1. TYPES OF STATISTICAL METHODS USED IN PSYCHOLOGY Statistics

2. Definitions Statistics is the use of mathematics to organize, summarize, and interpret numerical data. It can be descriptive (organize and summarize data) and inferential (interpret data and draw conclusions)

3. Graphing Data: 1. Frequency Distribution An orderly arrangement of scores indicating the frequency of each score of a group of scores

4. 2. Histogram A bar graph that presents data from a frequency distribution

5. 3. Frequency Polygon A line figure used to represent data from a frequency distribution a.Horizontal (X) axis- possible scores b.Vertical (Y) axis- frequency of each score

6. Scales of Measurement: Nominal Scale Nominal Scale: a set of categories for classifying objects Ex: Divide people in groups based on their eye color Since it only classifies and does not measure anything, it is the least informative

7. Ordinal Scales Scale indicating order of relative position of items according to some criteria (data rated first to last based on some criterion) Ex: Horse race- does not give details on how much faster the winning horse ran

8. Interval Scales Scales with equal distances between the points or values but without a true zero

9. Ratio Scales A scale that fits the number system The scale has a true zero and equal intervals, just like the real number system Examples: time, distance, number correct, weight, frequency of behavior Produces score data

10. Measurements of Central Tendencies When measuring the number of instances of any occurrences (Ex: height, weight, ratings of movies, etc), we get a distribution range. The majority will usually cluster around the middle and the is the central tendency They are measured by the mean or average, the mode and the median.

11. Normal Distribution Curve: A systematic bell curve

12. Normal Curve of Distribution If you take enough measurements of almost everything we usually get a normal curve. It will be ABSOLUTELY symmetrical with the left slope parallel to the right. Mode, mean and median are the highest points on the curve

13. Skewed Distributions: Asymmetrical curve Scores are gathered at either the high or low end—hump will sit to one side or the other& curve tail will be long.

14. Negative and Positive Skewed Distribution Both types- a few extreme scores at one of the ends pull the mean and to a lesser extent the median away from the mode. Mean can be misleading Which measure provides the BEST index for scores? Where would the mean, mode and median be located on a + or – distribution?

15. Bimodal Distributions: Two humps or clusters of data Each hump indicates a mode; the mean and the median may be the same. Ex: Survey of salaries- Might find most people checked the box for both $25,000-$35,000 AND $50,000-$60,000

16. Measures of Variation Variability: On a range of scores (distance between the smallest and largest measurements in a distribution) how much do the scores tend to vary or depart from the mean scores EX: golf scores of a mediocre, erratic golfer would be characterized by high variability while scores of a good consistent golfer would show less.

17. Standard Deviation: Statistical measure of variability in a group It is a way to use a single number to indicate how the scores in a frequency distribution are dispersed around the mean.

18. Calculating the SD Find the mean Subtract each score from the mean Square the difference Add up the column of squared differences Divide the sum of the squares by the number of scores in the distribution (that number is the VARIANCE) Find the square root of the number= SD

19. Results of the Standard Deviation In a normal distribution, 68% of scores will fall between one deviation above & below the mean Another 27% fall between one & two SD 4% fall between two & three SD Overall, 99% of scores fall between 3 SD below and above the mean Ex: Appendix B B.7 (SAT scores) Mean is arbitrarily at 500 and SD at 100. Same with IQ

20. Z SCORE The number of SD you are from the deviation Z = raw score- mean SD If you are a bowling coach and you have to pick one kid which one do you pick? Kid 1: 150 average SD 70 Kid 2: 150 average SD 30 WHY?

21. Correlation: Two variable are related to each other with no causation The strength of the correlation is defined with a statistic called the correlation coefficient (+1.00 to -1.00) Positive- Indicates the two variables go in the same direction EX: High school & GPA

22. Correlations Negative correlations indicate two variable that go in the opposite directions EX: Absences & Exam scores

23. Strength of the Correlation ( r) Numerical index of the degree of relationship between two variable or the strength of the relationship. Positive 0 to +1.00 Negative 0 to -1.00 Coefficient near zero indicates there is no relationship between the variable ( one variable shows no consistent relationship to the other 50%) Perfect correlation of +/- 1.00 rarely ever seen Positive or negative ONLY indicate the direction, NOT the strength

24. Correlation and Prediction As the correlation increases, so does the ability to predict one variable based on the other. EX: SAT scores & college GPA are positive correlation

25. Measuring Correlation Y= vertical on graph X= horizontal on graph Illusory correlation- a perceived correlation that does not really exist EX: When the moon is full, bizarre things happen Scatter plots- should be linear

26. How to plot Place your scores of the two variables on a graph called a scatter plot Each number represents an X and Y The Pearson Product- Moment correlation- formula to compute the correlation coefficient (See B. 10)

27. Coefficient of Determination-Index of correlation’s predictive power Percentage of variation in one variable that can be predicted based on the other variable To get this number, multiply the correlation coefficient by itself EX: A correlation of.70 yields a coefficient of determination of.49 (.70 X.70=.49) indicating that variable X can account for 49% of the variation in variable Y Coefficient of determination goes up as the strength of a correlation increases (B.11)

28. Applying Inferential Statistics to Correlations Is the observed correlation large enough to support our hypothesis or might a correlation of the size have occurred by chance? We need to test the Null Hypothesis or the assumption that there is no true relationship between the variables observed. Do our result REJECT the null hypothesis? Type I Error Type II Error Relate to meds Which is worse?

29. Statistical Significance It is said to exist when the probability that the observed findings are due to chance is very low, usually less than 5 chances in 100 When we reject our null hypothesis we conclude that our results were statistically significant.