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Psychology 230 Psychological Measurement and

Statistics

- There are three kinds of lies
- Lies, damned lies, and statistics.
- -Benjamin Disraeli

Interesting Statistics

- More than 60 of all accidents occur within 2

miles of ones home. - The national median salary is 30,000.
- There are more right-handed people than

left-handed people. - The safest way to travel is.FLYING!

How bad is this going to be?

- Statistics is not math (its a way or organizing

and interpreting infobut it does use some

mathematical procedures). - Math fears Basic Mathematical Review (Appendix A

in your book). - Dont be overwhelmed by research

papers/articles/reports. - Symbols (i.e. ?).
- Jargon (i.e. ANOVA analysis of variance). Based

in logic.

The Basics

- Terms and Concepts

Foundations and Common Terms Populations vs.

Samples

- Data numbers, measurements collected.
- Population complete set of people/objects

(scores) having some common characteristic. The

entire collection of events - denoted by N. - Sample subset of population that share same

characteristic used to infer characteristics of

the pop - denoted by n.

Describing Data Parameters vs. Stats

- Parameter value summarizing characteristic of

population constants Greek letters are used to

represent parameters. - Statistic value summarizing characteristic of a

sample variables use Roman letters to

represent. - Sampling error the discrepancy, of amount of

error that exists between a sample statistic and

the corresponding population parameter.

Research Methodology

- Statistics research methods are intricately

tied. - The stats you perform are partially determined by

the design of your experiment. - Some research projects are designed for use with

particular stats procedures. - This is NOT a research methods class. However

Foundations and Common Terms Variables

- Variable measurable characteristic that changes

with person, environment, experiment e.g.

height, IQ, learning (X or Y). - Constant a characteristic or condition that does

NOT change (e.g. ?, time of day, religion). - Discrete variable One that has limited number of

values (e.g. children cars). - Continuous variable One that has an infinite

number of values (e.g. exam scores, time, age).

Correlational Method

- Correlational method two variables are measured

and compared to see if there is a relationship -

observational.

Salary

More about Variables

- Independent Variable (IV) variable examined to

determine its effect on outcome of interest (DV) - manipulated variable (e.g. a dose of a drug).
- Subject or organismic variable / time variable

naturally occurring IV not controlled (e.g. eye

color, time of day). - Dependent Variable (DV) outcome of interest

measured to assess the effects of IV - not under experimental control (e.g. how a

person reacts to a drug) . - Confound DV is affected by a variable related to

IV - dont know what caused effect on DV (e.g. herbs

taken in addition to drug).

Experimental Method

- Experimental one variable is manipulated while

changes are observed in the other. Looking for

cause and effect relationships. Includes a

control group and an experimental group. - Random sample assign subjects to treatments in

EQUAL and INDEPENDENT manner to avoid bias.

Remaining Methodological Terms

- Theory statements about underlying mechanisms of

behavior. - Hypothesis a prediction about the relationship

between variables. - Constructs hypothetical concepts used to

organize behavior that cant be observed (e.g.

intelligence, attention). - Operational definition defines a construct in

terms of specific procedures or measurements that

result from them (e.g. an IQ test eye movement

to a display item).

Example Experimental Method

Which therapy works best for depressed patients?

- Construct Depression.
- Operational Def. Mood score.
- Hypothesis Meditation will be as good a

treatment for depression as talk therapy.

Experiment with Confound

Quasi-Experimental Method

- Quasi-experimental comparing groups like

experimental methodology but not manipulating one

of the groups. Uses subject/time variables.

Example

- Does the number of hours of sleep before a test

affect your performance on that test? - Correlation to look at each variables

relationship to the other. - Experiment if you divide participants into sleep

groups. - Sleep time 4, 6, or 8 hours (Independent

variable). - Performance on the exam (Dependent variable).

Example 2

- Does stress affect memory? Is it differentially

affected for men vs. women. - 1st question is requires an experimental design
- Independent variable is the amount of stress (a

construct). This variable needs to be

operationally defined, so look at the amount of

cortisol a correlate of stress. Give 3 groups

different amounts. Can you think of another way

of doing this? - Dependent variable is the performance on a memory

test (memory is also a construct and so needs an

operational def.). - Question 2 requires a quasi-experimental design

dividing the groups given cortisol into groups of

men vs. women and looking at their memory test

scores.

Gross Overview

Descriptive Statistics

- Procedures for summarizing and describing the

characteristics of a data set. - Examples
- Frequency or count.
- Ratio 137 women to men (do not reduce).
- Proportion 1/4 .25.
- Percentage.

Descriptive Statistics

- Employs exploratory data analysis, uses visual

aids, abbreviations, etc.

- percentage of words memorized from a list over

time

- ratio of students in this class who support the

death penalty

Inferential Statistics

- Predictive allows drawing inferences about the

characteristics of a pop. based on a sample. - Risk
- Claiming to know values that were never really

measured. - When done correctly, highly reliable and valid.
- Reliability degree to which repeated measures

give the same results. - Validity accuracy test/ measure actually

measures the thing of interest. - Men are generally taller than women.
- Shoe size is not a predictor of intelligence.

Descriptive vs. Inferential

- What would you need to know to determine whether

these statements were descriptive or inferential?

- Do you think these statements are descriptive or

inferential? - People who show up for class get better grades.
- Students eat pizza 2.354 times per week.
- Blondes have more fun.
- The average temperature at noon in Tucson in June

is 103. - In groups of 3-4 generate 3 examples of each type

of statistic descriptive and inferential.

Putting it all together The Role of Stats in

Research

- Step 1 Exp.
- Collect data
- Step 2 Descriptive
- Organize and simplify
- Step 3 Inferential
- Interpret results
- 2 ways
- Actually is no diff.
- its due to chance
- Sample reflects a true
- diff.

31

25

31

The Stevens System

- Method of classifying data introduced by S. S.

Stevens in 1946. - Helps in determining which statistical test

applies (this will be useful later on in the

course). - 4 categories of data.
- 1) Nominal scale.
- 2) Ordinal scale.
- 3) Interval scale.
- 4) Ratio scale.

The Nominal Scale

- Could be called labeling.
- Numbers are assigned to define a category.
- Therefore, all cases in the same category receive

the same designation, the same number. - Categories are independent/mutually exclusive.
- Makes no assumptions regarding the relationship

among measures. - e.g. political party affiliation, SSNs, kinds of

pets.

The Ordinal Scale

- Orders cases along a predetermined continuum.
- The distance between two successive points are

not assumed to be equal. - provides greater than and less than

information, without indicating how much. - Andy is taller than Jane.
- Marva is taller than George.
- Is the difference between Andy Janes heights

greater than, less than or equal to the

differences between Marva Georges? - Most common use rank ordering.
- e.g. grade level, military rankings.

The Interval Scale

- The distance between two successive points are

assumed to be equal. - Cant use ratio information because there is no

true zero. - Cant claim that one value is twice as large as

another. - No true zero point.
- e.g. temperature in degrees, calendar.

The Ratio Scale

- The distance between two successive points are

assumed to be equal. - True zero point can lack whatever is being

measured. - e.g. Height, weight, temperature in Kelvin.

General Properties of the Stevens Scale

- Order of complexity
- Ratio Interval Ordinal Nominal
- The more complex the scale, the more

sophisticated the statistical test/procedure that

can be performed. - All scales have the properties of the scales with

less complexity. - By and large, most psychological studies examine

interval or ratio data. - See Example 1.1 in the book pg. 22.

Qualitative vs. Quantitative data

- Qualitative a set of observations where any

single observation is a word or code that

represents a class or category. - Quantitative data a set of observations where

any single observation is a number that

represents an amount or count. - Examples
- Handedness.
- Gender.
- of men vs. women attending a jazz concert

(careful here always focus on the status of any

single observation rather than the entire set.

Data Type and the Stevens Scale

- Qualitative
- Nominal
- Ordinal

- Quantitative
- Interval
- Ratio

- State where you are from
- SATs
- size of french fry order
- response time
- points on an exam

Real Limits or True Limits

- Reminder
- Continuous variables - infinite number of

possible values fall between 2 observed values. - Discrete variables - separate indivisible

categories. - Real Limits - measurements of continuous

variables require assigning individuals to an

interval on a number line rather than a single

point (e.g. rounding your data). - Butthe real limits are not necessarily part of

the interval due to rounding.

Calculating Real Limits

- Real Limit - s that limit where the true value

lies. - /- 1/2 the unit of measurement.
- To get unit of measurement
- 3,4,5,6 unit 1 1/2 0.5 (limit value).
- 3 0.5 3.5 (upper limit of a value).
- 3 - 0.5 2.5 (lower limit of the value).

Calculating Real Limits

- 5,10,15,20 unit 5 5/2 2.5 (limit value).
- 10 2.5 12.5 (upper limit).
- 10 - 2.5 7.5 (lower limit).
- Intervals 15-20
- 14.5 and 20.5
- decimals
- Anything to the left 0.
- Last on the right 1 all others 0.
- 13.63 unit of measure 0.01 0.01/2 0.005

(limit value. - 13.63 0.005 13.635 (upper limit).
- 13.63 - 0.005 13. 625 (lower limit).

Statistical Notation

- Summation notation - Many statistical

computations require adding up a set of scores.

The Greek letter sigma, or ? stands for

summation. - X or Y symbol for a variable.
- Xi or Yi represents an individual observation.
- N or n data points in a set, number.

Order of Operations

- Mnemonic Please Excuse My Dear Aunt Sally
- (1) Parentheses
- (2) Exponents (squaring and the like)
- (3) Multiplication / Division (should be done in

order of left to right - (4) Addition / Subtraction (any order you like)
- Caveat Summation notion should be done after

step 3 but before step 4 (summation notation is

just another mathematical operation).

Examples

- Scores
- X1 4, X2 6, X31, X45, X52, X67
- Y13, Y24, Y36, Y41, Y52, Y61

(a) ? Xi (where i3 to 6) (b) ? Xi (where i1

to3) (c) ? Xi2 (where i 4 to 6) (d) (? Xi)2

(where i 4 to 6) (e) ? XY (where i 1 to

4) (f) ? XY - 1

Homework - Chapter 1

- 2, 3, 6, 8, 9, 12, 16, 17, 18,19, 22
- Find the real limits for
- The interval between 60-69.
- 10.5, 11.5
- -1.02, -1.03
- The interval between 25.5-27.5

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