1. PSYCH 3400 Statistical Methods CUNY Brooklyn College, Department of Psychology
Alla Chavarga
MTWR 11:50am-12:50pm
Room: 4607J
Office hours:
MT 1-3pm 4305 James

2. Approach of the Course
In this class you will learn both the theory and practice of statistics.
Homework is practice for the exams
Essay type answers
Statistical calculations by hand
SPSS analysis

3. Lab Format Announcements (make sure you are on time
Demonstration of new computer techniques required for that week’s homework
Period of questions and answers
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.
Contact info
Syllabus/ Semester Schedule
Lecture Slides
Homework Assignments/Problem Sets

5. Announcements Subject: PSYC3400 – YOUR NAME – TA’s NAME
Notices and updates from me will mainly be handled over .
Please log into your account and send an to
Subject: PSYC3400 – YOUR NAME – TA’s NAME
Ex: PSYC3400 – JANE SMITH – NAOMI / KAMIL
Required Text:
Pagano, Robert R. (2009) Understanding Statistics in the Behavioral Sciences. 9th Ed. Wadsworth Pub Co; ISBN:
Any edition from the 5th on will work
Appendix A if you feel shaky on the math
Required reading in ADVANCE of lecture.

6. Definition of a Statistic
OUR WORKING DEFINITION:
A number that organizes, summarizes or makes understandable a collection of data.
THE FORMAL DEFINITION:
A number calculated on sample data that quantifies a characteristic of the sample.

7. 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.”

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

9. How do we acquire knowledge?
Scientific Method
Intuition
Authority
Rationality

10. WHY do I have to learn Statistics?

11. Some VERY important definitions:
Experimental vs. Observational Methods
Population – the complete set of individuals, objects, or scores that the investigator is interested in studying.
Sample – a subset of the population.
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

12. 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 (y-axis)
Weight (x-axis)
Compare with a
CONSTANT
like p

13. Continuous and Discrete Variables1 2 3 4 5 6
Discrete Variable 2 3
Continuous
Variable
2.125
1/8
2.25
1/4
2.5
1/2
Can divide
in half
infinitely

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

15. Summarizing Samples with Math and GraphsGi =
Nominal
Ordinal
Interval
Ratio

16. Significant Figures and Rounding
It does not make sense to carry our calculations beyond the real limits of the variables we measure.
Ex: On a thermometer the smallest unit is half of a degree.
By convention, in this class we will round all numbers to the hundredths place (two places after the decimal).
5.624  5.62 when the 3rd decimal place is ≤4.
1.287  1.29 when the 3rd decimal place is ≥5.

17. Mathematical Notation
This is probably new to you. S
It means “summation”

18. Mathematical Notation: Summation Calculation
X =
Student Grade
ID (X) S
X = 550
Average of the variable X: 1 n
( ) S
= (1/7) 550
= 78.57 X

19. Order of Operations Order of operations: Read them like English
Parentheses,
Exponents,
Summation,
Multiplication/Division,
Addition/Subtraction
Read them like English
sentences or lists of things to do in order

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

21. 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}
Value Frequency
54 1
55 1
56 2
57 4
58 1
59 1
60 3
61 2
Frequency Table
Frequency Histogram

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 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}
Value 1 2 3 4 5
Frequency

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}
Value 1 2 3 4 5
Frequency 4

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}
Value 1 2 3 4 5
Frequency 4 8 5 2 1
Total

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}
Value 1 2 3 4 5
Frequency 4 8 5 2 1
Percent
Total

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}
Value 1 2 3 4 5
Frequency 4 8 5 2 1
Percent 20 20
= (4/20) x 100
= .20 x 100
= 20
Total

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 20
Cumulative
Percent 20 60 85 95
100
Value 1 2 3 4 5
Frequency 4 8 5 2 1
Percent 20 40 25 10 5 20
Total

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 3 2 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
Frequency 1 4 5 7 9 13 16 20
Cumulative
Percent 5 20 25 35 45 65 80
100
Intervals
23-30
31-38
39-46
47-54
55-62
63-70
71-78
79-86
87-94
95-102
Frequency 1 3 2 4
Percent 5 15 10 20

33. Choice of Interval is Important

34. Frequency Polygons

35. By Comparison…

36. These are commonly referred to as DISTRIBUTIONS
By Comparison…

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!

43. Is this a histogram?