1. Statistics Josée L. Jarry, Ph.D., C.Psych. Introduction to Psychology Department of Psychology University of Toronto June 9, 2003

2. Statistical Procedures Mathematical aids for summarizing and interpreting data Descriptive statistics –Used to summarize data sets Inferential statistics –Used to determine what conclusion can be drawn from data sets

3. Organizing and Summarizing Scores Frequency distribution Central tendency Variability

4. Frequency Distribution Rank order –Organize scores from lowest to highest Frequency distribution –Divide the range of scores into equal intervals –Determine how many scores fall into each interval Demonstrates the frequency of occurrence of each response or range of responses

8. Shapes of Frequency Distributions

9. Normal Distribution Maximum frequency lies in the center of the range of scores Frequency tapers off symmetrically on both sides Many measures in nature are normally distributed Found when a measure is determined by several independent factors

11. Bimodal Distributions Occurs when scores form two separate groupings Mode –the most frequently occurring score or range of scores in a frequency distribution Two separate areas of peak frequencies or two modes The normal curve is unimodal

13. Skewed Distributions Positively skewed distribution –Spread of scores above the mode is greater than the spread below –The tail extends in the direction of high scores Negatively skewed distributions –Spread of scores below the mode is greater than the spread above –The tail extends in the direction of low scores

16. Measures of Central Tendency Consists of summarizing an entire distribution with a single score that represents the centre of the distribution. Median –Is the middle score of a set of ranked scores. Mean –Found by adding all the scores and dividing by the total number of scores. M = sum of score N

18. Mean, Median, & Distributions In a normal distribution –Mean and median are identical In a positively skewed distribution –The mean is greater than the median; In a negatively skewed distribution –The mean is smaller than the median Mean is preferred in normal distributions Median is preferred in highly skewed distributions

22. Measures of Variability (1) Measures of variability tell us how widely the observations are spread around the centre Two distributions can both be normal and have the same mean, but have very different variability.

24. Measures of Variability (2) Range –The difference between the highest and the lowest scores in a distribution Variance –Takes into account the extent to which all of the scores in the distribution differ from each other Standard deviation –Expresses variability in the same unit of measurement as the original scores –The square root of the variance

26. Converting Scores for Purposes of Comparison Allows to compare different kinds of scores to each other To compare different kind of scores with each other, each score must be converted into a form that expresses directly its relationship to the whole distribution of scores from which it came

27. Percentile Rank The most straightforward way of comparing one person to another on a given measure Allows comparison between different measures Determine that person’s percentile rank on the measures of interest Percentile rank –the percentage of scores that are equal to that score or lower, out of a whole set of scores for that measure

29. Standardized Scores z-score –Expresses a score in terms of the number of standard deviations that the original score is away from the mean of the original scores Convert any score into a z-score –calculate its deviation from the mean –divide the deviation by the standard deviation of the distribution –z = score - mean Standard deviation

31. Correlation Coefficient (1) Is a mathematical means of describing the strength and direction of the relationship between two variables that have been mathematically measured Varies between -1 and +1 The sign (+ or -) of the correlation indicates the direction (positive or negative) of the relationship The absolute value of the coefficient (from 0 to 1) indicates the strength of the relationship

32. Correlation Coefficient (2) A positive correlation indicates that an increase in one variable corresponds to an increase in the other A negative correlation indicates that an increase in one variable corresponds to a decrease in the other Scatter plot –Visual display of a correlation –Each point represents a subject’s pair of scores