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Basic Statistics
STATGRAPHICS Centurion contains a complete selection of procedures for basic statistics. Among the many capabilities are:
1. Summary Statistics - calculation of sample means, medians, standard deviations, and other summary statistics.
2. One Sample Analysis - characterization of a sample of data taken from a single population.
3. Outlier Identification - statistical tests to determine whether one or more outliers are present in a data sample.
4. Comparison of Two Samples - comparison of data taken under two different sets of conditions.
5. Analysis of Attribute Data - methods for summarizing categorical data.
6. Sample Size Determination - calculation of required sample sizes for common statistical problems.
7. Probability Distributions - calculation of probabilities and generation of random numbers from 45 different probability distributions.
One of the purposes of calculating statistics is to summarize the information in a sample of data. In STATGRAPHICS Centurion, you can select from a large number of summary statistics. Included are statistics such as the Winsorized mean and Winsorized sigma, which are less sensitive to outliers than the usual sample mean and standard deviation. Also important are the standardized skewness and standardized kurtosis, which test whether the samples could reasonably have come from a normal distribution. The StatAdvisor highlights in red any samples with values that indicate significant non-normality.
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MPG City |
MPG Highway |
Horsepower |
Fueltank |
Length |
Width |
|
Count |
93 |
93 |
93 |
93 |
93 |
93 |
|
Average |
22.37 |
29.09 |
143.8 |
16.66 |
183.2 |
69.38 |
|
Median |
21.0 |
28.0 |
140.0 |
16.4 |
183.0 |
69.0 |
|
Mode |
18.0 |
26.0 |
|
|
|
67.0 |
|
Geometric mean |
21.78 |
28.65 |
135.1 |
16.33 |
182.6 |
69.28 |
|
5% Trimmed mean |
21.83 |
28.72 |
140.1 |
16.64 |
183.3 |
69.31 |
|
5% Winsorized mean |
22.04 |
28.85 |
142.6 |
16.59 |
183.3 |
69.38 |
|
Variance |
31.58 |
28.43 |
2743. |
10.75 |
213.2 |
14.28 |
|
Standard deviation |
5.62 |
5.332 |
52.37 |
3.279 |
14.6 |
3.779 |
|
Coeff. of variation |
25.13% |
18.33% |
36.41% |
19.68% |
7.971% |
5.447% |
|
Standard error |
0.5827 |
0.5529 |
5.431 |
0.3401 |
1.514 |
0.3919 |
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5% Winsorized sigma |
4.763 |
4.595 |
49.6 |
3.079 |
13.25 |
3.808 |
|
MAD |
3.0 |
3.0 |
30.0 |
2.1 |
9.0 |
3.0 |
|
Sbi |
4.566 |
4.675 |
49.21 |
3.311 |
14.35 |
3.817 |
|
Minimum |
15.0 |
20.0 |
55.0 |
9.2 |
141.0 |
60.0 |
|
Maximum |
46.0 |
50.0 |
300.0 |
27.0 |
219.0 |
78.0 |
|
Range |
31.0 |
30.0 |
245.0 |
17.8 |
78.0 |
18.0 |
|
Lower quartile |
18.0 |
26.0 |
103.0 |
14.5 |
174.0 |
67.0 |
|
Upper quartile |
25.0 |
31.0 |
170.0 |
18.8 |
192.0 |
72.0 |
|
Interquartile range |
7.0 |
5.0 |
67.0 |
4.3 |
18.0 |
5.0 |
|
1/6 sextile |
18.0 |
25.0 |
92.0 |
13.2 |
172.0 |
66.0 |
|
5/6 sextile |
28.0 |
33.0 |
185.0 |
20.0 |
198.0 |
74.0 |
|
Intersextile range |
10.0 |
8.0 |
93.0 |
6.8 |
26.0 |
8.0 |
|
Skewness |
1.704 |
1.23 |
0.9517 |
0.1081 |
-0.09009 |
0.264 |
|
Stnd. skewness |
6.71 |
4.842 |
3.747 |
0.4258 |
-0.3547 |
1.039 |
|
Kurtosis |
4.004 |
2.614 |
1.111 |
0.1272 |
0.4493 |
-0.2464 |
|
Stnd. kurtosis |
7.882 |
5.146 |
2.187 |
0.2504 |
0.8844 |
-0.4851 |
When n observations have been collected from a single population, it is common to display the data in the form of a histogram. Any of 45 probability distributions can then be fit to the data, so that predictions can be made about future samples from the underlying population.
Everyone who analyzes data has been faced with the problem of determining whether or not an apparent abnormality should be left in the data set or removed. The implications of wrongly making either decision can be serious. In STATGRAPHICS Centurion, the Outlier Identification procedure calculates several tests (including Grubbs' test and Dixon's test) to determine whether a suspected value is a likely outlier.
A very common statistical problem is that of comparing two samples and determining whether or not there is a significant difference between them. STATGRAPHICS Centurion provides procedures for comparing both paired and unpaired samples. t tests, F tests, and nonparametric signed rank tests are all available. In addition to the standard numerical output, the StatAdvisor provides guidance and suggestions regarding the analysis.
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Comparison of Means t test to compare means The StatAdvisor A t-test may also be used to test a specific hypothesis about the difference between the means of the populations from which the two samples come. In this case, the test has been constructed to determine whether the difference between the two means equals 0.0 versus the alternative hypothesis that the difference does not equal 0.0. Since the computed P-value is less than 0.05, we can reject the null hypothesis in favor of the alternative. NOTE: these results do not assume that the variances of the two samples are equal. In this case, the variances appear to be significantly different based on the results of an F-test to compare the standard deviations. You can see the results of that test by selecting Comparison of Standard Deviations from the Tabular Options menu. |
When the data consist of attributes rather than variables, the statistical methods needed to analyze it are different. In such cases, interest normally centers around rates or proportions. The Tabulation, Crosstabulation, Contingency Tables, Comparison of Proportions, and Comparison of Rates procedures are all relevant. For two categorical variables, the Mosaic Plot provides a useful way of visualizing any association.
STATGRAPHICS Centurion provides procedures for determining adequate sample sizes for problems involving means, standard deviations, rates or proportions. Sample sizes may be based on the desired width of a confidence interval or on the power of the relevant hypothesis test.
STATGRAPHICS Centurion contains routines for calculating 45 probability distributions. Tail areas, critical values, and random numbers can be generated.
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