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****
ME
AN
=
M
EA
N =
ME
DIA
N =
M
ED
IAN
=
MO
DE
=M
OD
E =
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****
ME
AN
=
$7
4,20
0M
EA
N =
$74,
200
ME
DIA
N =
$90
,000
ME
DIA
N =
$90
,000
MO
DE
=
AL
L #
SM
OD
E =
A
LL
#S
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