Statistical Methods I & I PSYC 2020 6.0G (F/W 2012)

1. Statistical Methods I & IPSYC 2020 6.0G (F/W 2012)

2. Course Instructor Lisa Fiksenbaum Office: 403 BSB Telephone: (416) 736-5125 E-Mail: lisafix@yorku.ca Office Hour: By Appointment Teaching Assistant Pearl Gutterman Office: 3023 Lassonde Telephone: (416)736-2100 (ext. 33113 ) Email: 2020guterman@gmail.com Office Hour: Tuesday 4:30-5:30 Contact Information

3. Correspondence by email or phone • Make sure that you identify yourself clearly (first and last name) • Please send emails from a York emailaccount and use PSYC2020 in the subject line; otherwise, emails will be will be deleted unread • Consult the syllabus for administrative information

4. Book Information Gravetter, F.J. & Wallnau, L.B. (2013) Statistics for the Behavioral Sciences, (9th ed). St. Paul: West Publishing Company.

5. Rounding • Do not round numbers you are computing until the final answer. • Rounding at each step results in answers that may be significantly different than the keyed answers for both exams and homework. • Round only your final answer (to two decimal places) only after all calculations have been performed.

6. Course Evaluation • 4 exams (definitions, multiple choice, true/false, matching, basic calculations, interpretation of data sets, and/or short essay questions ): • Exam 1 (20%) • Exam 2 (20%) • Exam 3 (20%) • Exam 4 (20%)

7. Course Evaluation • 4 assignments: • Assignment 1 (5%) • Assignment 2 (5%) • Assignment 3 (5%) • Assignment 4 (5%) • Due at the START of class (you will receive 0 if handed in late) • NO electronic submissions will be accepted • Do NOT simply report the final answer for a problem. Show the computations that produced that answer.

8. Exams • For the first exam: • you will be allowed to use one side of a 3 inch x 5 inch index card on which you may put anything you consider useful (e.g., formulas, definitions, etc.). • For all other exams: • you will be allowed to use both sides of the card

9. Missed Exams • Make-up exams will be granted ONLY under EXCEPTIONAL circumstances, such as serious illness, or death in the immediate family • Must contact the instructor or TA in person, by telephone, or by email, within 48 hours of the missed exam • PROPER DOCUMENTATION REQUIRED

10. Review of Preliminary Concepts • Variables • Measures of central tendency • Measures of variability • Hypothesis testing

11. Types of Variables • Variable: characteristics of objects, events, or people that can have different values • Constant: is a characteristic of objects, events, or people that does not vary • Continuous Variable: can take on an infinite number of values (e.g., reaction time) • Discrete Variable: can take on a finite number of values (e.g., gender)

12. Types of Variables, cont'd • Dependent Variable (DV): the variable being measured in an experiment, that is expected to be “dependent” on the independent variable • Independent Variable (IV): : The variable that is expected to influence the DV • Manipulated IV: an IV controlled by the experimenter (e.g., random assignment to groups) • Subject/Organismic IV: an IV that is an underlying characteristic of the population (e.g., sex, age)

13. Population/Sample • Population: the entire set of events (e.g., study habits of university students) to which are you are interested • Sample: a subset of a given population that is used to make inferences regarding the population (e.g., an intro psych class)

14. Parameters/Statistics • Parameter: a measure that refers to the entire population (Greek characters, e.g., µ, , ρ) • Statistic: a measure that refers to a sample (English characters, e.g., X s, r)

15. Branches of Statistical Methods • Descriptive Statistics: describing the data through frequency distributions, measures of central tendency and variability, etc. • Inferential Statistics: Making inferences about populations by utilizing samples (e.g., are there IQ differences between the sexes)

16. Measures of Central Tendency (Ch. 3 G & W) • Mean • in the population, this is symbolized by  • in the sample, this is symbolized byX • it is calculated by the following formula: X=X N

17. Mean • Suppose a psychotherapist noted how many sessions her last 10 patients had taken to complete brief therapy with her. The sessions were as follows: 7, 8, 8, 7, 3, 1,6, 9,3, 8 X=X = 60 = 6 N 10

18. Mean Advantages: • Familiar and intuitively clear to most people • Useful for performing statistical procedures Disadvantages: • May be affected by extreme values • Tedious to compute

19. Measures of Central Tendency (Ch. 3 G & W) • Median • the score that divides a distribution of scores into the upper and lower halves • aka the 50th percentile • median is better than the mean when there are a few extreme scores

20. Median • Odd number of scores: line up all scores from lowest to highest, middle score is median 3 ,4 ,5, 7, 8 Median = 5 • Even number of scores: list scores in order (lowest-highest), locate median by finding the point halfway between the middle 2 scores 3, 3 ,4 ,5, 7, 8 Median=4+5 = 4.5 2

21. Measures of Central Tendency (Ch. 3 G & W) • Mode • most frequently occurring score • may be more than one mode • not affected by extreme values

22. Mode - Examples • No ModeRaw Data: 10.3 4.9 8.9 11.7 6.3 7.7 • One ModeRaw Data: 6.3 4.9 8.9 6.3 4.94.9 • More Than 1 ModeRaw Data: 21 2828 41 4343

23. When Do You Use Which Measure? • Categorical or nominal data (e.g., eye colour) - use the mode • Quantitative data (e.g., height, age, test scores) – use the mean and median • Extreme scores - use the median • No extreme scores - use the mean

24. Central Tendency & Shape of Distribution • Normal Distribution • a purely theoretical distribution • perfectly symmetrical about its mean • Mean=Median=Mode

25. Central Tendency & Shape of Distribution • Skewed Distributions • Greater proportion of observations fall in one tail of distribution than the other.

26. Central Tendency & Shape of Distribution • Positively Skewed • tail to right • mode<median<mean

27. Central Tendency & Shape of Distribution • Negatively Skewed • tail to left • mean<median<mode

28. Measures of Variability (Ch. 4 G & W) “degree to which scores in a distribution are spread out or clustered” (G& W, p. 104) • Range • difference between the largest and smallest scores in a distribution of scores • isn’t really a good description of the variability for an entire distribution

29. Measures of Variability (Ch. 4 G & W) • Interquartile Range • difference between the 75th and 25th percentiles in a distribution of scores • the 75th percentile is the score where 75% of scores fall below and the 25th percentile is the score where 25% of the scores fall below

30. Measures of Variability (Ch. 4 G & W) • Standard Deviation (SD) & Variance • most widely used • determines whether scores are generally near or far from the mean • in the population, the SD is symbolized by  and the variance is symbolized by 2 • in the sample, the SD is symbolized by s and the variance is symbolized by s2

31. Calculating the Variance and/or Standard Deviation Variance: Standard Deviation:

32. -1 1 6 3 9 10 -2 4 5 -3 9 4 2 4 9 1 1 8 Example: Data: X = {6, 10, 5, 4, 9, 8}; N = 6 Mean: Variance: Standard Deviation: Total: 42 Total: 28

33. Hypothesis Testing • A hypothesis is a statement about a relationship between variables. The cornerstone of hypothesis testing is the concept of the null hypothesis. • The Null Hypothesis states there is no true difference between scores in the population.

34. Hypothesis Testing The alternative hypothesis Ha, is that the difference in our sample is truly reflecting a real difference in the population, that the difference is not due to sampling error.

35. One Tailed Directional hypothesis Eg: “Those receiving $1,000,000 will be happier than the general public” Two-tailed Direction not specified Eg: “Social skills program changes the level of productivity” One –Tailed vs Two-Tailed Hypothesis Tests

36. Uncertainty & Errors in Hypothesis Testing • Type I error • Null hypothesis is rejected, but it is true • Under control of researcher • α is the probability of making a Type I error

37. Uncertainty & Errors in Hypothesis Testing • Type II error • Fail to reject null hypothesis when it is false • β is the probability of making a Type II error

38. Possible Outcomes of Statistical Decision Do not reject Ho Reject Ho Correct Decision Type I Error Ho is True Reality Correct Decision Type II Error Ho is False

39. Hypothesis Tests in Research Articles (Wang et al, 1997, p. 148)