MGT223 Business Statistics
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Nonparametric solutions
MGT223 Business Statistics
Question 1
Independent samples t-test
Assumptions:
· Independent random samples - two separate samples so definitely independent. Will have to assume the random element.
· Interval/ratio data – electricity consumption in KWH – a ratio measure.
· Normality (sample sizes < 30) – check below
· Also need to check equal variances as part of the test.
Checking the assumption of normality:
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Descriptives |
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Insulation |
Statistic |
Std. Error |
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Consumption |
Experimental |
Mean |
7890.14 |
748.765 |
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95% Confidence Interval for Mean |
Lower Bound |
6057.98 |
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Upper Bound |
9722.31 |
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5% Trimmed Mean |
7954.49 |
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Median |
8022.00 |
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Variance |
3924545.810 |
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Std. Deviation |
1981.047 |
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Minimum |
4307 |
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Maximum |
10315 |
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Range |
6008 |
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Interquartile Range |
3008 |
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Skewness |
-.822 |
.794 |
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Kurtosis |
1.034 |
1.587 |
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Control |
Mean |
10976.75 |
907.114 |
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95% Confidence Interval for Mean |
Lower Bound |
8831.77 |
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Upper Bound |
13121.73 |
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5% Trimmed Mean |
11017.11 |
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Median |
11387.50 |
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Variance |
6582853.357 |
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Std. Deviation |
2565.707 |
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Minimum |
6584 |
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Maximum |
14643 |
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Range |
8059 |
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Interquartile Range |
3724 |
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Skewness |
-.480 |
.752 |
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Kurtosis |
-.084 |
1.481 |
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Experimental: Skewness -0.822 (s.e. = 0.794); Kurtosis: 1.034 (s.e.= 1.587)
Control: Skewness -0.480 (s.e. = 0752); Kurtosis: -0.084 (s.e.= 1.481)
No evidence of skewness or kurtosis in populations for either group (ratios all within range -2 to +2).
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Tests of Normality |
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Insulation |
Kolmogorov-Smirnova |
Shapiro-Wilk |
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Statistic |
df |
Sig. |
Statistic |
df |
Sig. |
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Consumption |
Experimental |
.240 |
7 |
.200* |
.928 |
7 |
.537 |
|
Control |
.167 |
8 |
.200* |
.969 |
8 |
.889 |
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*. This is a lower bound of the true significance. |
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a. Lilliefors Significance Correction |
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Shapiro-Wilk test provides no evidence against normality in populations for either group (Experimental: p = 0.537, Control: p = 0.889)
Points lie fairly close to diagonal on normal probability plots.
The boxplot on next page appears to be fairly symmetrical.
No evidence against normality.
Boxplot of Consumption
The boxplot appears to show reduced consumption under experimental conditions.
Consumption under control conditions appears to be more variable.
Both of these observations can be checked formally below.
(i)
T-Test
|
Group Statistics |
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INSULATION |
N |
Mean |
Std. Deviation |
Std. Error Mean |
|
CONSUMPTION |
1 Experimental |
7 |
7890.14 |
1981.047 |
748.765 |
|
2 Control |
8 |
10976.75 |
2565.707 |
907.114 |
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Independent Samples Test |
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Levene's Test for Equality of Variances |
t-test for Equality of Means |
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F |
Sig. |
t |
df |
Sig. (2-tailed) |
Mean Difference |
Std. Error Difference |
95% Confidence Interval of the Difference |
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Lower |
Upper |
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CONSUMPTION |
Equal variances assumed |
.762 |
.399 |
-2.577 |
13 |
.023 |
-3086.607 |
1197.759 |
-5674.209 |
-499.005 |
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Equal variances not assumed |
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|
-2.624 |
12.836 |
.021 |
-3086.607 |
1176.225 |
-5630.986 |
-542.228 |
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NPar Tests
Mann-Whitney Test
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Ranks |
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Insulation |
N |
Mean Rank |
Sum of Ranks |
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Consumption |
1 Experimental |
7 |
5.29 |
37.00 |
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2 Control |
8 |
10.38 |
83.00 |
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Total |
15 |
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2023-03-23