statistical testing

• statistical test are used to determine whether a difference or association/correlation found in a particular investigation is statistically significant like whether the result could have occurred by chance or there is a real effect
• the 3 criteria for statistical (inferential) tests are:

  • looking for a difference or correlation
  • if experimental design related (repeated measures/matched pairs) or unrelated (independent groups)
  • what the level of measurement is
• the statistical test for unrelated and nominal data is chi-squared
• the statistical test for unrelated ordinal data is Mann-whitney
• the statistical test for unrelated interval data is unrelated t-test
• the statistical test for related nominal data is sign test
• the statistical test for related ordinal data is wilcoxon
• the statistical test for related interval data is related t-test
• the statistical test for correlation and nominal data is chi-squared
• the statistical test for correlation and ordinal data is spearmans rho
• the statistical test for correlation and interval data is Pearsons R
• nominal data is when each item can only appear in one category and there is no order. For example, people naming their favourite football team
• ordinal data is when data is collected on a numerical, ordered scale but intervals are variable. Ordinal data lacks precision because it is based on subjective opinion rather than objective measures. For example, asking someone to rate psychology on a scale from 1-10
• interval data is based on numerical scales that include units of equal, precisely defined size. This included counting observations in an observational study or public unit of measurement. For example, time or temperatures
• null hypothesis states there is no difference or no correlation between the conditions
• probability is a measure of the likelihood that a particular event will occur called significance level which is the point at which the null hypothesis is accepted or rejected
• to find critical value, need to know:

  • whether hypothesis is directional or non-directional
  • number of participants or degrees of freedom (N-1)
  • level of significance
• to check for significant difference, compare the calculated value with the critical value. If calculated value is higher than critical value, reject null hypothesis. If calculated value lower, accept null hypothsis
• the usual significance level is 0.05 or 5%. It means that there is a 5% chance that the results of a particular study sample occurred even if there was no real difference in the population
• type 1 error is when the null hypothesis is rejected and the alternative hypothesis is accepted when the null hypothesis is actually true. False, positive as a significant difference is found when one doesn't exist
• type 2 error is when the null hypothesis is accepted and the alternative hypothesis is rejected when the alternative hypothesis is actually true. False, negative as a significant difference wasn't found when one does actually exist
• a type 1 error is likely to occur when the significance level is too lenient like 0.1/10%
• a type 2 error is likely to occur when the significance level is too stringent like 0.01/1%