Transcript
Statistics for Psychology:
An Introduction
Gravetter and Wallanau (G&W)
Chapter 1
You should be able to . . .
Define statistics
and tell the difference between descriptive and inferential statistics
Tell the difference between
populations and samples
parameters and statistics
Define data
and tell the difference between qualitative and quantitative data
and tell the difference between discrete and continuous data
You should be able to . . .
Understand key components of experiment designs
variables and constants
independent and dependent variables
control and experimental conditions
experimental and correlational studies
Define the four scales of measurement and tell the difference among them:
1. nominal
2. ordinal
3. interval
4. ratio
What’s a Statistic?
A set of tools used to organize, describe, and analyze numerical observations
Why are they important?
These tools are used to describe and analyze numerical observations derived from populations and samples
Lying with Statistics
Inappropriate Averages (e.g., tax refunds)
Small Sample sizes
Biased Samples (e.g., CNN/Fox News viewer polls)
Illusory Correlations
Populations and Samples
Population
The set of all individuals of interest
depressed humans
Sample
A subset of a population
those individuals in our research study
Populations and Samples
We use different terms to refer to the statistics used for populations and samples
Parameter
A numerical description of a characteristic of a population
average # of hours of sleep for entire population of depressed individuals
Statistic
A numerical description of a characteristic of a sample
average # of hours of sleep for those in our study
Parameters and Statistics
The term statistics is used to refer to the whole set of tools we use to describe and analyze numerical observations
A statistic refers to a specific tool applied to samples
E.g., an average for a sample
A parameter refers to a specific tool applied to populations
E.g., an average for a population
Statistic
Sample
Parameter
Population
describes
describes
Descriptive vs Inferential Statistics
Descriptive statistics
Statistical procedures used to summarize, organize, and simplify the data
Examples: Arithmetic Average (statistical mean), standard deviation, Quartiles, etc
Inferential statistics
Techniques to study samples and make use of generalizations about the population from which they were selected
T-statistic, F-Statistic, Chi-Square, correlation coefficient (r)
Inferential Statistics
Tools for making inferences from observations
Tools for generalizing beyond the available observations
Allows for inferences about populations based on samples
Population
Select
(draw sample)
Sample
infer
Sampling Error
There may be discrepancies between the sample and the population
A sample is not a perfect picture of a population
The discrepancy between the sample statistic and the population parameter is sampling error
For example: Average # of hours depressed people sleep
For sample = 12 hrs/per night
population 11.25 hrs/per night
The .75 difference can be attributed to sampling error
Another Example of Sampling Error
Sample #1
Sample Statistics
Nelly 4413
Lil’ Kim 4474
Nicki Minaj 4162
Lupe Fiasco 4439
Jay-Z 4506
Average = 4398.8
40% Female, 60% Male
Sample #2
Sample Statistics
Drake 3522
Missy Elliott 3874
Redman 5331
ICP 4149
Wiz Khalifa 3707
Average = 4116.6
20% Female, 80 % Male
Population
of 85 Hip Hop Artists
Number of unique words used in their lyrics
Parameters
Average = 4604.5
4% Female, 96% Male
Wu-Tang Clan
Sample Statistics
Method Man 4951
Raekwon 5001
Ghostface Killah 5774
RZA 5905
GZA 6426
Average = 5611.4
100% Male
Data extracted from:
http://rappers.mdaniels.com.s3-website-us-east-1.amazonaws.com/
Data
Collection of numerical observations from a survey or experiment
a single datum is a raw score
Qualitative versus Quantitative Data
Qualitative data
A single observation which represents a class or category (sometimes referred to as categorical data)
Marital status, religious affiliation, etc.
Quantitative Data
A single observation is an amount or a count
Reaction time, height, performance accuracy, etc.
Quantitative OR Qualitative?
Political Party
Amount of Coffee
Body Temperature
Biological Sex
Finishing position in World Cup
Discrete versus Continuous Data
Discrete data consist of a countable number of possible values
e.g., number of cars in a parking lot
countable with integers
Continuous data consist of an infinite number of possible values on a scale in which there are no gaps or interruptions
heights: 72.5 inches, 72.55 inches, 72.575 inches . . . .
weights: 160.00 pounds, 160.5 pounds . . .
number of hours of sleep: 8.6 hours, 6.4 hours, 10.2 hours . . .
Discrete versus Continuous Data
Qualitative data are always discrete
there’s no gray area with categories
But, Quantitative data are not always continuous:
number of cars in parking lot is discrete and quantitative
Experimental Design
and Other Considerations
Experimental Design
Variable
A characteristic or property of organisms, events, or objects that can take on different values
height, weight, IQ, mood, degree of anxiety, personality type, etc.
Can be identified by letters such as X, Y, or Z
Experimental Design
Constant
A characteristic or property that does not change
? is a constant : 3.1416 . . .
to convert proportions to percentages, you multiply by a constant:
.5 X 100 = 50%
Experimental Design
Independent Variable (IV)
a variable that is manipulated by the investigator
Dependent Variable (DV)
a variable that is measured by the investigator
Experimental Design
We conduct an experiment to determine if a new antidepressant drug is effective
We have two groups of depressed participants
Importance of Random Assignment in controlling for extraneous variables
We give one group an antidepressant drug
Experimental or treatment condition
We give the other group a placebo
Control condition (i.e., no treatment)
We measure symptoms of depression over the course of a month for both groups
Why Random Assignment?
Random Assignment
SAMPLE
Control Group
Experimental Group
Test for Differences
Control Group
Experimental Group
Why Random Assignment?
Confounding Variables
SAMPLE
Are differences due to manipulation or confounding variable?
Why Random Assignment?
No Confounding Variables
SAMPLE
Control Group
Experimental Group
Differences are due to manipulation, not an extraneous variable, because mood is randomly determined.
Independent and Dependent Variables: Example
What is the independent variable?
Drug: antidepressant vs. placebo
What is the dependent variable?
symptoms of depression
Importance of Operational Definitions
A highly specific definition of a construct of interest
Different Example :
Want to know alcohol consumption affects memorization of word lists.
Experimental Design overview
Other Relevant Study Designs
Independent Measures
Sometimes known as Between-Subjects
{5C22544A-7EE6-4342-B048-85BDC9FD1C3A}Cond 1 (Sub #)
Cond 2 (Sub #)
Cond 3 (Sub #)
Cond 4 (Sub #)
80 (1)
36 (5)
43 (10)
81 (14)
25 (2)
49 (7)
45 (11)
79 (15)
39 (3)
27 (8)
78 (12)
66 (16)
17 (4)
89 (9)
56 (13)
68 (17)
{93296810-A885-4BE3-A3E7-6D5BEEA58F35}Subject #
Cond 1
Cond 2
Cond 3
Cond 4
1
77
87
88
67
2
55
56
45
56
3
32
12
46
65
4
44
65
76
40
Repeated Measures
Sometimes known as Within-Subjects
NOTE:
These are all different participants
NOTE:
These are the same participants
Other Relevant Study Designs
Quasi-Experimental (“non-experimental”)
Cases where researcher has no control of group assignment
Used when you cannot manipulate IV yourself
Example, when comparing pre-existing , categorical groups
Gender, trauma/abuse, relationship status, etc.
Inability to rigorously control for extraneous variables
Example:
Pre- and Post-Test studies
Changes observed in DV may be a product of the passage of time.
Non-Equivalent Groups
Inability to control assignment to group due to previously established membership
Other Relevant Study Designs
Correlational study
Investigator measures two DVs and looks for a relationship
Is there a relationship between vocabulary size and age?
Key limitation: CORRELATION DOES NOT DETERMINE CAUSATION
Concept Check
Correct
Alphonso wants to test the prediction that drinking “red bull” enhances memory. He has one group of students drink a can of “red bull” while reading a list of words. Another group reads the same list without drinking the energy drink. Afterwards, all participants complete a memory test for the list.
What kind of research design is this?
Concept Check
Correct
Alphonso wants to test the prediction that drinking “red bull” enhances memory. He has one group of students drink a can of “red bull” while reading a list of words. Another group reads the same list without drinking the energy drink. Afterwards, all participants complete a memory test for the list..
In this experiment, exposure to Red Bull is the _____.
Concept Check
Correct
Alphonso wants to test the prediction that drinking “red bull” enhances memory. He has one group of students drink a can of “red bull” while reading a list of words. Another group reads the same list without drinking the energy drink. Afterwards, all participants complete a memory test for the list..
In this experiment, the memory test is the _____.
Scales of Measurement
The answers to the following three questions appear to be the same:
What number did you wear in
the drinking contest? 10
What place did you finish? 10
How many minutes did it take
you to finish? 10
Are these answers equivalent?
No, because each answer of piece of data represents a different scale of measurement
Scales of Measurement are . . .
The methods of assigning numbers to objects or events
There are four scales of measurement:
Nominal
Ordinal
Interval
Ratio
Nominal Measurement Scale
Refers to data that consist of names, labels, or categories
“nominal” from Latin for “name”
Numeric associations with labels are arbitrary and are used only to identify an object or event
Data cannot be meaningfully arranged in order
NAME
Nominal Measurement Scale
There is nothing in particular that requires use of numbers -- any label would suffice
Examples
Clothing brands/designs: Supreme, Obey . . .
Rat strains: Long-Evans, Sprague-Dawley
The number you wore in the drinking contest
10
Ordinal Measurement Scale
Refers to data or scores that can be arranged in some order
Numbers are used to identify an object or event (nominal) and to tell us the rank order of each object or event
ORDER
Ordinal Measurement Scale
Examples
Ranks in high school graduating class: 1st, 20th, 100th . . .
Tests of elementary students: Below average, average, above average, gifted
Place of finish in drinking contest: 10
10th
Interval Measurement Scale
Refers to data that have meaningful differences between scores
Numbers are used to identify an object or event (nominal) and to tell us the rank order of each object or event (ordinal)
NAME + ORDER + INTERVALS
Two defining principles:
1.) Equidistant scale
2.) no true zero (AKA absolute zero)
Interval Measurement Scale
Equidistant Scales
Those values whose intervals are distributed in equal units
The differences or distances (intervals) between the scores are meaningful, unlike nominal or ordinal data
If someone concluded: “Satsifaction ratings were three-times greater among man than women” wouldn’t be appropriate
Interval Measurement Scale
However, a zero point may be lacking or it may be arbitrary
0?
0
1
2
-2
-1
Average
Very Good
Poor
Interval Measurement Scale
Celsius and Fahrenheit temperature scales are both interval scales
Zero degrees in both is determined “arbitrarily”
That is, zero does not mean the absence of heat
Another example:
Personality
Interval Measurement Scale: Example
A difference can be determined between 25 and 50 degrees Fahrenheit
. . . but 50 degrees is not twice as hot as 25
What about the Kelvin scale?
There is an absolute zero
0 degrees K is the temperature at which movement ceases
Ratio Measurement Scale
Refers to data on a scale with a true zero point
Has all properties of nominal, ordinal, and interval scale
Is an interval scale with a true zero
True zero point: Complete absence of data being measured
0!
Ratio Measurement Scale
NAME + ORDER + INTERVALS + TRUE ZERO
Ratio Measurement Scale
Examples
Height
Weight
The time it takes to finish the drinking contest
Blood Alcohol Concentration (BAC)
Concept Check
Correct
Name the Measurement scale for …
Military Title: Lieutenant, Captain, Major
Concept Check
Name the Measurement scale for …
Number of Errors committed on Exam
Correct
Because you can have zero errors and zero is meaningful
Concept Check
Name the Measurement scale for …
Class Rank
(Freshman, Sophomore, Junior, Senior, Super-Senior)
Correct
Because it indicates order/direction (high versus low)
Concept Check
Name the Measurement scale for …
Time as measured using a 12 hour clock
Correct
Moves along a continuous measure (milliseconds, seconds, minutes, hours, etc) without a zero point in time and with equal intervals
Concept Check
Name the Measurement scale for …
Social Security Number
Correct
Because it represents who you are, the number themselves are arbitrary
Note on Statistical Notation
summation sign (? “sigma”)
Summation Sign (? “sigma”)
?
read as “the sum of”
?X
means to add all the scores for variable X
Summation Sign (? “sigma”)
?X2
means first square each value of X, then add all of those squared values
?(X+1)
means first add 1 to each value of X, then add all of those new values
Summation Sign (? “sigma”)
?(X+1)2
means (1) add 1 to each value of X, (2) square each of those new values, (3) add all of those squared values
In G&W textbook, see section 1.5 (p. 25) for more on statistical notation and order of operations.
Example (Ch.1, Problem 19)
Find...
X
4 a. ?X
6
0
3
2
= 15
Example (Ch.1, Problem 19)
Find...
X
4 a. ?X = 15
6
0 b. ?(X2)
3
2
Example (Ch.1, Problem 19)
X Find...
4 => 16 a. ?X = 15
6 => 36
0 => 0 b. ?(X2)
3 => 9
2 => 4
Example (Ch.1, Problem 19)
X Find...
4 => 16 a. ?X = 15
6 => 36
0 => 0 b. ?(X2) = 65
3 => 9
2 => 4
Example (Ch.1, Problem 19)
X Find...
4 a. ?X = 15
6
0 b. ?(X2) = 65
3
2 c. ?(X+1)
Example (Ch.1, Problem 19)
X Find...
4 => 5 a. ?X = 15
6 => 7
0 => 1 b. ?X2 = 65
3 => 4
2 => 3 c. ?(X+1)
Example (Ch.1, Problem 19)
X Find...
4 => 5 a. ?X = 15
6 => 7
0 => 1 b. ?X2 = 65
3 => 4
2 => 3 c. ?(X+1) = 20
Example (Ch.1, Problem 19)
X Find...
4 a. ?X = 15
6
0 b. ?X2 = 65
3
2 c. ?(X+1) = 20
d. ?(X+1)2
Example (Ch.1, Problem 19)
X Find...
4 => 5 a. ?X = 15
6 => 7
0 => 1 b. ?X2 = 65
3 => 4
2 => 3 c. ?(X+1) = 20
d. ?(X+1)2
Example (Ch.1, Problem 19)
X Find...
4 => 5 => 25 a. ?X = 15
6 => 7 => 49
0 => 1 => 1 b. ?X2 = 65
3 => 4 => 16
2 => 3 => 9 c. ?(X+1) = 20
d. ?(X+1)2
Example (Ch.1, Problem 19)
X Find...
4 => 5 => 25 a. ?X = 15
6 => 7 => 49
0 => 1 => 1 b. ?X2 = 65
3 => 4 => 16
2 => 3 => 9 c. ?(X+1) = 20
d. ?(X+1)2 = 100
More examples…
Variable x = [1 2 3 4]
?x = _________
(?x) + 10 = _______
?(x + 10) = _________
(?x) 2 = _______
?(x 2) = _________