17.1.1.1 The Statistics on Columns Dialog Box

Each column will be treated as separate dataset. Statistical operations will be performed on each, independently.

All columns will be treated as a whole.

Specify the data range to be performed:

Data Range

The input data range

Group

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 , Move Down button , Remove button , Select All button , Select button in toolbar .
The grouping columns are set as categorical if most of the column values are text. So you can easily reorder the output columns.

Weighting Range

The range that contains weighting information. The value in each cell specifies the weight of the corresponding data.

Total number of data points, denoted by n

Number of missing values

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 \(\frac 1n\sum_{i=1}^n x_i\).

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

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

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

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

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 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

\[ s^2\ \]

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 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.

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

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

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

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

Standard deviation times 2.

\[2s \,\]

Standard deviation times 3.

\[3s \,\]

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

Note:: Weights are ignored for the geometric mean.

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.

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

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

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.

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

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

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

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

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

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

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

\[Q_3-Q_1\,\]

Maximum - Minimum

Request computation of custom percentiles.

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

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

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

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

\(w_{i}=c_{i}\,\!\), where \(c_{i}\,\!\) is the ith value of weighting dataset.

\(w_{i}=\frac 1{\sigma _{i}^2}\,\!\), where \(\sigma_{i}\,\!\) is the value in a designated error bar column.

\(w_{i}=\frac 1{x_{i}}\,\!\), where \(x_{i}\,\!\) is the input data.

\[d=n-1\,\]

\[d=n\,\]

\[d=w-1\,\]

\[d=w\,\]

\(y = \begin{cases} x_k,& \mbox{if }\ g\neq \frac 12 \\ x_j, & \mbox{if }\ g=\frac 12 \mbox{ and j is even} \\ x_{(j+1)},& \mbox{if }\ g=\frac 12 \mbox{ and j is odd} \end{cases}\) where k is the integer part of \(np+\frac 12\,\)

\(y=(1-g)x_{(j)}+gx_{(j+1)}\,\) where \(x_{(n+1)}\,\)is taken to be \(x_{(n)}\,\)

\(y=(1-g)x_{(j)}+gx_{(j+1)}\,\) where \(x_0\,\)is taken to be \(x_1\,\)

\(m = \begin{cases} \frac n2,& \mbox{if n is even} \\ \frac{(n+1)}2,& \mbox{if n is odd} \end{cases} \) \( k = \begin{cases} \frac m2,& \mbox{if m is even} \\ \frac{(m+1)}2,& \mbox{if m is odd} \end{cases}\)

Then we have:

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

\( Q_1= \begin{cases} x_k,& \mbox{if m is odd} \\ \frac 12(x_{(k)}+x_{(k+1)}),& \mbox{if m is even} \end{cases}\) \(Q_2= \begin{cases} x_m,& \mbox{if n is odd} \\ \frac 12(x_{(m)}+x_{(m+1)}),& \mbox{if n is even} \end{cases}\)

\[Q_3= \begin{cases} x_{(n-k-1)},& \mbox{if m is odd} \\ \frac 12(x_{(n-k)}+x_{(n-k+1)}),& \mbox{if m is even} \end{cases}\]

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

Arrange Graphs into Columns

Specify number of columns to arrange output graphs.

Arrange Plots of Same Type in One Graph

Check to plot all graphs of same type in one graph window.

Identifier

Select from the list:

• Range

Use the range syntax.

• Book Name

Use the workbook long name.

• Sheet Name

Use the worksheet name.

• Name

Use column Long Name if it exists, otherwise Short Name.

• Short Name

Use column Short Name.

• Long Name

Use column Long Name.

• Units

Use column Units.

• Comments

Use column Comments.

• <Custom>

Use custom formats to define a data identifier. For usage information, please refer to Advanced legend text customizations.

Show Identifier in Flat Sheet

Use the dataset identifier in resulting flat sheet(s).

Book

The target workbook.

• <none>: Do not output report worksheet tables.
• <source>: The source data workbook.
• <new>: A new workbook.
• <existing>: An existing workbook.

BookName

The target workbook. Must be source (uneditable), new or existing (editable), otherwise blank.

Sheet

The target worksheet, always <new>.

SheetName

Name of the target sheet.

Results Log

Output the report to the Results Log.

Script Window

Output the report to the Script Window.

Notes Window

Specify the target Notes window:

• <none>: Do not output to a Notes window.
• <new>: Output to a new Notes window.

Book

Specifies the destination workbook

• <none>: Do not output quantities
• <source>: The source data workbook
• <report>: The Report Tables workbook
• <new>: A new workbook.
• <existing>: A specified existing workbook

BookName

The target workbook. Must be source (uneditable), new or existing (editable), otherwise blank.

Sheet

• <new>: A new worksheet.
• <source>: The source data worksheet
• <existing>: A specified existing worksheet

SheetName

Name of the target sheet.

Notes

Notes table

Input Data

Table for input data

Masked Data

Table for masked data

Missing Data

Table for missing data

When this box is selected, the branch is expanded. In this branch,

• The Data Height drop-down determines the Y axis of the histogram.

• Count: Y axis displays bin counts.
• Relative Frequency: Y axis displays individual bin counts divided by total count.
• Density: Y axis displays relative frequency (no. of observations in a given bin) divided by bin width.

• The Automatic Binning check box is selected by default. Bin Size, Number of Bins, Begin, End are shown automatically when Automatic Binning is clear.