Psych 3400 Statistics for the Behavioral Sciences CUNY Brooklyn College, Department of Psychology

1. Psych 3400 Statistics for the Behavioral SciencesCUNY Brooklyn College, Department of Psychology AllaChavarga alla.chavarga@gmail.com MTWR 11:50am-12:45pm Room: 4607J Office hours: MT 1pm-3pm Room 4305J Ashley Polokowski apolokowski@brooklyn.cuny.edu MW 12:55-2:10pm Class room: 4607J

2. Approach of the course • Homework is practice for the exams • Essay type answers • Statistical calculations by hand • SPSS analysis • Exams are practice for the cumulative final • In this class you will learn both: practice (lab) of statistics. the theory ( lecture)

3. Lab format • Each lab will contain: • Announcements (make sure you are on time) • 2. Demonstration of new computer techniques • required for that week’s homework • 3. Period of questions and answers • 4. Opportunity for you to work with SPSS when • your TA is present You should think of the lab section as training, you will complete most of the homework on your own time.

4. Announcements: • Notices and updates from me will mainly be handled over email. • Please log into your email account and send an email to alla.chavarga@gmail.com • Put your NAME and “STATISTICS 3400” in the subject field • Required Text: • Pagano, Robert R. (2009) Understanding Statistics in the Behavioral Sciences. 9th Edition. Wadsworth Pub Co; ISBN: 0534353908 • Any edition from the 5th on will work • Appendix A if you feel shaky on the math • Practice exercises at the end of most chapters Although I do not teach strictly from the book, you will be required to read it in ADVANCE of lecture.

5. Definition of a statistic: Our working definition: A number that organizes, summarizes or makes understandable a collection of data. The formal definition from Pagano (the textbook): A number calculated on sample data that quantifies a characteristic of the sample.

6. Which of these makes more sense? “In our calculations, we noted large differences in pupil size between males and females. The male group had pupil diameters (mm) of 3.2, 4.1, 4.6, 7.2, 4.1, 5.3, 8.1, 6.3, 4.8, 4.6, 4.8, while females had the following pupil diameters: 4.6, 7.1, 4.7, 3.7, 8.0, 4.8, 6.2, 4.5, 4.9, 7.1, 6.8. Obviously, there is a noticeable difference.” vs. “In our calculations, we noted large differences in pupil size between males and females. The male group had an average pupil diameter of 4.9, while females had an average pupil diameter of 6.1. Obviously, there is a noticeable difference.”

7. Pay Hours worked Pay Hours worked Pay Hours worked We can also use statistics to describe relationships that we can depict Graphically, such as in these SCATTERPLOTS.

8. Four ways of acquiring knowledge Scientific Method Authority Intuition Rationality

9. WHY do I have to learn statistics?

10. Some VERY important definitions: • Population – the complete set of individuals, objects, or scores that the investigator is interested in studying. • Sample – a subset of the population. • Experimental vs. Observational Methods • Variable – any property or characteristic of some event, object, or person that may have different values at different times depending on the conditions • Independent: the variable that is systematically manipulated by the investigator • Dependent: the variable that is measured to determine the effect of the independent variable • Data - the measurements made on the subjects of an experiment • Statistic – a number calculated on sample data that quantifies a characteristic of the sample. (Note: Parameter). • Descriptive vs. inferential statistics

11. The Concept of a Variable Any measurable property of a person, event or object that may take on different values at different times or under different conditions. • Height, symbolized as H (or y if we choose) • Weight, symbolized as W (or x if we choose) Compare with a CONSTANT likep

12. 1 2 3 4 5 6 Continuous Variable 2 2.5 1/2 3 2.25 1/4 Can divide in half infinitely 2.125 1/8 Continuous and Discrete Variables Discrete Variable

13. Names or categories Order: a sense of greater or lesser but not by how much Ordinal and how much greater & lesser: each interval is equal Interval with an absolute zero - ratios of scores have meaning. Scales of measurement • Nominal • Ordinal • Interval • Ratio

14. Summarizing Samples with Math and Graphs S Gi = Nominal Ordinal Interval Ratio

15. Significant figures and rounding It does not make sense to carry our calculations beyond the real limits of the variables we measure. Example: On a thermometer the smallest unit is half of a degree. By convention we will round all numbers to two places. 5.624  5.62 when the fourth decimal place is 4 or less 1.287  1.29 when the fourth decimal place is 5 or more

16. Mathematical Notation Part I S XY - (S X) (S Y) n = S X2 - (S X)2S Y2 - (S Y)2 n n r [ [ ] ]

17. Mathematical Notation Part II S XY - (S X) (S Y) n = S X2 - (S X)2S Y2 - (S Y)2 n n r [ ] [ ] This one is probably new to you. S It means “summation” These you already know.

18. Student Grade ID (G) 1 93 2 75 3 88 4 77 5 65 6 55 7 97 [ ] 1 n S G = Math Notation: summation calculation Student Grade ID (G) G1 = 93 G2 = 75 G3 = 88 G4 = 77 G5 = 65 G6 = 55 G7 = 97 Average of the variable G: S G G1 + G2 + G3 + G4 + G5 + G6 + G7 = 93 + 75 +88 + 77 + 65 + 55 + 97 = 550 Average = (1/7) 550 = 78.57

19. S XY - (S X) (S Y) n = S X2 - (S X)2SY2 - (S Y)2 n n r [ ] [ ] Mathematical Notation Part III Order of operations: Parentheses, Exponents, Summation, Multiplication/Division, Addition/Subtraction Read them like English sentences or lists of things to do in order

20. S x2 Important Example for order of operations x: { 1 , 2, 3} (S x )2 “Sum of the squared x’s” “Square of the summed x’s” x 1 2 3 x 1 2 3 x2 (1)2=1 (2)2=4 (3)2=9 62 = 36 6 14

21. Frequency Table Frequency Histogram How can data be described? Summarized? Here is a set of 15 height measurements (in inches). { 55, 56, 56, 58, 60, 61, 57, 57, 59, 60, 60, 61, 54, 57, 57} ValueFrequency 54 1 55 1 56 2 57 4 58 1 59 1 60 3 61 2

22. How can data be described? Summarized? How to create a detailed frequency table: Example: How many siblings do you have? Set of scores: x: {2, 1, 5, 0, 2, 1, 2, 0, 1, 1, 3, 1, 2, 1, 1, 0, 0, 2, 3 , 1} Value 0 1 2 3 4 5

23. How can data be described? Summarized? How to create a detailed frequency table: Example: How many siblings do you have? Set of scores: x: {2, 1, 5, 0, 2, 1, 2, 0, 1, 1, 3, 1, 2, 1, 1, 0, 0, 2, 3 , 1} Frequency Value 0 1 2 3 4 5

24. How can data be described? Summarized? How to create a detailed frequency table: Example: How many siblings do you have? Set of scores: x: {2, 1, 5, 0, 2, 1, 2, 0, 1, 1, 3, 1, 2, 1, 1, 0, 0, 2, 3 , 1} Frequency 4 Value 0 1 2 3 4 5

25. How can data be described? Summarized? How to create a detailed frequency table: Example: How many siblings do you have? Set of scores: x: {2, 1, 5, 0, 2, 1, 2, 0, 1, 1, 3, 1, 2, 1, 1, 0, 0, 2, 3 , 1} Frequency 4 8 5 2 0 1 Value 0 1 2 3 4 5 Total 20

26. How can data be described? Summarized? How to create a detailed frequency table: Example: How many siblings do you have? Set of scores: x: {2, 1, 5, 0, 2, 1, 2, 0, 1, 1, 3, 1, 2, 1, 1, 0, 0, 2, 3 , 1} Frequency 4 8 5 2 0 1 Percent Value 0 1 2 3 4 5 Total 20

27. How can data be described? Summarized? How to create a detailed frequency table: Example: How many siblings do you have? Set of scores: x: {2, 1, 5, 0, 2, 1, 2, 0, 1, 1, 3, 1, 2, 1, 1, 0, 0, 2, 3 , 1} Frequency 4 8 5 2 0 1 Percent Value 0 1 2 3 4 5 20 20 = (4/20) x 100 = .20 x 100 = 20 Total 20

28. How can data be described? Summarized? How to create a detailed frequency table: Example: How many siblings do you have? Set of scores: x: {2, 1, 5, 0, 2, 1, 2, 0, 1, 1, 3, 1, 2, 1, 1, 0, 0, 2, 3 , 1} Cumulative Frequency 4 12 17 19 19 20 Cumulative Percent 20 60 85 95 95 100 Frequency 4 8 5 2 0 1 Percent Value 0 1 2 3 4 5 20 40 25 10 0 5 20 Total 20

29. How can data be described? Summarized? How to create a detailed frequency table: Example: TEST GRADES!!? • Set of scores: x: {100, 23, 65, 98, 84, 72, 50, 49, 52, 99, 83, 79, 89, 90 • 56, 63, 72, 92, 83, 100} • What if our range is very large? • We use class intervals instead of single values • Rule for # of intervals for use in this class: 10 • To determine the width that each interval should be given the range of data we have, use the following formula: • = (Highest score – Lowest score)/10 • = (100 – 23)/10 • = 77/10 • = 7.7  round this to the next whole number, 8.

30. How can data be described? Summarized? How to create a detailed frequency table: Example: TEST GRADES!!? Set of scores: x: {100, 23, 65, 98, 84, 72, 50, 49, 52, 99, 83, 79, 89, 90 56, 63, 72, 92, 83, 100} Intervals 23-30 31-38 39-46 47-54 55-62 63-70 71-78 79-86 87-94 95-102

31. How can data be described? Summarized? How to create a detailed frequency table: Example: TEST GRADES!!? Set of scores: x: {100, 23, 65, 98, 84, 72, 50, 49, 52, 99, 83, 79, 89, 90 56, 63, 72, 92, 83, 100} Intervals 23-30 31-38 39-46 47-54 55-62 63-70 71-78 79-86 87-94 95-102 Frequency 1 0 0 3 1 2 2 4 3 4

32. How can data be described? Summarized? How to create a detailed frequency table: Example: TEST GRADES!!? Set of scores: x: {100, 23, 65, 98, 84, 72, 50, 49, 52, 99, 83, 79, 89, 90 56, 63, 72, 92, 83, 100} Cumulative Percent 5 5 5 20 25 35 45 65 80 100 Cumulative Frequency 1 1 1 4 5 7 9 13 16 20 Percent 5 0 0 15 5 10 10 20 15 20 Intervals 23-30 31-38 39-46 47-54 55-62 63-70 71-78 79-86 87-94 95-102 Frequency 1 0 0 3 1 2 2 4 3 4

33. Choice of interval: 43-48 49-54 55-60 61-66 67-72 45-47 48-50 51-53 54-56 57-59 60-62 63-65 66-68 69-71

34. Frequency Polygons

35. Frequency Polygons

36. Frequency Polygons These are commonly referred to as DISTRIBUTIONS

37. Common Shapes of Frequency Distributions

38. Common Shapes of Frequency Distributions

39. Common Shapes of Frequency Distributions Symmetrical Bell-shaped Positively Skewed Negatively Skewed

40. Multimodal Distributions • When describing a distribution, always specify: • -Is it unimodal, bimodal, multimodal? • Is it symmetrical? • Is it skewed, positive or negative?

41. A real example…

42. IT’S THE HUMAN HISTOGRAM!!!!!!