30,000 or 200 million. You can make a good check on how salty a well stirred bowl of soup is by tasting one spoonful – whatever the size of the bowl What’s the surprise? There is no effect! The Surprising Effect of Population Size *.