17.1.3.1 Side-by-Side Statistics Dialog Box

Side-by-Side Statistics dialog.png


Contents

Input

Specify the input data range.

Groups

Multiple grouping columns contains grouping information can be inserted into the Group box. Different grouping values indicate the data in the corresponding cells are from different groups. You can add, remove, order grouping columns via controlling buttons: Move Up button Button Group List Move Up.png, Move Down button Button Group List Move Down.png, Remove button Button Group List Remove.png, Select All button Button Group List Select All.png, Select button Button Group List Add.png in toolbar Group List Toolbar.png.
The grouping columns are set as categorical if most of the column values are text. So you can easily reorder the output columns.

Quantities

Let \(x_i\,\) be the \(i\,\)th sample and \(w_i\,\) be the \(i\,\)th weight:

N Total

Total number of data points, denoted by n

N Missing

Number of missing values

Mean

The mean (average) score

\(\bar{x}=\frac 1w\sum_{i=1}^n x_iw_i\). If there is no WEIGHT variable, the formula reduces to \(\frac 1n\sum_{i=1}^n x_i\).

Standard deviation

\[s=\sqrt{\sum_{i=1}^n w_i(x_i-\bar{x})^2/d}\]

where \(d=n-1 \,\)

Note: In OriginPro, \(d\) has 4 more options, which are defined in the Variance Divisor of Moment branch.

SE of Mean Standard error of mean:

\[\frac s{\sqrt{w}}\]

Lower 95% CI of Mean

Lower limit of the 95% confidence interval of mean

\[\bar{x}-t_{(1-\alpha /2)}\frac s{\sqrt{n}}\]

where \(t_{(1-\alpha /2)}\) is the \((1-\alpha /2)\) critical value of the Student's t-statistic with n-1 degrees of freedom

Upper 95% CI of Mean

Upper limit of the 95% confidence interval of mean

\[\bar{x}+t_{(1-\alpha /2)}\frac s{\sqrt{n}}\]

where \(t_{(1-\alpha /2)}\) is the \((1-\alpha /2)\) critical value of the Student's t-statistic with n-1 degrees of freedom

Variance

\[ s^2\ \]

Sum \(\sum_{i=1}^n x_iw_i\). If there is no WEIGHT variable, the formula reduces to \(\sum_{i=1}^n x_i\).
Skewness

Skewness measures the degree of asymmetry of a distribution. It is defined as

\[\gamma_1=\frac n{(n-1)(n-2)}\sum_{i=1}^n w_i^{\frac 32}(\frac{x_i-\bar{x}}s)^3 ,\mbox{for DF}\]

\[\gamma_1=\frac 1n\sum_{i=1}^n w_i^{\frac 32}(\frac{x_i-\bar{x}}s)^3,\mbox{for N}\]

\[\gamma_1=\frac 1d\sum_{i=1}^n w_i^{\frac 32}(\frac{x_i-\bar{x}}s)^3,\mbox{for WVR}\]

Note: When the WDF or WS methods are chosen, skewness is returned as a missing value.

Kurtosis

Kurtosis depicts the degree of peakedness of a distribution.

\[\gamma_2=\frac{n(n+1)}{(n-1)(n-2)(n-3)}\sum_{i=1}^n w_i^2(\frac{x_i-\bar{x}}s)^4-\frac{3(n-1)^2}{(n-2)(n-3)},\mbox{for DF}\]

\[\gamma_2=\frac 1n\sum_{i=1}^n w_i^2(\frac{x_i-\bar{x}}s)^4 -3,\mbox{for N}\]

\[\gamma_2=\frac 1d\sum_{i=1}^n w_i^2(\frac{x_i-\bar{x}}s)^4 -3,\mbox{for WVR}\]

Note: When the WDF or WS methods are chosen, kurtosis is returned as a missing value.

Uncorrected Sum of Squares

\[\sum_{i=1}^n w_ix_i^2\]

Corrected Sum of Squares

\[\sum_{i=1}^n w_i(x_i-\bar{x})^2\]

Coefficient of Variance

\[\frac s{\bar{x}}\]

Mean absolute Deviation

\[\frac{ \sum_{i=1}^n w_i|x_i-\bar{x}|}w\]

SD times 2

Standard deviation times 2.

\[2s \,\]

SD times 3

Standard deviation times 3.

\[3s \,\]

Geometric Mean

\[\bar{x}_g=\left( \prod_{i=1}^n x_i\right) ^{\frac 1n}\]

Note:: Weights are ignored for the geometric mean.

Geometric SD

The geometric standard deviation \(e^{std(\log x_i)}\) Where std is the unweighted sample standard deviation.

Note: Weights are ignored for the geometric standard deviation.

Mode

The mode is the element that appears most often in the data range. If multiple modes are found, the smallest will be chosen.

Sum of Weights

\[w=\sum_{i=1}^n w_i\]

Harmonic Mean

harmonic mean (sometimes called the subcontrary mean)


without weight: \(\frac n{\frac 1{x_1} + \frac 1{x_2} + ... + \frac 1{x_n}}=\left(\frac {\sum_{i=1}^n (x_i)^{-1}}n\right)^{-1}\)

with weight: \(\frac {\sum_{i=1}^n w_i}{\sum_{i=1}^n \frac {w_i}{x_i}}=\left(\frac {\sum_{i=1}^n w_i x_i^{-1}}{\sum_{i=1}^n w_i}\right)^{-1}\)

if any \(x_i\) or weight is negative, return missing; if any \(x_i\) or weight is 0, return 0.

Minimum

\[x_{(1)}\,\]

Index of Minimum

The index number of Minimum in the original (input) dataset

1st Quartile (Q1)

First (25%) quantile, Q1. See Interpolation of quantiles for computational methods

Median

Median or second (50%) quantile, Q2. See Interpolation of quantiles for computational methods

3rd Quartile (Q3)

Third (75%) quantile, Q3. Interpolation of quantiles for computational methods

Maximum

\[x_{(n)}\,\]

Index of Maximum

The index number of Maximum in the original (input) dataset

Interquartile Range (Q3-Q1)

\[Q_3-Q_1\,\]

Range (Maximum-Minimum)

Maximum - Minimum

Custom Percentile(s)

Request computation of custom percentiles.

Percentile list

This option is only available when Custom Percentile(s) is checked. Percentiles are computed for all the values listed.

Median Absolute Deviation For a univariate data set X1, X2, ..., Xn, the MAD is defined as the median of the absolute deviations from the data's median:

\[MAD = median(|{X_i} - median(X)|)\,\]

that is, starting with the residuals (deviations) from the data's median, the MAD is the median of their absolute values.

Robust Coefficient of Variation

\[(MAD/norminv(0.75))/Median\,\]

Output

Output for Each Row of Input Output corresponding statistics result on the right of each row of data.
Output All Combinations for Groups Output statistics result on each combination groups on right side of source data.

Note:

  • When Output for Each Row of Input option is checked, this option is not available.
  • If there are two groups, for example Group1: A1, A2 and Group2: B1,B2, the output group will with A1-B2, A1-B2, A2-B1,A2-B2. Even if there is no A1-B2 is source data, it will be output as a row.
Output Group as Columns Output group information on the columns.