LowHigh Equal Distance Quantification Individual Differences 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16...
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Low High Equal Distance Quantification Individual Differences Individual Differences 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
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Transcript of LowHigh Equal Distance Quantification Individual Differences 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16...
Low High
Equal Distance Quantification
Individual DifferencesIndividual Differences
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
20 19 10 2 1
Interval & RatioInterval & Ratio
1st2nd
3rd4th
5th
NominalNominal
WinnersTops
LosersBottom
OrdinalOrdinal
M Md Mode Mode Md MMeanMedianMode
Xis unbiased, consistent and efficient estimate of µ
Central Tendency & SkewnessCentral Tendency & Skewness
Percentile is the value on a scale below which a given percentage of cases fall.
25th percentile is called lower quartile.
75th percentile is called upper quartile.
1n
)x(xs
n
1
2i
2
Average squared deviation from the mean
2ss Average deviation from the mean
s2 is unbiased, consistent, efficient estimate of σ2
Variability (& Kurtosis)Variability (& Kurtosis)σ2
σ2
σ2
Bar ChartBar Chart
Bar ChartBar Chart
Line ChartLine Chart
Box PlotBox Plot
+
+
+
Stem and Leaf PlotStem and Leaf Plot
2 1 7
1 33 2
2 3 4
3 * 4
3 3 10
9 2 5
4 3 3
20 6 2
4 5 2
1 * *
3 3 4
2 3 4
3 2 3
2 4
1 000
2 000000000
3 00000000000
4 0000000
5 00
6 0
7 0
8
9 0
10 0
HI 20,33
Data Stem–and-Leaf
Missing = 3
SB IQ
T-score 20 30 40 50 60 70 80
GRE, SAT200 300 400 500 600 700 800
Wechsler IQ55 70 85 100 115 130 145
52 68 84 100 116 132 148
Test of this course5 15 25 35 45
µ = 0, σ= 1
µ = 50, σ= 10
µ = 500, σ= 100
µ= 100, σ= 15
µ= 100, σ= 16
µ= 25, σ= 10
Linear Transformation & Standard ScoresLinear Transformation & Standard Scores
- 4.0 -3.0 - 2.0 -1.0 0 +1.0 +2.0 +3.0 +4.0
z-score
-3 -2 -1 0 1 2 3
.1359 .1359
.3413 .3413
.0228 .0228
Normal Normal DistributionDistribution
1.640
0.05
P (X > 1.64)
-3 -2 -1 0 1 2 3
.1359 .1359
Area between -1 and -2
X= 35, s = 5, % above 40
.1587
20 25 30 35 40 45 50
-3 -2 -1 0 1 2 3
X= 35, s = 5, % above 30
.8413
20 25 30 35 40 45 50
-3 -2 -1 0 1 2 3
X= 35, s = 5, % below 25
.0228
20 25 30 35 40 45 50
-3 -2 -1 0 1 2 3
X= 35, s = 5, % between 25 and 30
.1587 – 0.0228
20 25 30 35 40 45 50
-3 -2 -1 0 1 2 3
X= 35, s = 5, 95th percentile
20 25 30 35 40 45 50
-3 -2 -1 0 1 2 31.64
43.2
X= 35, s = 5, 75th percentile
20 25 30 35 40 45 50
-3 -2 -1 0 1 2 3.67
38.35
CI 90CI 90
-1.64 1.64-3 -2 -1 0 1 2 3
-3 -2 -1 0 1 2 3
-1.96 1.96
CI 95CI 95
