measures of central tendency tendency 1. mean 1. mean 2. median 2. median 3. mode 3. mode

MEASURES OF CENTRAL MEASURES OF CENTRAL TENDENCYTENDENCY

1. Mean1. Mean

2. Median2. Median

3. Mode3. Mode

CHARACTERISTICS OF MEANCHARACTERISTICS OF MEAN

• Measure of averageMeasure of average

• Influence by extremeInfluence by extreme scores (especially if scores (especially if distribution is small)distribution is small)

• Interval or ratio data Interval or ratio data

CHARACTERISTICS OF MEDIANCHARACTERISTICS OF MEDIAN

• Measure of positionMeasure of position

• NotNot influenced by extreme scores influenced by extreme scores • Ordinal or interval dataOrdinal or interval data

CHARACTERISTICS OF MODECHARACTERISTICS OF MODE

• Measure of frequencyMeasure of frequency

• NotNot influence by extreme influence by extreme ScoresScores

• Nominal DataNominal Data

Would you accept an education position Would you accept an education position Smart High School where the average Smart High School where the average salary is $74,200?salary is $74,200?

Would you accept an education position Would you accept an education position Smart High School where the average Smart High School where the average salary is $74,200?salary is $74,200?

TEACHER A: $100,000TEACHER A: $100,000TEACHER B: $95,000TEACHER B: $95,000TEACHER C: $90,000TEACHER C: $90,000TEACHER D: $85,000TEACHER D: $85,000TEACHER E: $1,000TEACHER E: $1,000****

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MEASURES OF VARIABILITY EXAMPLEMEASURES OF VARIABILITY EXAMPLE

GROUP A: 86.00 84.00 83.00 82.00 80.00GROUP A: 86.00 84.00 83.00 82.00 80.00

GROUP B: 95.00 90.00 90.00 75.00 65.00GROUP B: 95.00 90.00 90.00 75.00 65.00

MEASURES OF VARIABILITYMEASURES OF VARIABILITY

1. Range1. Range

2. Quartile Deviation2. Quartile Deviation

3. Mean Deviation3. Mean Deviation

4. Standard Deviation4. Standard Deviation

CHARACTERISTICS OF RANGECHARACTERISTICS OF RANGE

• Measure of distance between high Measure of distance between high high score and low score high score and low score • Indicates nothing about Indicates nothing about variability of scores between variability of scores between extreme scores extreme scores

• Does not consider all scores Does not consider all scores

CHARACTERISTICS OF QUARTILE CHARACTERISTICS OF QUARTILE DEVIATIONDEVIATION

• Measure of middle 50.00% of scores Measure of middle 50.00% of scores

• Quartile deviation is added to, Quartile deviation is added to, and subtracted from, medianand subtracted from, median

• Does not consider all scores Does not consider all scores

CHARACTERISTICS OF MEAN CHARACTERISTICS OF MEAN DEVIATIONDEVIATION

• Measure of middle 57.50% of scores Measure of middle 57.50% of scores • Mean deviation is added to, and Mean deviation is added to, and subtracted from, meansubtracted from, mean

• Considers all scores, but not Considers all scores, but not mathematically sound. mathematically sound.

CHARACTERISTICS OF STANDARD CHARACTERISTICS OF STANDARD DEVIATIONDEVIATION

• MEASURE OF VARIATIONMEASURE OF VARIATION AROUND MEANAROUND MEAN

• A RELATIVELY SMALL SD A RELATIVELY SMALL SD INDICATES LITTLE VARIABILITY. INDICATES LITTLE VARIABILITY. A RELATIVELY LARGE SD A RELATIVELY LARGE SD INDICATES MUCH VARIABILITYINDICATES MUCH VARIABILITY

• CONSIDERS ALL SCORESCONSIDERS ALL SCORES

CORRELATIONAL TECHNIQUESCORRELATIONAL TECHNIQUES

1. PEARSON PRODUCT-MOMENT1. PEARSON PRODUCT-MOMENT CORRELATION CORRELATION

2. SPEARMAN RANK-ORDER 2. SPEARMAN RANK-ORDER CORRELATIONCORRELATION

CHARACTERISTICS OF CORRELATIONCHARACTERISTICS OF CORRELATION

• CORRELATION COEFFICIENTSCORRELATION COEFFICIENTS RANGE FROM +1.00 TO -1.00RANGE FROM +1.00 TO -1.00

• SIGN INDICATES TYPE OFSIGN INDICATES TYPE OF CORRELATION AND NUMBER CORRELATION AND NUMBER INDICATES DEGREE OF INDICATES DEGREE OF CORRELATION CORRELATION

• POSITIVE CORRELATION POSITIVE CORRELATION INDICATES A DIRECTINDICATES A DIRECT RELATIONSHIPRELATIONSHIP

• NEGATIVE CORRELATIONNEGATIVE CORRELATION INDICATES AN INVERSE INDICATES AN INVERSE RELATIONSHIPRELATIONSHIP

• CANNOTCANNOT INFER CAUSE-AND- INFER CAUSE-AND- EFFECT EFFECT

t-TEST t-TEST

1. t-TEST BETWEEN SAMPLE AND 1. t-TEST BETWEEN SAMPLE AND POPULATION MEAN POPULATION MEAN

2. INDEPENDENT t-TEST2. INDEPENDENT t-TEST

3. DEPENDENT t-TEST3. DEPENDENT t-TEST

t-TEST BETWEEN SAMPLE AND t-TEST BETWEEN SAMPLE AND POPULATION MEAN POPULATION MEAN

DESIGN SCHEMADESIGN SCHEMA

R TR TA1A1 O O

RR = RANDOM ASSIGNMENT = RANDOM ASSIGNMENT

T T = TREATMENT = TREATMENT

OO = OBSERVATION OR TEST = OBSERVATION OR TEST

ANALYSIS OF VARIANCE ANALYSIS OF VARIANCE

1. SIMPLE ANOVA1. SIMPLE ANOVA

2. FACTORIAL ANOVA2. FACTORIAL ANOVA

ONE-WAY ANOVA (THREE GROUPS)ONE-WAY ANOVA (THREE GROUPS)

DESIGN SCHEMADESIGN SCHEMA

TTA1A1 O O (00 HOURS PRACTICE)(00 HOURS PRACTICE)

R TR TA2A2 O O (05 HOURS PRACTICE)(05 HOURS PRACTICE)

TTA3A3 O O (10 HOURS PRACTICE)(10 HOURS PRACTICE)

TWO-WAY ANOVA (2 x 2)TWO-WAY ANOVA (2 x 2)

DESIGN SCHEMADESIGN SCHEMA

TTA1B1A1B1 O O (GROUP 01, MALES)(GROUP 01, MALES)

TTA1B2A1B2 O O (GROUP 01, FEMALES)(GROUP 01, FEMALES)

RR TTA2B1A2B1 O O (GROUP 02, MALES)(GROUP 02, MALES)

TTA2B2A2B2 O O (GROUP 02, FEMALES)(GROUP 02, FEMALES)

ANALYSIS OF VARIANCE WITH ANALYSIS OF VARIANCE WITH REPEATED MEASURESREPEATED MEASURES

1. ONE-WAY ANOVA WITH 1. ONE-WAY ANOVA WITH REPEATED MEASURESREPEATED MEASURES

2. TWO-WAY ANOVA WITH 2. TWO-WAY ANOVA WITH REPEATED MEASURESREPEATED MEASURES

TWO-WAY ANOVA WITH REPEATED TWO-WAY ANOVA WITH REPEATED MEASURES (2 x 4)MEASURES (2 x 4)

DESIGN SCHEMADESIGN SCHEMA

TTA1B1A1B1 O T O TA1B2 A1B2 O TO TA1B3 A1B3 O TO TA1B4 A1B4 OO

RR TTA2B1A2B1 O T O TA2B2 A2B2 O TO TA2B3 A2B3 O TO TA2B4 A2B4 OO