probability and significance

• Probability

  • A measure of the likelihood that a particular event will occur
  • 0 = statistical impossibility
  • 1 = statistical certainty
  • No statistical certainties in psychology but there is a significance level (the point at which the null hypothesis is accepted or rejected)
• significance and null hypothesis

  • Is the statistical test is not significant = null hypothesis is accepted
  • If the statistical test is significant = null hypothesis is rejected
• use of statistical tables

  • To check for statistical significance the calculated value (resulted of the statistical test) is compared with a critical value (in a table of critical values based on probabilities)
  • To find the correct critical value:
  • Is hypothesis one-tailed (directional) or two-tailed (non-directional)
  • Number (N) of participants of degrees of freedom (df)
  • Level of significance (or p value)
  • Usual level of significance = 0.05 or 5%
  • Means there is a 5% chance that the results of a particular study sample occurred even if there was no real difference in the population
  • Helps to avoid type l and type ll errors
• type l error

  • The null hypothesis is rejected and the alternative hypothesis is accepted, when the null hypothesis is ‘true’
  • Optimistic error/false positive = as a significant difference or correlation is found when one does not exist
  • Significant level may be too lenient = eg 0.1 or 10%
• type ll error

  • The null hypothesis is accepted but, in reality, the alternative hypothesis is ‘true’
  • A pessimistic error or false negative
  • Significant level may be too stringent = eg 0.01 or 1%