psych 3400 statistics for the behavioral sciences cuny brooklyn college, department of psychology
DESCRIPTION
Psych 3400 Statistics for the Behavioral Sciences CUNY Brooklyn College, Department of Psychology. Alla Chavarga [email protected] 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 - PowerPoint PPT PresentationTRANSCRIPT
PSYCH 3400Statistical Methods
CUNY Brooklyn College, Department of Psychology
Alla [email protected]
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
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 whenyour TA is present
You should think of the lab section as training, you will complete most of the homework on your own time.
http://psychfiles.net
• Contact info• Syllabus/ Semester Schedule• Lecture Slides• Homework Assignments/Problem Sets
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.
“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.”
Which of these makes more sense?
Hours worked
Pay
Hours worked
Pay
Hours workedPa
y
We can also use statistics to describe relationships that we can depict graphically, such as in these
SCATTERPLOTS.
How do we acquire knowledge?
AuthorityIntuition
Scientific Method
Rationality
WHY do I have to learn Statistics?
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
The Concept of a Variable
Textile Workers
45
50
55
60
65
70
75
80 100 120 140 160
Weight (lbs)
Hie
ght (
inch
es)
Height (y-axis)Weight (x-axis)
Any measurable property of a person, event or object that may take on different values at different times or under different conditions.
Compare with aCONSTANT like p
Continuous and Discrete Variables
1 2 3 4 5 6
2.51/2
2.1251/8
2.251/4
Discrete Variable
2 3
Continuous Variable
Can dividein halfinfinitely
Scales of Measurement
Nominal Names or categories
Order: a sense of greateror 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
Summarizing Samples with Math and Graphs
=S Gi NominalOrdinalIntervalRatio
Class Heights (Raw Scores)
0
5
10
15
54 55 56 57 58 59 60 61 62 63 64
Height (inches)
Freq
uenc
y (n
umbe
r of
indi
vidu
als)
Significant Figures and RoundingIt 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.
Mathematical Notation
This is probably new to you.S
It means “summation”
Mathematical Notation: Summation Calculation
Student Grade ID (X) 1 93 2 75 3 88 4 77 5 65 6 55 7 97
Average of the variable X:
S X1n ( )
SX =
= (1/7) 550= 78.57
93 + 75 +88 + 77 + 65 + 55 + 97
SX = 550
Order of Operations
Order of operations:Parentheses, Exponents,Summation, Multiplication/Division, Addition/Subtraction
Read them like Englishsentences or lists of things to do in order
Important Example
x: { 1, 2, 3}
S x2 (S x )2
“Sum of the squared x’s” “Square of the summed x’s”
x123
x2
(1)2=1(2)2=4(3)2=9
14
x123
6 62 = 36
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}
How can data be described? Summarized?
Value Frequency54 155 156 257 458 159 160 361 2
Frequency Table
Frequency Histogram
HEIGHT
61.060.059.058.057.056.055.054.0
HEIGHT
Freq
uenc
y
5
4
3
2
1
0
Std. Dev = 2.20
Mean = 57.9
N = 15.00
How can data be described? Summarized?How to create a detailed frequency table:
Set of scores: x: {2, 1, 5, 0, 2, 1, 2, 0, 1, 1, 3, 1, 2, 1, 1, 0, 0, 2, 3 , 1}Example: How many siblings do you have?
Value012345
How can data be described? Summarized?How to create a detailed frequency table:
Set of scores: x: {2, 1, 5, 0, 2, 1, 2, 0, 1, 1, 3, 1, 2, 1, 1, 0, 0, 2, 3 , 1}Example: How many siblings do you have?
Value012345
Frequency
How can data be described? Summarized?How to create a detailed frequency table:
Set of scores: x: {2, 1, 5, 0, 2, 1, 2, 0, 1, 1, 3, 1, 2, 1, 1, 0, 0, 2, 3 , 1}Example: How many siblings do you have?
Value012345
Frequency4
How can data be described? Summarized?How to create a detailed frequency table:
Set of scores: x: {2, 1, 5, 0, 2, 1, 2, 0, 1, 1, 3, 1, 2, 1, 1, 0, 0, 2, 3 , 1}Example: How many siblings do you have?
Value012345
Frequency485201
Total 20
How can data be described? Summarized?How to create a detailed frequency table:
Set of scores: x: {2, 1, 5, 0, 2, 1, 2, 0, 1, 1, 3, 1, 2, 1, 1, 0, 0, 2, 3 , 1}Example: How many siblings do you have?
Value012345
Frequency485201
Total 20
Percent
How can data be described? Summarized?How to create a detailed frequency table:
Set of scores: x: {2, 1, 5, 0, 2, 1, 2, 0, 1, 1, 3, 1, 2, 1, 1, 0, 0, 2, 3 , 1}Example: How many siblings do you have?
Value012345
Frequency485201
Percent
Total 20
= (4/20) x 100= .20 x 100= 20
2020
How can data be described? Summarized?How to create a detailed frequency table:
Set of scores: x: {2, 1, 5, 0, 2, 1, 2, 0, 1, 1, 3, 1, 2, 1, 1, 0, 0, 2, 3 , 1}Example: How many siblings do you have?
Value012345
Frequency485201
Percent
Total 20
2040251005
CumulativeFrequency41217191920
CumulativePercent2060859595100
20
How can data be described? Summarized?How to create a detailed frequency table:
Set of scores: x: {100, 23, 65, 98, 84, 72, 50, 49, 52, 99, 83, 79, 89, 9056, 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.
Example: TEST GRADES!!?
How can data be described? Summarized?How to create a detailed frequency table:
Set of scores: x: {100, 23, 65, 98, 84, 72, 50, 49, 52, 99, 83, 79, 89, 9056, 63, 72, 92, 83, 100}
Example: TEST GRADES!!?
Intervals23-3031-3839-4647-5455-6263-7071-7879-8687-9495-102
How can data be described? Summarized?How to create a detailed frequency table:
Set of scores: x: {100, 23, 65, 98, 84, 72, 50, 49, 52, 99, 83, 79, 89, 9056, 63, 72, 92, 83, 100}
Example: TEST GRADES!!?
Intervals23-3031-3839-4647-5455-6263-7071-7879-8687-9495-102
Frequency1003122434
How can data be described? Summarized?How to create a detailed frequency table:
Set of scores: x: {100, 23, 65, 98, 84, 72, 50, 49, 52, 99, 83, 79, 89, 9056, 63, 72, 92, 83, 100}
Example: TEST GRADES!!?
Intervals23-3031-3839-4647-5455-6263-7071-7879-8687-9495-102
Frequency1003122434
Percent5001551010201520
CumulativeFrequency1114579131620
CumulativePercent555202535456580100
Choice of Interval is Important
HEIGHT
64.059.555.050.546.0
HEIGHT
Fre
quen
cy
30
20
10
0
43-48 49-54 55-60 61-66 67-72
HEIGHT
65.062.560.057.555.052.550.047.545.0
HEIGHT
Freq
uenc
y
20
10
0
45-47 48-50 51-53 54-56 57-59 60-62 63-65 66-68 69-71
Frequency Polygons
HEIGHT
61.0060.0059.0058.0057.0056.0055.0054.00
Cou
nt5.0
4.0
3.0
2.0
1.0
0.0
HEIGHT
61.060.059.058.057.056.055.054.0
HEIGHTFr
eque
ncy
5
4
3
2
1
0
Std. Dev = 2.20
Mean = 57.9
N = 15.00
HEIGHT
61.0060.0059.0058.0057.0056.0055.0054.00
Cou
nt
5.0
4.0
3.0
2.0
1.0
0.0
By Comparison…
HEIGHT
61.060.059.058.057.056.055.054.0
HEIGHTFr
eque
ncy
5
4
3
2
1
0
Std. Dev = 2.20
Mean = 57.9
N = 15.00
HEIGHT
61.0060.0059.0058.0057.0056.0055.0054.00
Cou
nt
5.0
4.0
3.0
2.0
1.0
0.0
By Comparison…These are commonly referred
to as DISTRIBUTIONS
Common Shapes of Frequency Distributions
HEIGHT
60.059.058.057.056.055.054.0
HEIGHT
Freq
uenc
y
7
6
5
4
3
2
1
0
HEIGHT
60.059.058.057.056.055.054.0
HEIGHT
Freq
uenc
y
7
6
5
4
3
2
1
0
HEIGHT
60.059.058.057.056.055.054.0
HEIGHT
Freq
uenc
y
7
6
5
4
3
2
1
0
Common Shapes of Frequency Distributions
SymmetricalBell-shaped
PositivelySkewed
NegativelySkewed
Common Shapes of Frequency Distributions
Multimodal Distributions
HEIGHT
60.059.058.057.056.055.054.0
HEIGHT
Freq
uenc
y
8
6
4
2
0
HEIGHT
62.061.060.059.058.057.056.055.054.0
HEIGHT
Fre
quen
cy
14
12
10
8
6
4
2
0
When describing a distribution, always specify:-Is it unimodal, bimodal, multimodal?- Is it symmetrical?- Is it skewed, positive or negative?
Psych Stats 3400 First Exam GradesN=66 students
0
2
4
6
8
10
12
14
16
20-28 29-36 37-44 45-52 53-60 61-68 69-76 77-84 85-92 93-100
Grade
Freq
uenc
yA real example…
IT’S THE HUMAN HISTOGRAM!
Is this a histogram?