11. Statistical Tests

• Statistical testing

  • Used to determine whether a difference or association found is significant i.e more than could have occurred by chance
  • This has implications on whether we accept or reject the null hypothesis
• Three factors used to decide

  1. Difference or correlation
  2. Experimental design
  3. Levels of measurement
• Experimental design

  • Related - repeated measures or matched pairs
  • Unrelated - independent groups
  • ONLY relevant if there is a difference
• Types of data/measurement

  • Nominal - frequency or count data that is discrete and often uses categories
  • Ordinal - data presented in rank order and does not have equal intervals between each unit, lacks precision as it is based on subjective opinion
  • Interval - data measured in fixed units with equal distance between points on a scale eg. weight, thermometer, ruler - most precise data in psychology
• Statistical Tests

  • Carrots - Chi-Squared
  • Should - Sign Test
  • Come - Chi-Squared
  • Mashed - Mann-Whitney
  • With - Wilcoxin
  • Swede - Spearman's rho
  • Under - Unrelated t-test
  • Roast - Related t-test
  • Potatoes - Pearson's r
• The null hypothesis

  • A hypothesis written at the beginning of an investigation can be referred to as an alternative hypothesis
  • A null one states there is 'no difference' between the conditions
  • The statistical test will determine which hypothesis is the most accurate
• Levels of significance and probability

  • Statistical tests work on the basis of probability and have a significance level - in psychology it is usually p is equal to or less than 5%
  • Psychologists can never be 100% certain about a result as they have not tested all members of a population, they use a conventional level of probability where they are prepared to accept the results may have occurred by chance
• Calculated and critical values

  • To check for significance the calculated value must be compared to the critical value
  • Each test has its own table of critical values
  • Statistical tests with the letter 'r' in their name - calculated value must be equal to or more than the critical value
  • Statistical tests without the letter 'r' in their name - calculated value must be equal to or less than the critical value
• Using the table of critical values

  • One tailed or two tailed test? - one tailed for directional and two tailed for non-directional
  • Number of pps in the study - appears as the N value
  • Level of significance - 0.05 (5%) is the standard level in psychology
• Type 1 and Type 2 Errors

  • Type 1 - A 'false positive' as the researcher claims to have found a significant difference or correlation when one does not exist. More likely to happen if the significance level is too high eg. 0.1 rather than 0.05%
  • Type 2 - A false negative. More likely if the significance level is too low eg. 0.01%