PA LESSON 3

• Measures of Central Tendency

  Statistics that indicates the average or midmost score between the extreme scores in a distribution
• Goal of Measures of Central Tendency

  • Identify the most typical or representative of entire group
• Measures of central location

  Measures of Central Tendency
• Mean


  • The average of all the raw scores
  • Equal to the sum of the observations divided by the number of observations
  • Used for interval and ratio data (when normal distribution)
  • Point of least squares
  • Balance point for the distribution
  • Susceptible to outliers
• Median


  • The middle score of the distribution
  • Used for ordinal, interval, ratio data
  • Used for extreme scores
  • Identical for sample and population
  • Used when there has an unknown or undetermined score
  • Used in "open-ended" categories
  • Used for ordinal data
  • Used for ratio/interval data when distribution is skewed
• Mode


  • Most frequently occurring score in the distribution
  • Bimodal distribution: if there are 2 scores that occur with highest frequency
  • Not commonly used
  • Useful in analyses of qualitative or verbal nature
  • Used for nominal scales, discrete variables
  • Gives an indication of the shape of the distribution as well as a measure of central tendency
• Measures of Spread or Variability


  • Statistics that describe the amount of variation in a distribution
  • Gives idea of how well the measure of central tendency represent the data
  • Large spread of values means large differences between individual scores
• Range


  • Equal to the difference between highest and the lowest score
  • Provides a quick but gross description of the spread of scores
  • When its value is based on extreme scores, the resulting description of variation may be understated/overstated
• Interquartile range


  Difference between Q1 and Q2
• Semi-Quartile range


  Interquartile range divided by 2
• Standard deviation


  • Approximation of the average deviation around the mean
  • Gives detail of how much above or below a score to the mean
  • Equal to the square root of the average squared deviations about the mean
  • Equal to the square root of the variance
  • Distance from the mean
• Variance


  Equal to the arithmetic mean of the squares of the differences between the scores in a distribution and their mean
• Percentile or Percentile rank


  • Not linearly transformable, converged at the middle and the outer ends show large interval
  • Expressed in terms of the percentage of persons in the standardization sample who fall below a given score
  • Indicates the individual's relative position in the standardization sample
• Quartile


  • Dividing points between the four quarters in the distribution
  • Specific point
  • Quarter: refers to an interval
• Decile / STEN


  • Divide into 10 equal parts
  • A measure of the asymmetry of the probability distribution of a real – valued random about its mean
• Correlation Types


  • Pearson R (Interval/ratio + interval/ratio)
  • Spearman Rho (Ordinal + ordinal)
  • Biserial (Artificial dichotomous + interval/ratio)
  • Point biserial (True dichotomous + interval/ratio)
  • Phi coefficient (Nominal (true dic) + nominal (true/artificial dic.))
  • Tetrachoric (Art. Dichotomous + art. Dichotomous)
  • Kendall's (3 or more ordinal/rank)
  • Rank biserial (Nominal + ordinal)
• Difference Tests


  • T – test Independent (2 separate groups, random assignment)
  • T- test dependent (One group, two scores)
  • One – way ANOVA (3 or more groups, tested once)
  • One-way repeated measures (1 group, measured at least 3 times)
  • Two – way ANOVA (3 or more groups. Tested for 2 variables)
  • ANCOVA (Used when you need to control for an additional variable)
  • ANOVA Mixed design (2 or more groups measured more than 3 times)
• Non-Parametric Tests


  • Mann Whitney U Test (T – test independent)
  • Wilcoxon Signed Rank Test (T – test dependent)
  • Kruskal – Wallis H Test (One – way/ two – way ANOVA)
  • Friedman Test (ANOVA repeated measures)
  • Lambda (For 2 groups of nominal data)
• Chi-Square Tests


  • Goodness of Fit (Used to measure differences and involves nominal data and only one variable with 2 or more categories)
  • Test of Independence (Used to measure correlation and involves nominal data and 2 variables with 2 or more categories)
• Linear Regression of Y on X


  • Y = a + bX
  • Used to predict the unknown value of variable Y when value of variable X is known
• Linear Regression of X on Y


  • X = c + dY
  • Used to predict the unknown value of variable X using the known variable Y
• True dichotomy


  Dichotomy in which there are only fixed possible categories
• Artificial Dichotomy


  Dichotomy in which there are other possibilities in a certain category