Statistical testing

• Types of test

  • Sign test
  • Wilcoxon
  • Related t-test
  • Chi-squared
  • Mann-whitney
  • Unrelated t-test
  • Spearman's rho
  • Pearson's R
• Sign Test

  • Nominal data
  • Related design (test of difference)
  • matched pairs or repeated measures
• Wilcoxon

  • Ordinal data
  • Related design (test of difference)
• Related t-test

  • Interval data
  • Related design
• Chi-squared

  • Nominal data
  • Both a test of difference or test for association
  • Can be a unrelated or correlation
• Mann-whitney

  • Ordinal data
  • Unrelated design (individual groups)
• Unrelated t-test

  • Interval data
  • Unrelated design
• Spearman's-rho

  • Ordinal data
  • Test of association/correlation
• Pearson's R

  • Interval data
  • test of correlation/association
• How should nominal data be measured?

  • Central tendency- mode
• How should ordinal data be measured

  • Central tendency- median
  • Measure of dispersion- range
• How should interval data be measured?

  • Central tendency- mean
  • Measure of dispersion- standard deviation
• What is nominal data?

  • Categorical data
  • E.g. putting people into categories such as ethnicity ~
• What is ordinal data?

  • Ordering/ranking/rating data
  • E.g. scale of 1-10 to rate the like of something
• What is interval data?

  • Numerical scales of data
  • Units of equal and defined size, detailed
  • E.g. measuring something in terms of beats per minute
• What tests are parametric?

  • T-test, unrelated and Pearson's R
  • They all use interval data
  • Data should be drawn from a population with normal distribution to avoid skewed/anomalies
  • Must have homogeneity of variance (set of scores should have similar dispersion)
• What is a type 1 error?

  • Occurs when the null hypothesis is incorrectly rejected (finding a significant result when there really isn’t one).
  • .10 significance level increases risk of this
  • Means the psychologist is willing to accept a 10% chance of making a Type I error.
• Why may psychologists use .10 significance level?

  • exploratory/early-stage research, psychologists may prioritize detecting potential effects over the risk of making false positives.
  • May identify possible effects that might warrant further investigation.
  • Field lacks prior data or established theories to provide strong guidance.
  • Small sample sizes, harder to detect statistically significant effects, using a 0.10 level makes it easier to identify potential trends or effects that would be missed at the 0.05 level.
• What is a Type II error?

  • When the null hypothesis is incorrectly accepted (failing to detect a real effect/significance) when it should've been rejected
  • A .01 significance level increases the risk of this
• When may psychologists use a .01 significance level?

  • When analysis needs to be more stringent
  • High-stakes research, If the consequences of making a false positive are serious (e.g., drug treatments for mental health disorders or dangerous interventions), stricter threshold to ensure findings are reliable.
  • Replications of studies to ensure consistency of findings
  • Large sample size means anomalies are less likely to be detected as significant
  • Sensitive research such as criminal, gender, cultural
• How do inferential statistics/tests improve investigations?

  • Allows inferences to be made about the relationship between co-variables
  • Significance can be assessed through probability
• Significance at a 0.05 sig level?

  • It means that there is a 5% chance (or less) that the results occurred by random chance.
  • In other words, there is a 95% probability that the results reflect a real effect.
  • This is the standard level used in psychology research and is often written as p ≤ 0.05.