statistics

• Sign Test


  A method used in inferential statistics to determine whether or not an observed result (from an experiment) is significant or not
• Sign Test


  • It is a non-parametric test which means that there is no assumption that the data will follow a normal distribution
  • It is known as the Sign Test as it is based on the number of plus or minus signs present in the data after the calculations have taken place
• Advantages of the Sign Test

  • It is a simple test which is easy to carry out
  • It can be applied across a range of situations where a normal distribution cannot be assumed
• Disadvantages of the Sign Test

  • Nominal data is the least powerful type of data which means that the Sign Test can sometimes be unreliable
  • It may not be suitable for use with small samples or when the median has been used as the measure of central tendency
• An abnormal distribution is one of the criteria for using the Sign Test
• Probability


  Psychologists are interested in finding out if the results of their studies show real differences or correlations, or if the results are due to chance factors
• Significance


  • To determine whether results are significant and not due to chance factors, researchers use a measure of the level of significance
  • The level of significance is expressed as a decimal value where 'p' stands for the probability that chance factors are responsible for the results
  • For most purposes in psychology, the 5% level of significance is appropriate which is expressed as p < 0.05
• Inferential statistics enable us to draw inferences about the population whereas descriptive statistics can only tell us about the sample taken from that population
• The Use of Statistical Tables

  1. The observed value needs to be compared to the critical value in the statistical tables

  2. Is the test one-tailed or two-tailed?

  3. What is the N value (how many participants)?

  4. Which level of significance is being applied?
• Maguire's (2000) research using London taxi drivers clearly gets the thumbs up for passing the p < 0.05 test
• Type I Error


  Occurs when the null hypothesis is rejected when it should have been accepted (a false positive)
• Type II Error


  Occurs when the null hypothesis is accepted when it should have been rejected (a false negative)
• Using a 0.05 significance level guards against making either a Type I or a Type II Error
• Statistical tests to know

  • Mann-Whitney test (non-parametric)
  • Wilcoxon test (non-parametric)
  • Chi-squared test (non-parametric)
  • Spearman's rho (non-parametric)
  • Unrelated t-test (parametric)
  • Related t-test (parametric)
  • Pearson's r (parametric)
• Difference between parametric and non-parametric tests

  • Parametric tests assume a normal distribution; non-parametric tests do not
  • Parametric tests use interval data: non-parametric tests may use nominal or ordinal data
  • Parametric tests assume homogeneity of variance; non-parametric tests do not
  • Parametric tests are more powerful than non-parametric tests
• Godden & Baddeley's (1975) research on context-dependent forgetting using divers is an example of a test of difference
• Statistical tests by data type and design

  • TESTS OF DIFFERENCE:

  RELATED DESIGN: Sign Test, Wilcoxon test, Related t-test

  UNRELATED DESIGN: Mann-Whitney test, Chi-squared, Unrelated t-test

  TESTS OF ASSOCIATION:

  ORDINAL DATA: Spearman's rho

  INTERVAL DATA: Pearson's r
• Bella should be able to carry out a parametric test on her data as it is interval data (body temperature measurements) and she can expect a normal distribution and homogeneity of variance in her elite athlete sample