inferential testing

• Type 1 error : the psychologist wrongly accepts the alternative hypothesis
• Type 2 error: psychologist wrongly accepts the null hypothesis and rejects the alternative hypothesis
• chi-squared :

  • difference (association)
  • independent measure design
  • nominal data
• spearmans rho:

  • correlation
  • ordinal data
• unrelated t-test:

  • difference
  • independent measure design
  • interval data
• related T-test

  • difference
  • repeated measure design
  • interval data
• sign test :

  • difference
  • repeated measures design
  • nominal data
• Mann- Whitney:

  • difference
  • independent measure design
  • ordinal
• Wilcoxon :

  • difference
  • repeated measure design
  • ordinal data
• pearsons r :

  correlation

  interval data
• Inferential statistics refers to the use of statistical tests which tell psychologists whether the differences or relationships they have found are statistically significant or not.
• calculated observed value < _ ( equal to or less than) critical value
• In statistics, probability and significance are used to interpret the results of a hypothesis test, helping researchers determine whether their findings are likely due to chance or reflect a real effect.
• Critical Value:

  • The critical value is a threshold used in hypothesis testing to decide whether the test statistic is statistically significant.
• P-value:

  • The p-value is a measure of the probability that the observed data would occur if the null hypothesis were true.
  • A smaller p-value suggests that the observed effect is less likely to be due to random chance.
  • Typically, a p-value of 0.05 or less is considered statistically significant. This means that there is less than a 5% chance that the result occurred by chance.
• Statistical Tables:

  • Statistical tables (e.g., z-table, t-table) help researchers determine the critical values for different types of statistical tests. These tables show the values of test statistics at various significance levels and degrees of freedom (for t-tests
• Steps for Interpreting Significance Using Statistical Tables and Critical Values:

  • To conduct a statistical analysis, set two hypotheses: the null hypothesis (H₀) and the alternative hypothesis (H₁). Choose a significance level (α) of 0.05 (5%), allowing a 5% chance of a Type I error. Calculate the test statistic based on the type of test, and find the critical value using the appropriate distribution table. If the test statistic is extreme, reject the null hypothesis, while if it falls within the acceptance region, fail to reject the null hypothesis
• What is the first step in finding the sign test?

  Collect paired observations data
• Why do you collect paired observations for the sign test?

  To compare pre-test and post-test scores
• How do you calculate differences in the sign test?

  Subtract one value from the other
• What do you assign if the difference is positive?

  Assign a "+" sign
• What do you assign if the difference is negative?

  Assign a "−" sign
• What should you do with pairs where the difference is zero?

  Ignore those pairs
• What do you count in the sign test?

  Count positive and negative signs
• How is the sample size for the sign test determined?

  By counting non-zero differences
• What is the null hypothesis in the sign test?

  The median difference is zero
• What is the alternative hypothesis in the sign test?

  The median difference is not zero
• How is the test statistic T calculated in the sign test?

  It is the smaller of the two counts
• What do you use to find the critical value in the sign test?

  Sign test table or binomial distribution
• What does it mean if T is less than or equal to the critical value?

  Reject the null hypothesis
• What does it mean if T is greater than the critical value?

  Do not reject the null hypothesis
• What should you do after determining the test statistic and critical value?

  Interpret results in context
• What is the significance level commonly used in hypothesis testing?

  α=0.05
• Why is it important to interpret results in the context of your study?

  To understand the practical implications