Descriptive and summary statistics
The output generated by this tool provides a variety of measures of central tendency and data dispersion for each column of sample data. This is advantageous before conducting further analysis in the form of hypothesis tests. The overall nature of the sample data gathered from this output may be influential in choice of subsequent parametric or non-parametric tests. For further details follow this linked section on statistical analysis.
Script operation
This tool operates in much the same way as most of the others with no specific departures from the usual methods needed.
Click here for information about general script usage.
Raw sample data may be entered as single or multiple samples, the data being arranged in columns. Typical output is shown below. Note that the statistics are computed for the three example columns and these have been labelled in the output under the headings 'Group A', 'Group B' and 'Group C'. Notice how the original samples were labelled in the same manner and that these titles have been incorporated in the output by inclusion in the input data range.
Raw data: Group A Group B Group C 22 6.2 18 15 5.0 16 9 8.9 31 7 7.8 8 4 6.4 2 45 11.4 36 19 5.8 12 26 6.2 16 35 7.1 47 49 10.4 22 9.7 37 8.7 52 6.4 7.7 7.8 7.4 Spreadsheet output: Statistics Group A Group B Group C Count: 10 16 12 Sum: 231 122.9 297 Mean(Arith.): 23.1 7.6813 24.75 Mean(Geo.): 17.7873 7.4992 18.8119 Mean(Harm.): 12.8471 7.3259 11.3004 Mean(Quad.): 27.4645 7.8688 28.9698 Mode: None Multi_(See_below) 16 First Quartile: 9 6.4 16 Median: 20.5 7.55 20 Third Quartile: 35 8.9 37 Range: 45 6.4 50 Maximum: 49 11.4 52 Minimum: 4 5 2 Std. Error: 4.9519 0.4409 4.5396 Std. Deviation: 15.6592 1.7638 15.7256 Mean Deviation: 12.52 1.3688 13.2083 Variance: 245.2111 3.111 247.2955 Skewness: 0.4588 0.5742 0.355 Kurtosis: -1.0607 -0.4642 -1.016 Confidence Level (95%)-low: 13.3943 6.817 15.8524 Confidence Level (95%)-high: 32.8057 8.5455 33.6476 Confidence Level (99%)-low: 10.3242 6.5436 13.0378 Confidence Level (99%)-high: 35.8758 8.8189 36.4622 Mode Count 6.2 2 6.4 2 7.8 2
Interpretation
There is much useful information contained within the output and the following points are particularly worth noting:
In this case it is preferable to employ a non-parametric testing approach.
Related tools:
Goodness of fit (x²) for normality: Detect normality using chi-square goodness of fit test.
F-Ratio test: Variance ratio test.
A leptokurtic distribution is represented by a negative score less than zero (as in all samples 'Groups A, B, and C' above) and is characterised by many data elements in between the mean and the 'tails' of the distribution.
Related tools:
Goodness of fit (x²) for normality: Detect normality using chi-square goodness of fit test.
Frequency histograms: Analyse data frequency
distributions.