Download Good example of proj..

PSYCH 818 – *********
Project 1 : Stats review
1) + 2) Histograms, distributions and descriptive statistics
The following graphs plot the histograms for each item. Also, the mean and standard
deviation for each item are given.
Locomotive – Item 1
Locomotive – Item 2
PSYCH 818 – *********
loco3
150
Frequency
120
90
60
30
Mean = 4.1583
Std. Dev. = 0.67837
N = 240
0
0.00
1.00
2.00
3.00
4.00
5.00
loco3
Locomotive – Item 3
Locomotive – Item 4
6.00
PSYCH 818 – *********
Locomotive – Item 5
loco6
120
100
Frequency
80
60
40
20
Mean = 2.8333
Std. Dev. = 0.87104
N = 240
0
0.00
1.00
2.00
3.00
loco6
4.00
5.00
Locomotive – Item 6
6.00
PSYCH 818 – *********
Locomotive – Item 7
Locomotive – Item 8
PSYCH 818 – *********
Locomotive – Item 9
Locomotive – Item 10
PSYCH 818 – *********
Locomotive – Item 11
Locomotive – Item 12
PSYCH 818 – *********
Assessment – Item 1
Assessment – Item 2
PSYCH 818 – *********
Assessment – Item 3
Assessment – Item 4
PSYCH 818 – *********
Assessment – Item 5
Assessment – Item 6
PSYCH 818 – *********
Assessment – Item 7
Assessment – Item 8
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Assessment – Item 9
Assessment – Item 10
PSYCH 818 – *********
Assessment – Item 11
Assessment – Item 12
As the attached table (below) and the attached histograms (above) show, items 1, 6
and 8 of the locomotion scale are positively skewed, the other items are negatively
skewed. For some of these items, the skew is due to outliers (i.e. item 4).
PSYCH 818 – *********
Statistics
N
Valid
Missing
Std. Deviation
Skewness
Std. Error of Skewness
loco1
240
0
.72320
-.452
.157
loco2
240
0
1.08463
.315
.157
loco3
240
0
.67837
-.854
.157
loco4
240
0
.76791
-.617
.157
loco5
240
0
.78408
-.456
.157
loco6
240
0
.87104
.254
.157
loco7
240
0
.84684
-.285
.157
loco8
240
0
.87024
.106
.157
loco9 loco10 loco11 loco12
240
240
240
240
0
0
0
0
1.02336 .79458 .82262 .84106
-.575
-.538
-.229
-.262
.157
.157
.157
.157
Also, as the attached table (below) and the attached histograms (above) show, items 5
and 10 of the assessment scale or positively skewed, the other items of the assessment
scale are negatively skewed.
Statistics
N
Valid
Missing
Std. Deviation
Skewness
Std. Error of Skewness
assess1 assess2 assess3 assess4 assess5 assess6 assess7 assess8 assess9 assess10 assess11 assess12
240
240
240
240
240
240
240
240
240
240
240
240
0
0
0
0
0
0
0
0
0
0
0
0
.88257 1.00456
.98587 1.09770
.99567
.77940
.97400
.98559 1.04937
.94285
.97156 1.04900
-.565
-.119
-.294
-.576
.058
-.613
-.428
-.147
-.217
.248
-.533
-.275
.157
.157
.157
.157
.157
.157
.157
.157
.157
.157
.157
.157
Mean and Standard Deviation:
For the locomotion scale, the means of the 12 items range from 2.7 (item 2) or 2.8
(item 6) to values of 4.1 for item 4 and 4.2 for item 3. Considering the measures of
the items, these means appear “healthy”.
For the assessment scale, low mean values can be found for items 5 and 10 with
means of 2.9 and 2.8. High mean values can be found for items 1 and 6, reaching
values of 3.8. Interestingly, the mean values of the 12 items of the two scales are
similar.
Overall, the items show a satisfying degree of variance.
Items one and three of the locomotion scale have a relatively small standard deviation
with values of .67 and .72. However, compared to common standard deviations of
other scales used to measure personality characteristics (NEO-FFM), these values are
still acceptable, providing enough variance for following substantial data analysis.
Items 2 and 9 show relatively higher standard deviation with values of up to 1.1.
PSYCH 818 – *********
Also, the assessment scale shows satisfying degrees of variance, with standard
deviations ranging from .78 to a maximum of 1.1 for item 4. Other items with
relatively high variance are items 2, 4 and 12.
In the 5-point scale used here, it is not possible to receive higher standard
deviations than means. (i.e. for a given standard deviation of >1.5, no mean smaller
than 2.5 is possible.) However, on different scales, we can obtain standard deviations
that are larger than the mean (i.e. for standardized z-scores, where the mean is 0 and
the standard deviation is 1).
3) + 4)
Variance-Covariance Matrix
I have attached the variance-covariance matrix for the 12 locomotion items as well as
for the 12 assessment items. The variances (highlighted in the diagonals) equal the
squared standard deviations reported above.
loco 1
loco 2
loco 3
loco 4
loco 5
loco 6
loco 7
loco 8
loco 9
loco 10
loco 11
loco 12
loco 1
loco 2
loco 3
loco 4
loco 5
loco 6
loco 7
loco 8
loco 9
loco 10
loco 11
loco 12
0.523
0.279
0.144
0.201
0.213
0.121
0.166
0.13
0.246
0.154
0.197
0.183
0.279
1.176
0.134
0.162
0.284
0.22
0.156
0.281
0.313
0.195
0.258
0.33
0.144
0.134
0.46
0.266
0.184
0.144
0.143
0.119
0.16
0.119
0.104
0.141
0.201
0.162
0.266
0.59
0.342
0.107
0.19
0.201
0.377
0.183
0.179
0.251
0.213
0.284
0.184
0.342
0.615
0.216
0.196
0.255
0.398
0.13
0.228
0.37
0.121
0.22
0.144
0.107
0.216
0.759
0.105
0.331
0.21
0.066
0.031
0.169
0.166
0.156
0.143
0.19
0.196
0.105
0.717
0.286
0.176
0.155
0.189
0.153
0.13
0.281
0.119
0.201
0.255
0.331
0.286
0.757
0.227
0.235
0.096
0.219
0.246
0.313
0.16
0.377
0.398
0.21
0.176
0.227
1.047
0.191
0.304
0.445
0.154
0.195
0.119
0.183
0.13
0.066
0.155
0.235
0.191
0.631
0.217
0.1
0.197
0.258
0.104
0.179
0.228
0.031
0.189
0.096
0.304
0.217
0.677
0.287
0.183
0.33
0.141
0.251
0.37
0.169
0.153
0.219
0.445
0.1
0.287
0.707
PSYCH 818 – *********
ase1234567890
ase10.79235468
ase20.1943856
ase30.25489761
ase40.27513896
ase50.16234798
ase60.18923745
ase70.26135984
ase80.13627459
ase90.14862735
ase10.46287359
ase10.38762945
ase120.5384769
While some variables produce higher covariances within the given scales (item 10
produces high covariances, suggesting high factor loadings while item 7 produces
relatively low covariances, suggesting low factor loadings), it is still justified to speak of
homogenuous covariances. This will be confirmed by the correlation matrices, which
follow below.
PSYCH 818 – *********
Correlations
loco1
loco1
loco2
loco3
loco4
loco5
loco6
loco7
loco8
loco9
loco10
loco11
loco12
Pearson Correlation
Sig. (2-tailed)
N
Pearson Correlation
Sig. (2-tailed)
N
Pearson Correlation
Sig. (2-tailed)
N
Pearson Correlation
Sig. (2-tailed)
N
Pearson Correlation
Sig. (2-tailed)
N
Pearson Correlation
Sig. (2-tailed)
N
Pearson Correlation
Sig. (2-tailed)
N
Pearson Correlation
Sig. (2-tailed)
N
Pearson Correlation
Sig. (2-tailed)
N
Pearson Correlation
Sig. (2-tailed)
N
Pearson Correlation
Sig. (2-tailed)
N
Pearson Correlation
Sig. (2-tailed)
N
1
240
.356**
.000
240
.294**
.000
240
.362**
.000
240
.376**
.000
240
.193**
.003
240
.272**
.000
240
.206**
.001
240
.332**
.000
240
.268**
.000
240
.331**
.000
240
.301**
.000
240
loco2
.356**
.000
240
1
240
.182**
.005
240
.194**
.003
240
.334**
.000
240
.233**
.000
240
.170**
.008
240
.298**
.000
240
.282**
.000
240
.226**
.000
240
.289**
.000
240
.361**
.000
240
**. Correlation is significant at the 0.01 level (2-tailed).
*. Correlation is significant at the 0.05 level (2-tailed).
loco3
.294**
.000
240
.182**
.005
240
1
240
.510**
.000
240
.345**
.000
240
.243**
.000
240
.250**
.000
240
.202**
.002
240
.230**
.000
240
.221**
.001
240
.187**
.004
240
.247**
.000
240
loco4
.362**
.000
240
.194**
.003
240
.510**
.000
240
1
240
.568**
.000
240
.161*
.013
240
.292**
.000
240
.301**
.000
240
.480**
.000
240
.299**
.000
240
.284**
.000
240
.389**
.000
240
loco5
.376**
.000
240
.334**
.000
240
.345**
.000
240
.568**
.000
240
1
240
.317**
.000
240
.295**
.000
240
.374**
.000
240
.496**
.000
240
.209**
.001
240
.353**
.000
240
.562**
.000
240
loco6
.193**
.003
240
.233**
.000
240
.243**
.000
240
.161*
.013
240
.317**
.000
240
1
240
.143*
.027
240
.436**
.000
240
.235**
.000
240
.096
.139
240
.043
.509
240
.231**
.000
240
loco7
.272**
.000
240
.170**
.008
240
.250**
.000
240
.292**
.000
240
.295**
.000
240
.143*
.027
240
1
240
.387**
.000
240
.203**
.002
240
.230**
.000
240
.271**
.000
240
.215**
.001
240
loco8
.206**
.001
240
.298**
.000
240
.202**
.002
240
.301**
.000
240
.374**
.000
240
.436**
.000
240
.387**
.000
240
1
240
.255**
.000
240
.340**
.000
240
.134*
.037
240
.299**
.000
240
loco9
.332**
.000
240
.282**
.000
240
.230**
.000
240
.480**
.000
240
.496**
.000
240
.235**
.000
240
.203**
.002
240
.255**
.000
240
1
240
.235**
.000
240
.362**
.000
240
.517**
.000
240
loco10
.268**
.000
240
.226**
.000
240
.221**
.001
240
.299**
.000
240
.209**
.001
240
.096
.139
240
.230**
.000
240
.340**
.000
240
.235**
.000
240
1
240
.332**
.000
240
.149*
.021
240
loco11
.331**
.000
240
.289**
.000
240
.187**
.004
240
.284**
.000
240
.353**
.000
240
.043
.509
240
.271**
.000
240
.134*
.037
240
.362**
.000
240
.332**
.000
240
1
240
.414**
.000
240
loco12
.301**
.000
240
.361**
.000
240
.247**
.000
240
.389**
.000
240
.562**
.000
240
.231**
.000
240
.215**
.001
240
.299**
.000
240
.517**
.000
240
.149*
.021
240
.414**
.000
240
1
240
PSYCH 818 – *********
Correlations
assess1
assess2
assess3
assess4
assess5
assess6
assess7
assess8
assess9
assess10
assess11
assess12
Pearson Correlation
Sig. (2-tailed)
N
Pearson Correlation
Sig. (2-tailed)
N
Pearson Correlation
Sig. (2-tailed)
N
Pearson Correlation
Sig. (2-tailed)
N
Pearson Correlation
Sig. (2-tailed)
N
Pearson Correlation
Sig. (2-tailed)
N
Pearson Correlation
Sig. (2-tailed)
N
Pearson Correlation
Sig. (2-tailed)
N
Pearson Correlation
Sig. (2-tailed)
N
Pearson Correlation
Sig. (2-tailed)
N
Pearson Correlation
Sig. (2-tailed)
N
Pearson Correlation
Sig. (2-tailed)
N
assess1
1
assess2
assess3
assess4
assess5
assess6
assess7
assess8
assess9
assess10
assess11
assess12
.215**
.270**
.254**
.184**
.275**
.304**
.153*
.160*
.055
.452**
.135*
.001
.000
.000
.004
.000
.000
.018
.013
.394
.000
.037
240
240
240
240
240
240
240
240
240
240
240
240
.215**
1
.443**
.367**
.300**
.267**
.312**
.319**
.379**
.175**
.370**
.220**
.001
.000
.000
.000
.000
.000
.000
.000
.007
.000
.001
240
240
240
240
240
240
240
240
240
240
240
240
.270**
.443**
1
.390**
.441**
.424**
.291**
.275**
.180**
.280**
.305**
.372**
.000
.000
.000
.000
.000
.000
.000
.005
.000
.000
.000
240
240
240
240
240
240
240
240
240
240
240
240
.254**
.367**
.390**
1
.345**
.383**
.504**
.406**
.422**
.181**
.262**
.352**
.000
.000
.000
.000
.000
.000
.000
.000
.005
.000
.000
240
240
240
240
240
240
240
240
240
240
240
240
.184**
.300**
.441**
.345**
1
.242**
.189**
.313**
.261**
.324**
.249**
.330**
.004
.000
.000
.000
.000
.003
.000
.000
.000
.000
.000
240
240
240
240
240
240
240
240
240
240
240
240
.275**
.267**
.424**
.383**
.242**
1
.322**
.467**
.319**
.169**
.340**
.287**
.000
.000
.000
.000
.000
.000
.000
.000
.009
.000
.000
240
240
240
240
240
240
240
240
240
240
240
240
.304**
.312**
.291**
.504**
.189**
.322**
1
.307**
.432**
.115
.332**
.181**
.000
.000
.000
.000
.003
.000
.000
.000
.074
.000
.005
240
240
240
240
240
240
240
240
240
240
240
240
.153*
.319**
.275**
.406**
.313**
.467**
.307**
1
.342**
.333**
.211**
.264**
.018
.000
.000
.000
.000
.000
.000
.000
.000
.001
.000
240
240
240
240
240
240
240
240
240
240
240
240
.160*
.379**
.180**
.422**
.261**
.319**
.432**
.342**
1
.201**
.334**
.152*
.013
.000
.005
.000
.000
.000
.000
.000
.002
.000
.018
240
240
240
240
240
240
240
240
240
240
240
240
.055
.175**
.280**
.181**
.324**
.169**
.115
.333**
.201**
1
.104
.211**
.394
.007
.000
.005
.000
.009
.074
.000
.002
.108
.001
240
240
240
240
240
240
240
240
240
240
240
240
.452**
.370**
.305**
.262**
.249**
.340**
.332**
.211**
.334**
.104
1
.089
.000
.000
.000
.000
.000
.000
.000
.001
.000
.108
.171
240
240
240
240
240
240
240
240
240
240
240
240
.135*
.220**
.372**
.352**
.330**
.287**
.181**
.264**
.152*
.211**
.089
1
.037
.001
.000
.000
.000
.000
.005
.000
.018
.001
.171
240
240
240
240
240
240
240
240
240
240
240
240
**. Correlation is significant at the 0.01 level (2-tailed).
*. Correlation is significant at the 0.05 level (2-tailed).
The diagonal values equal 1 in the correlation matrix because these values represent the
correlation of the twelve items with themselves. Consequently, these values will always equal
5) Single score for set of 12 items. Histogram, standard deviation and mean.
Below, I have attached the histograms for the locomotion and assessment scale scores.
These also include the means and standard deviation.
PSYCH 818 – *********
Interestingly, the standard deviations of the two scales is significantly smaller than
the standard deviations reported for the individual items. By averaging the individual
item scores (with values ranging from 2.8 to 4.2), outliers play a less significant role than
they have for the individual items. Therefore, the standard deviation decreases.
Of course, the new mean values equal the mean of the individual item scores as the two
scale scores have been computed by averaging the individual item scores.
6)
Covariance and correlation between the two summated scale scores. Coefficient
of determination
The attached table shows the covariances and correlation for the two scale scores. It can
be suggested that the two variables do not correlate with each other / do not share
common variance. The coefficient of determination between the two scale scores is
.074*.074 = .0054. Therefore, only 0.5% of the variance in the two scale scores can be
explained by the other scale score.
PSYCH 818 – *********
Correlations
locomotion scale
assessment scale
Pearson Correlation
Sig. (2-tailed)
Sum of Squares and
Cross-products
Covariance
N
Pearson Correlation
Sig. (2-tailed)
Sum of Squares and
Cross-products
Covariance
N
locomotion
scale
1
assessment
scale
.074
.256
59.390
5.041
.248
240
.074
.256
.021
240
1
5.041
79.041
.021
240
.331
240
7) Regression
I have attached the regression analysis for both locomotion and assessment below.
Coefficientsa
Model
1
(Constant)
locomotion scale
Unstandardized
Coefficients
B
Std. Error
74873.620 15621.873
26.972
4339.218
Standardized
Coefficients
Beta
.000
t
4.793
.006
Sig.
.000
.995
a. Dependent Variable: Overall score
The regression relationship is very weak when we use locomotion as predictor.
Consequently, the coefficient of determination is equal to zero (i.e. no variance in task
performance can be explained by locomotion). If we plotted the relationship between
locomotion and task performance, we would obtain a flat line with an intercept equalling
the constant shown in the table above.
Below, I have attached the regression analysis when we use assessment scale as
predictor. Again, no significant relationship can be detected. According to the coefficient
of determination, approximately 0.5% of the variance in task performance can be
explained by the the predictor (assessment). The coefficient of determation can be
obtained by dividing the sum of squares due to regression by the sum of squares due to
PSYCH 818 – *********
error. Again, if we plotted the relationship between assessment and task performance, we
would obtain a flat lign with an intercept equalling the constant shown in the table below.
Coefficientsa
Model
1
(Constant)
assessment scale
Unstandardized
Coefficients
B
Std. Error
61773.991 12843.549
3911.074
3752.772
Standardized
Coefficients
Beta
.067
t
4.810
1.042
Sig.
.000
.298
a. Dependent Variable: Overall score
Model Summary
Model
1
R
.067a
R Square
.005
Adjusted
R Square
.000
Std. Error of
the Estimate
33364.110
a. Predictors: (Constant), assessment scale
Question 8:
The two new composites (standardized and weighted composites) for each of the two sets
of items has been computed in SPSS (the file, incl. syntax, will be sent to the instructor).
In order to obtain a reasonable weighting scheme, I have factor analyzed the two scales.
After having used a Varimax rotation, I have assigned weights of 0.6 to those items that
load highly on the first emerging factor. The other items, which load lower on this first
factor, or which load on other factors, have been weighted by 0.4. By assigning this set of
weights, the different relevance of the individual items for the overall scale score is taken
into consideration.
Question 9: Mean, SD and intercorrelations of the 6 scale scores
The first two rows contain descriptive statistics for the two weighted scale scores (see
above). Rows 3 and 4 contain the standardized scores for the locomotion and assessment
scales. Rows 5 and 6 are the unstandardized scale scores for locomotion and assessment.
As can be expected, the mean and the standard deviation for the standardized scores are 0
PSYCH 818 – *********
and 1 respectively. Also, and as expected, the mean of the standardized scores remained 0
and the standard deviation did not deviate significantly from 1 after having assigned
weights to the scales. The descriptive statistics for the locomotion and assessment scales
have already been discussed before.
Descriptive Statistics
N
WeightLocoscore
WeightAssessscore
Zscore: locomotion
scale standardized
Zscore: assessment
scale standardized
locomotion scale
assessment scale
Valid N (listwise)
240
240
Minimum
-2.99
-3.17
Maximum
2.39
2.88
Mean
.0000
.0000
Std. Deviation
1.00501
.97821
240
-2.91087
2.68802
.0000000
1.00000000
240
-3.57617
2.83512
.0000000
1.00000000
240
240
240
2.08
1.33
4.92
5.00
3.5656
3.3740
.49849
.57508
PSYCH 818 – *********
Correlations
Weight
Locoscore
WeightLocoscore
WeightAssessscore
Zscore: locomotion
scale standardized
Zscore: assessment
scale standardized
locomotion scale
assessment scale
Pearson Correlation
Sig. (2-tailed)
Sum of Squares and
Cross-products
Covariance
N
Pearson Correlation
Sig. (2-tailed)
Sum of Squares and
Cross-products
Covariance
N
Pearson Correlation
Sig. (2-tailed)
Sum of Squares and
Cross-products
Covariance
N
Pearson Correlation
Sig. (2-tailed)
Sum of Squares and
Cross-products
Covariance
N
Pearson Correlation
Sig. (2-tailed)
Sum of Squares and
Cross-products
Covariance
N
Pearson Correlation
Sig. (2-tailed)
Sum of Squares and
Cross-products
Covariance
N
1
Weight
Assessscore
.018
.783
Zscore:
Zscore:
locomotion
assessment
scale
scale
standardized
standardized
.869**
.104
.000
.109
4.196
208.812
1.010
240
.018
.783
.018
240
1
.874
240
.019
.768
4.196
228.698
4.465
196.573
.957
240
.019
.768
.019
240
1
.822
240
.081
.210
4.465
239.000
19.429
118.948
1.000
240
.081
.210
.081
240
1
.498
240
.075
.244
19.429
239.000
8.994
137.364
1.000
240
.075
.244
.038
240
1
.575
240
.074
.256
8.994
59.390
5.041
.248
240
.074
.256
.021
240
1
208.812
.874
240
.104
.109
24.893
.104
240
.867**
.000
103.859
.435
240
.101
.118
.019
240
.841**
.000
196.573
.822
240
.014
.833
1.597
.007
240
.839**
.000
.081
240
.998**
.000
118.948
.498
240
.079
.221
.104
240
.841**
.000
.038
240
.999**
.000
103.859
assessment
scale
.101
.118
241.403
.018
240
.869**
.000
24.893
locomotion
scale
.867**
.000
13.984
.435
240
.014
.833
1.597
.059
240
.839**
.000
112.847
.007
240
.998**
.000
.472
240
.079
.221
10.900
.046
240
.999**
.000
13.984
112.847
10.900
137.364
5.041
79.041
.059
240
.472
240
.046
240
.575
240
.021
240
.331
240
**. Correlation is significant at the 0.01 level (2-tailed).
As expected, all diagnoal values equal 1, representing the auto-correlations of the scales.
Moreover, as discussed above, the assessment scale and the locomotion scale are always
uncorrelated, no matter if an unstandardized, a standardized or a weighted scale is used.
However, the high intercorrelations among the unstandardized, standardized and weighted scales
(values of >0.8) which were built from the same items confirm that standardization and assigning
weights to the items does not change the nature of the intercorrelations.
PSYCH 818 – *********
While this pattern was expected for the standardized score, it was rather surprising for the
weighted score: The goal of assigning weights was to maximize the impact of variables loading
high on the overall scale, thereby changing the nature of the original scale. The results obtained
in this analysis suggests that assigning weights does not lead to significantly different
intercorrelation patterns among variables. Therefore, the process of assigning weights to the
different items of one scale score becomes redundant in most cases.