intro to statistics chapter 1 & 2

8/9/2019 Intro to Statistics Chapter 1 & 2

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Research Methods and Statistics I: PSYC 063


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C H A P T E R 1

INTRODUCTION TO

PSYCHOLOGICAL STATISTICS


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STATISTICS

Statistics: a set of methods for dealingwith numerical facts, that is data.

State % Bachelor's Rank

West Virginia 17.30% 50

Arkansas 18.90% 49

Mississippi 19.60% 48

Kentucky 21.00% 47

Louisiana 21.40% 46

Nevada 21.80% 45

Alabama 22.00% 44

Indiana 22.50% 43

Oklahoma 22.70% 42

Tennessee 23.00% 41

Idaho 23.90% 39

Ohio 24.10% 38

South Carolina 24.30% 37

Bachelors Degree:Mean = 27.38%, SD = 4.82%

Confederate States (n = 11) = 24.36%Non-Confederate States = 28.24%

HS graduation rate and Bachelors: r (50) = .53

Are these findings due to randomchance?


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DESCRIPTIVE VS. INFERENTIAL

STATISTICS

Descriptive Statistics: summarize a sample set of dataa researcher has collected. Conclusions focus onthat sample only. (mean, SD)

Inferential Statistics: when a sample set of data isused to draw conclusions about the largerpopulation it is drawn from. (null hypothesis tests)

Inferences about population

Population

Sample


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MEASUREMENT

Measurement: a system for assigning

numerical values to observations.


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SCALE OF MEASUREMENT DETERMINED BY MEASUREMENT

PROCEDURE NOT THE THING BEING MEASURED.

Ordinal Scale

1st

Sample

2nd Sample

3rd Sample

4th Sample

5th Sample

Nominal Scale

Hot = 1

Warm = 3

Cold = 2

Variablemolecular motion

Interval Scale Interval Scale Ratio Scale


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SCALES OF MEASUREMENT

FOUR TYPES

1. Nominal Scale or Categorical Scale – numbers are assigned arbitrarily, only aslabels. So mathematical operations donot make sense.

Examples:

Males = 1, Females = 2 Independent = 1, Democrat = 2,

Republican = 3

Red Car = 1, Blue Car = 2, Orange Car = 3


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FOUR TYPES

2. Ordinal Scale – a rank ordering of behaviors orcharacteristics.

Examples:

▪ order of finishers in a race

▪ student rankings at graduation

▪ pictures ranked for attractiveness

Note: Ranking gives no information

about the distance between

observations.

Shani Davis 2010 Olympics


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FOUR TYPES

3. Interval Scale – each number equidistant from

the next, but there is no true zero point.

Examples:IQ scores: IQ 90-100 and 100-110 are same distance,

but zero point does not mean absence of IQ

Farenheit or Celcius temperature10°-20° and 30°-40° is the same distance,but the zero point does not mean absence ofmolecular motion.


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FOUR TYPES

4. Ratio Scale – double the number means you havetwice as much. It contains a true zero point.

Examples:• Weight (10lb – 20lb)

• Number of questions correct (5 vs. 10)

• Time to complete task (30 sec vs. 60 sec)


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TEST YOUR KNOWLEDGE

Which Scale of Measurement?

Nominal/Categorical

Ordinal

Interval

Ratio

Dog characteristics:

weight (pounds)

terrier, working, herding, hound

placement in dog show

height they can jump (inches)

temperature (in Fahrenheit at vet)

obedience test score (range 20-50)

1st, 2nd, or 3rd dog a family has had

curly, double coat, smooth coat,hairless


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School of Social Work

(Lindsay)Douglass Hall

Syllabus: Lab Class Locations


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INDEPENDENT AND DEPENDENT

VARIABLES

Independent Variable (IV): the first variable, thepredictor variable, the antecedent, or the cause.

Dependent Variable (DV): the last variable, theoutcome, the consequence, or the effect.

It is hypothesized to depend on the independentvariable.


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TYPES OF RESEARCH: EXPERIMENTAL

Experimental:

Researcher manipulates which participants receivewhich level of the independent variable (IV).

Participants are randomly assigned to conditions.

Examples:

Tutoring/not (IV) -> Test Performance (DV)

Warm milk/not (IV) -> Time to Sleep (DV)


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TYPES OF RESEARCH:

NON-EXPERIMENTAL

Non-Experimental or Observational:

Researcher measures the level of each participanton the independent variable (IV).

Examples:

High School GPA (IV) Test Performance (DV)

Caffeine during the day (IV) Time to Sleep (DV)


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Scale of measurement of dependent variable

and example statistics.

Scale for DV Example Statistics

Nominal χ2(Chi-square)

Ordinal Rank-order tests

Interval F-test, t-testRatio F-test, t-test, and math operations


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REMINDERS

• Purchase the textbook and lab manual

• Complete practice problems indicated on

Blackboard before lab class Friday

• Go to lab class Friday

• Make sure your contact e-mail is up to date

on Blackboard

• No lab class Monday (holiday)• You need a calculator


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CHAPTER 1B:

BASIC STATISTICAL PROCEDURES

Average December high temperature for lastdecade?

High Temperatures in December, 2014:70, 46, 55, 47, 44, 53, 50, 38, 47, 51, 45, 47, 49, 57, 58,50, 58, 43, 43, 39, 45, 40, 48, 59, 61, 51, 60, 58, 48, 45, 39

Each day varies, so normally we would assign them adifferent variable (X, Y, Z).

N is our overall sample size. With N = 31 observations,we run out of letters, so we need a new notation.


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WHY USE SIGMA?

To shorten, use a subscript instead: X i

Temperatures in Dec: 70, 46, 55 … 39

So now X 1 = 70, X

2 = 46, X

3 = 55 … X

31 = 39

Subscript i indicates which observation 1 to N (1st to 31nd day in December).

To sum across all observations,

use the summation sign, or sigma:

N

i

i X

1


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PARTS OF SIGMA

= X 1 + X

2 + X

3 + … + X

31

= 70° +46° +55° +… +39°

N overall sample size (31 days)

i variable that ranges from 1 to N, the number ofobservations (from 1-31 for days)

X = observed variable (high temperatures)

N

i

i X

1


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TO THE BOARD: SIGMA RULES 1-4


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CHAPTER 2--TO THE BOARD:

FREQUENCY TABLE & BAR GRAPH


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ROUNDING OFF

During calculations: retain all numbers to the right ofthe decimal point.

Final answers:

Round to two decimals: .6666 .67

Round up if the number to the right is >50

Ex: .8651 .87

Round down if the number to the right is


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intro to statistics chapter 1 & 2

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