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Page 1 Homework 2 1 Your Name Institutional Affiliation Course Number Course Title Tutor’s Name Homework 2 Date
Page 1
Homework 2 1
Your Name
Institutional Affiliation
Course Number
Course Title
Tutors Name
Homework 2
Date
Page 2
Homework 2 2
DV: Reading Time measured on a scale of 0-1600 seconds. Score is measured during the test
IV: Ambient Lighting. Categorical Variable with four groups
Design: The IV is manipulated within groups which are randomly assigned by block so it is a true
experiment.
EXAMINE VARIABLES=ReadingTime
/PLOT BOXPLOT STEMLEAF HISTOGRAM NPPLOT
/COMPARE GROUPS
/MESTIMATORS HUBER(1.339) ANDREW(1.34) HAMPEL(1.7,3.4,8.5) TUKEY(4.685)
/STATISTICS DESCRIPTIVES EXTREME
/CINTERVAL 95
/MISSING LISTWISE
/NOTOTAL.
Explore [DataSet1] C:\Users\DREW\Downloads\HW2_ereader.sav
Case Processing Summary
Cases
Valid Missing Total
N Percent N Percent N Percent
Reading time in seconds 20 100.0% 0 0.0% 20 100.0%
Reading time mean score : 1032.1995
Standard Deviation : 307.432
Skewness and Kurtosis tell more about distribution
Descriptives
Statistic Std. Error
Reading time in seconds Mean 1032.1995 68.74523
95% Confidence Interval Lower Bound for Mean
Upper Bound
888.3141
1176.0849
5% Trimmed Mean 1028.0006
Median 1085.9200
Variance 94518.120
Std. Deviation 307.43799
Minimum 551.34
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Homework 2 3
Maximum 1588.64
Range 1037.30
Interquartile Range 501.28
Skewness .026 .512
Kurtosis -.905 .992
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Homework 2 4
M-Estimators
Huber's M- Estimatora
Tukey's
Biweightb
Hampel's M-
Estimatorc
Andrews'
Waved
Reading time in seconds 1035.9210 1033.4395 1028.6167 1033.5063
a. The weighting constant is 1.339.
b. The weighting constant is 4.685.
c. The weighting constants are 1.700, 3.400, and 8.500
d. The weighting constant is 1.340*pi.
No outliers as indicated by the extreme values table.
Extreme Values
Case Number Value
Reading time in seconds Highest 1 5 1588.64
2 4 1501.26
3 9 1395.44
4 15 1308.35
5 6 1290.54
Lowest 1 18 551.34
2 16 583.03
3 12 634.06
4 14 641.96
5 8 741.65
Tests of Normality
Kolmogorov-Smirnova Shapiro-Wilk
Statistic Df Sig. Statistic df Sig.
Reading time in seconds .111 20 .200* .965 20 .655
*. This is a lower bound of the true significance.
a. Lilliefors Significance Correction
The distribution is not normal
Reading time in seconds
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Homework 2 5
Histogram
5 Mean = 1032.20 Std. Dev. = 307.438 N = 20
4
3
2
1
0 500.00
750.00
1000.00
1250.00
1500.00
Reading time in seconds
Reading time in seconds Stem-and-Leaf Plot
Frequency Stem & Leaf
Stem width: 1000.00
Each leaf: 1 case(s)
Fre
qu
en
cy
9.00 0 . 556678889
9.00 1 . 000122233
2.00 1 . 55
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Homework 2 6
Normal Q-Q Plot of Reading time in seconds
3
2
1
0
-1
-2
500 750 1,000 1,250 1,500 1,750
Observed Value
Ex
pe
cte
d N
orm
al
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Homework 2 7
Detrended Normal Q-Q Plot of Reading time in seconds
0.2
0.0000
-0.2
-0.4
500 750 1,000
Observed Value
1,250 1,500
De
v f
rom
No
rma
l
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Homework 2 1
1500.00
1250.00
1000.00
750.00
500.00
Reading time in seconds
Boxplot looks asymmetrical therefore indicating that the distribution is not normal but the
skewness might be as a result of working with a small sample size
Sample sizes in the IV were normal even though categorical
IV ANALYSIS
EXAMINE VARIABLES=Condition
Page 2
Homework 2 2
/PLOT BOXPLOT STEMLEAF HISTOGRAM NPPLOT
/COMPARE GROUPS
/MESTIMATORS HUBER(1.339) ANDREW(1.34) HAMPEL(1.7,3.4,8.5) TUKEY(4.685)
/STATISTICS DESCRIPTIVES EXTREME
/CINTERVAL 95
/MISSING LISTWISE
/NOTOTAL.
Explore [DataSet1] C:\Users\DREW\Downloads\HW2_ereader.sav
Case Processing Summary
Cases
Valid Missing Total
N Percent N Percent N Percent
Ambient illumination level 20 100.0% 0 0.0% 20 100.0%
Descriptives
Statistic Std. Error
Ambient illumination level Mean 2.50 .256
95% Confidence Interval Lower Bound for Mean
Upper Bound
1.96
3.04
5% Trimmed Mean 2.50
Median 2.50
Variance 1.316
Std. Deviation 1.147
Minimum 1
Maximum 4
Range 3
Interquartile Range 3
Skewness .000 .512
Kurtosis -1.401 .992
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Homework 2 3
M-Estimators
Huber's M- Estimatora
Tukey's
Biweightb
Hampel's M-
Estimatorc
Andrews'
Waved
Ambient illumination level 2.50 2.50 2.50 2.50
a. The weighting constant is 1.339.
b. The weighting constant is 4.685.
c. The weighting constants are 1.700, 3.400, and 8.500
d. The weighting constant is 1.340*pi.
Extreme Values
Case Number Value
Ambient illumination level Highest 1 16 4
2 17 4
3 18 4
4 19 4
5 20 4
Lowest 1 5 1
2 4 1
3 3 1
4 2 1
5 1 1
Tests of Normality
Kolmogorov-Smirnova Shapiro-Wilk
Statistic df Sig. Statistic df Sig.
Ambient illumination level .169 20 .139 .863 20 .009
a. Lilliefors Significance Correction
Ambient illumination level
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Homework 2 4
Histogram
5 Mean = 2.5 Std. Dev. = 1.147 N = 20
4
3
2
1
0 1 2 3 4
Ambient illumination level
Ambient illumination level Stem-and-Leaf Plot
Frequency Stem & Leaf
Stem width: 1
Each leaf: 1 case(s)
Fre
qu
en
cy
5.00 1 . 00000
.00 1 .
5.00 2 . 00000
.00 2 .
5.00 3 . 00000
.00 3 .
5.00 4 . 00000
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Homework 2 5
Normal Q-Q Plot of Ambient illumination level
2
1
0
-1
-2
0 1 2 3 4 5
Observed Value
Ex
pe
cte
d N
orm
al
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Homework 2 6
Detrended Normal Q-Q Plot of Ambient illumination level
0.3
0.2
0.1
0.0000
-0.1
-0.2
-0.3
1.0 1.5 2.0 2.5
Observed Value
3.0 3.5 4.0
De
v f
rom
No
rma
l
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Homework 2 7
4.0
3.5
3.0
2.5
2.0
1.5
1.0
Ambient illumination level
UNIANOVA ReadingTime BY Condition
/METHOD=SSTYPE(3)
/INTERCEPT=INCLUDE
/PRINT=TEST(LMATRIX) OPOWER ETASQ DESCRIPTIVE PARAMETER
/CRITERIA=ALPHA(.05)
/DESIGN=Condition.
Univariate Analysis of Variance [DataSet1] C:\Users\DREW\Downloads\HW2_ereader.sav
Between-Subjects Factors
Value Label N
Ambient illumination level 1 200 lx 5
2 500 lx 5
3 1000 lx 5
4 1500 lx 5
Descriptive Statistics
Dependent Variable: Reading time in seconds
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Homework 2 8
Ambient illumination level Mean Std. Deviation N
200 lx 1250.1880 297.53116 5
500 lx 1096.5940 258.71975 5
1000 lx 914.0060 298.14101 5
1500 lx 868.0100 298.11137 5
Total 1032.1995 307.43799 20
Tests of Between-Subjects Effects
Dependent Variable: Reading time in seconds
Source
Type III Sum
of Squares
df
Mean Square
F
Sig.
Partial Eta
Squared
Corrected Model 462967.666a 3 154322.555 1.853 .178 .258
Intercept 21308716.16 1 21308716.16 255.792 .000 .941
Condition 462967.666 3 154322.555 1.853 .178 .258
Error 1332876.614 16 83304.788
Total 23104560.44 20
Corrected Total 1795844.279 19
This table showed information about the significance of the groups as well as the eta squared. The p-value was
.0, so less than .05, which means it is significant in difference
between ambient lighting that means we can reject the null hypothesis, which would assume that the groups
have the same outcomes under the different ambient lighting .
The partial eta squared shows how big of a difference exists between groups, and the value of .24 indicates
that there is ~24% of the variance is due to the ambient lighting used.
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Homework 2 9
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Homework 2 1
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Homework 2 2
Tests of Between-Subjects Effects
Dependent Variable: Reading time in seconds
Source
Noncent.
Parameter
Observed
Powerb
Corrected Model 5.558 .390
Intercept 255.792 1.000
Condition 5.558 .390
Error
Total
Corrected Total
a. R Squared = .258 (Adjusted R Squared = .119)
b. Computed using alpha = .05
Parameter Estimates
Dependent Variable: Reading time in seconds
Parameter
B
Std. Error
t
Sig.
95% Confidence Interval
Lower Bound Upper Bound
Intercept 868.010 129.077 6.725 .000 594.378 1141.642
[Condition=1] 382.178 182.543 2.094 .053 -4.796 769.152
[Condition=2] 228.584 182.543 1.252 .228 -158.390 615.558
[Condition=3] 45.996 182.543 .252 .804 -340.978 432.970
[Condition=4] 0a
. . . . .
Parameter Estimates
Dependent Variable: Reading time in seconds
Parameter
Partial Eta
Squared
Noncent.
Parameter
Observed
Powerb
Intercept .739 6.725 1.000
[Condition=1] .215 2.094 .503
[Condition=2] .089 1.252 .218
[Condition=3] .004 .252 .056
[Condition=4] . . .
a. This parameter is set to zero because it is redundant.
b. Computed using alpha = .05
Contrast Coefficients (L' Matrix)
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Homework 2 1
Intercept
Parameter
Contrast
L1
Intercept 1
[Condition=1] .250
[Condition=2] .250
[Condition=3] .250
[Condition=4] .250
The default
display of this
matrix is the
transpose of the
corresponding L
matrix.
Based on Type III Sums
of Squares.
Condition
Parameter
Contrast
L2 L3 L4
Intercept 0 0 0
[Condition=1] 1 0 0
[Condition=2] 0 1 0
[Condition=3] 0 0 1
[Condition=4] -1 -1 -1
The default display of this matrix
is the transpose of the
corresponding L matrix.
Based on Type III Sums of Squares.
UNIANOVA ReadingTime BY Condition
/METHOD=SSTYPE(3)
/INTERCEPT=INCLUDE
/PLOT=PROFILE(Condition)
/PRINT=TEST(LMATRIX) OPOWER ETASQ DESCRIPTIVE PARAMETER
/CRITERIA=ALPHA(.05)
/DESIGN=Condition.
Univariate Analysis of Variance [DataSet1] C:\Users\DREW\Downloads\HW2_ereader.sav
Between-Subjects Factors
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Homework 2 2
Value Label N
Ambient illumination level 1 200 lx 5
2 500 lx 5
3 1000 lx 5
4 1500 lx 5
Descriptive Statistics
Dependent Variable: Reading time in seconds
Ambient illumination level Mean Std. Deviation N
200 lx 1250.1880 297.53116 5
500 lx 1096.5940 258.71975 5
1000 lx 914.0060 298.14101 5
1500 lx 868.0100 298.11137 5
Total 1032.1995 307.43799 20
Tests of Between-Subjects Effects
Dependent Variable: Reading time in seconds
Source
Type III Sum
of Squares
df
Mean Square
F
Sig.
Partial Eta
Squared
Corrected Model 462967.666a 3 154322.555 1.853 .178 .258
Intercept 21308716.16 1 21308716.16 255.792 .000 .941
Condition 462967.666 3 154322.555 1.853 .178 .258
Error 1332876.614 16 83304.788
Total 23104560.44 20
Corrected Total 1795844.279 19
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Homework 2 3
Tests of Between-Subjects Effects
Dependent Variable: Reading time in seconds
Source
Noncent.
Parameter
Observed
Powerb
Corrected Model 5.558 .390
Intercept 255.792 1.000
Condition 5.558 .390
Error
Total
Corrected Total
a. R Squared = .258 (Adjusted R Squared = .119)
b. Computed using alpha = .05
Parameter Estimates
Dependent Variable: Reading time in seconds
Parameter
B
Std. Error
t
Sig.
95% Confidence Interval
Lower Bound Upper Bound
Intercept 868.010 129.077 6.725 .000 594.378 1141.642
[Condition=1] 382.178 182.543 2.094 .053 -4.796 769.152
[Condition=2] 228.584 182.543 1.252 .228 -158.390 615.558
[Condition=3] 45.996 182.543 .252 .804 -340.978 432.970
[Condition=4] 0a
. . . . .
Parameter Estimates
Dependent Variable: Reading time in seconds
Parameter
Partial Eta
Squared
Noncent.
Parameter
Observed
Powerb
Intercept .739 6.725 1.000
[Condition=1] .215 2.094 .503
[Condition=2] .089 1.252 .218
[Condition=3] .004 .252 .056
[Condition=4] . . .
a. This parameter is set to zero because it is redundant.
b. Computed using alpha = .05
Contrast Coefficients (L' Matrix)
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Homework 2 4
Intercept
Parameter
Contrast
L1
Intercept 1
[Condition=1] .250
[Condition=2] .250
[Condition=3] .250
[Condition=4] .250
The default
display of this
matrix is the
transpose of the
corresponding L
matrix.
Based on Type III Sums
of Squares.
Condition
Parameter
Contrast
L2 L3 L4
Intercept 0 0 0
[Condition=1] 1 0 0
[Condition=2] 0 1 0
[Condition=3] 0 0 1
[Condition=4] -1 -1 -1
The default display of this matrix
is the transpose of the
corresponding L matrix.
Based on Type III Sums of Squares.
Profile Plots
Page 5
Homework 2 5
Estimated Marginal Means of Reading time in seconds
1300.00
1200.00
1100.00
1000.00
900.00
800.00
200 lx 500 lx 1000 lx 1500 l
Es
tim
ate
d M
arg
ina
l M
ea
ns
Page 6
Homework 2 6
Ambient illumination level
This histogram shows the difference between the 4 groups. It indicates that those in the low ambient lighting exhibit longer reading times than those in the high ambient lighting. I think that a bar chart or a scatter plot with best fit line would be a better way to show the data since it would be easier to read and show the actual numbers without having to guestimate.
