Manual InnerSoft STATS

InnerSoft STATS

Application Manual v0.4

APPLICATION MANUAL V0.4 InnerSoft STATS

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INDEX

1. Installation and Activation

1.1. Installation

1.2. Trial Version

1.3. Activation

1.4. License

1.4.1. Upgrades

1.4.2. License Renewal

2. Introduction to ISSTATS

2.1. Open and Save files

2.2. Technical Limitations and Recommendations

3. Working in the Main window

3.1. File Menu

3.2. Analyze Menu

3.3. Help Menu

4. Working in the Worksheet window

4.1. File Menu

4.2. Edit Menu

4.3. Options Menu

5. Working in the Output window

6. Descriptive Statistics

7. One Sample Test

7.1. Z Test

7.2. T Test

7.3. Variance Test

8. Two-Sample Test

8.1. 2-Sample t-Test

8.2. Paired t-Test

8.3. 2 Variances F-Test

9. One-Way ANOVA

10. Homoscedasticity Tests

11. Methods and Formulas Help


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1. – Installation and Activation

1.1. – Installation

Click on setup.exe to install the application.

1.2. – Trial Version

InnerSoft STATS works initially as limited trial version. You will not be allowed to use following tools:

Open or Save any Project or Worksheet.

Using Paste or Insert when editing cells.

1.3. – Activation

In order to use InnerSoft STATS Full Version, user must purchase a license before activating the product.

To purchase InnerSoft STATS Full Version, you must first contact with us by email

[email protected]

[email protected]

You can also call us (Spain number phone):

There are different payment methods that you can find at:

http://isstats.itspanish.org/index.htm#buy

Once product has been paid, you can activate it. Just enter Help/Activate ISSTATS and follow instructions.

For a successful activation process, InnerSoft requires permissions to read/write files in its installation

folder, usually: 'C:\Program Files\ISSTATS\'.

So may you have to login to Windows as Administrator or have to modify User Account Control in order

to activate successfully InnerSoft STATS.

mailto:[email protected]?subject=Buy%20InnerSoft

mailto:[email protected]?subject=Buy%20InnerSoft

http://isstats.itspanish.org/index.htm#buy


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1.4. – License

Registering data is chained to a PC Computer. When you pay a license, you can run InnerSoft STATS in

3 different computers. Thus you can ask for 3 Activation Codes.

You will not lose the license when formatting the hard drives or changing Windows S.O., BUT if you

make changes of hardware the activation code may become invalid.

Extra Activation Codes (more than 3) for same user have an additional cost.

1.4.1. – Upgrades

You will receive the Activation Codes for the product upgrades at no cost during one year. If you do not

renew the license after one year, will not lose the license of the product version that you purchased, BUT

will not receive new Activation Codes for the new software versions.

1.4.2. – License Renewal

The renewal will let you receive the Activation Codes for the new versions of the software during a year.


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2. – Introduction to ISSTATS

When you start ISSTATS, a new, empty project is opened for you. You will see three windows:

Main window

o Project Manager window

o Worksheet window

o Output window

Controlling Windows

You can open and minimize ISSTATS windows just as you would other windows in your operating

system. You can also control ISSTATS windows with commands on the Window menu.

ISSTATS Environment

The project contains:

A Worksheet that contains your data. You can NOT have multiple worksheets in one project. Your data

will be displayed as columns. There is a Data window for your worksheet in the project. You can enter

and edit data directly in the Data window.

A Project Manager, which contains:

A Root folder for setting the project information.

A Settings folder for setting some options.

A Variables folder for your worksheet. This folder displays a summary of the columns used in the

worksheet.

An Output window that displays your results.

Multiple Toolbars for issuing commands and a Status Bar.

2.1. – Open and Save files

Use the file menu to open, close or save the three file types that ISSTATS can use.

Projects—contain a worksheet, along with project settings and project information

Worksheets—contain only your columns data

Outputs—contain the computed outputs

When you open a project file, the worksheet that were inside that project when you last saved is available

to you. When you save a project, the worksheet is saved within that project file.

The output results must be saved apart from the project file.

ISSTATS does not support multiple Worksheets or multiple Output documents. If you create a new table

or document, remember to save the previous data before it disappears.

You can save a project or worksheet in XML or Binary file format. The advantages and disadvantages of

using each format are:


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XML

XML format is human readable and editable in plain text

Can be imported by lot of applications (Excel…)

Takes high size: storing a variable with 1’5 millions of values will take around 50 Mb in a XML

file

Has a high compression rate: a XML file of 50 Mb will get only 1 Mb of size once compressed in

zip format

Opening and saving is fast

Binary

Binary format is not human readable

Can be only open by ISSTATS

Takes less size than XML: storing a variable with 1’5 millions of values will take around 30 Mb

in a Binary file.

Has a low compression rate: a Binary file of 50 Mb will get 6 Mb of size once compressed in zip

format.

Opening and saving is slow.

Thus XML compressed in zip is the better way of storing large amounts of data.

2.2. – Technical Limitations and Recommendations

ISSTATS uses decimal data type instead of double data type. Decimal is specially used for financial and

monetary calculation which requires higher accuracy. It is not adequate for scientific applications because

of its lower range: the largest value is +/–7.9228162514264337593543950335, and the smallest nonzero

value is +/–0.0000000000000000000000000001 (+/–1E–28). So if you need to analyses social or

scientific data with large numbers (astronomy distances, human stupidity…), just use a different statistical

package.

ISSTATS work with on–memory data (no database storage). Thus it can compute quickly. In the other

hand, memory usage is huge.

ISSTATS can handle millions of data. It can compute all descriptive parameters of a variable with 1’5

million values in only a few seconds (Processor: Pentium R Dual Core CPU E 6600 @ 3.06 GHz 3.07

GHz RAM: 8.0 GB SO: Windows 7 64 Bits). In the other hand, the Data table can easily crash if you try

to manipulate this huge data. Operations like copying, pasting, removing and selecting cells in such a big

table can hang the application. It really depends on the total number of cells in the table. To avoid this

problem, limit the number of table columns when operating with huge data. If you want to handle

variables with millions of values, set the number of table columns to minimum in the Worksheet

OPTIONS menu: if you are using only 4 variables, set only 4 columns.

You should perform operations with columns as much as possible. If you want to clear a variable, select

the column and clear the column; avoid selecting all cells in the column and clearing these cells. If you

want to copy a variable then copy the column, not the cells.

Actually, undo/redo history has no limits. A limit will be implemented in a future. If you feel that

ISSTATS is consuming too much memory in your PC, you should save your project, restart the

application and open your project again. This will clear the undo/redo history.

Please, remember this is 0.4 version.


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3. – Working in the Main window

3.1. – File Menu

New Project

Creating a new project closes the current project. If your current project has been changed since it was

last saved, ISSTATS will prompt you to save all or part of the project before closing it.

Open Project

Opening a new project closes the current project. If your current project has been changed since it was

last saved, ISSTATS will prompt you to save all or part of the project before closing it.

Save Project

Saves the current project in a XML or Binary file. If the project has been saved before, Save Project

saves the file with the current file name without displaying a dialog box. If the project has not been saved

before, Save Project opens the Save Project As dialog box.

When you save the project, you save the input information about your work:

the contents of project settings and project information

the columns of data in the Worksheet window

The output document will not be saved in your project file.

Save Project As

Saves the current project in a XML or Binary file with a different name. If the project has not been saved

before, choosing File > Save Project also opens this dialog box.

Dialog box items

Save in: Choose a drive and folder.

File name: Enter a file name.

Save as type: Choose a file type from the list.

o XML files (*.xml)

o DAT files (*.dat)

Exit

Exits you from ISSTATS. ISSTATS will prompt you to save the changes before closing the application.

3.2. – Analyze Menu

Descriptive Statistics: See Chapter 6. – Descriptive Statistics

One Sample Test: See Chapter 7. – One Sample Test

Two-Sample Test: See Chapter 8. – Two-Sample Test


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One-Way ANOVA: See Chapter 9. – One-Way ANOVA

Homoscedasticity Tests: See Chapter 10. – Homoscedasticity Tests

3.3. – Help Menu

Contents

Open this PDF.

Buy ISSTATS

Open a web page with information about buying InnerSoft STATS.

Activate ISSTATS

Open the menu to activate ISSTATS in order to use all features.

About

Shows ISSTATS version and contact information.


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4. – Working in the Worksheet window

4.1. – File Menu

New Worksheet

Creating a new worksheet adds an empty worksheet to the current project. An empty Data window will

appear.

Open Worksheet

Copies data from a file into the current project. When you open a file, you copy the contents of the file

into the current project. Any changes you make to the file while in the project will not affect the original

file.

Save Worksheet

Saves the current worksheet in the same file and format as the file name displayed in the window title. If

the current worksheet is untitled, File > Save Worksheet brings up a dialog box where you can specify a

file name and location in which to save your data. See File > Save Worksheet As for a description of this

dialog box.

Choose File > Save Worksheet As to rename your worksheet or save it to a new location.

Save Worksheet As

Saves the worksheet data in a file. Use this command if you want to rename your worksheet or save it to a

new location.

Dialog box items

Save in: Choose a drive and folder.

File name: Enter a file name.

Save as type: Choose a file type from the list.

o XML files (*.xml)

o DAT files (*.dat)

Export to Excel

This tool will export to Excel only those columns that has a variable defined. Empty columns will not be

exported.

Exporting to Excel has some limitations. As worksheet limit size in Excel 2010 is 65,536 rows, ISSTATS

will divide the data collection in different sheets of 65530 rows everyone. If you are going to export 1’5

million values, the application will create 23 different Excel worksheets with 65530 rows each one. As

columns limit in Excel 2010 is 256 columns, ISSTATS will not export the data of more than 256

variables.

4.2. – Edit Menu

Undo & Redo


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To undo an action, click Undo Button on the Toolbar.

To redo an action that you undid, click Redo Button on the Toolbar.

Cut Cells

The selection will be copied to the clipboard buffer. The selection will be moved to a new location as

soon as you choose Paste command as described below.

Please note that the selection will remain in its current location until you paste it. If you want to delete a

selection without pasting it to a new location, use Delete command instead.

Copy Cells

The selection will be copied to the clipboard buffer. The selection will be copied to a new location as

soon as you choose Paste command as described below.

You can copy all the cells of a column or a row selecting the rows or columns and using the COPY

CELLS button. To avoid copying the variable names, when you select some columns and click the COPY

CELLS button, the name cells of the column is deselected.

Paste Cells

The contents of the clipboard will be pasted in the spreadsheet so that the selected cell becomes the top

left corner of the selection.

When you paste cells, the blank cells that you cut/copied will not modify any existing value and will not

add any new value to the column. The missing values that you copied will add new missing values or will

replace the existing ones with missing values.

If you copy a discontinuous group of cells, by selecting cells or block of cells while holding down the Ctrl

key, ISSTATS will paste it as a continuous selection where non selected cells are converted in empty

strings.

Insert Cells

You can insert copied cells above of the active cell on your worksheet, shifting other cells in the same

column down.

After you insert cells, the blank cells that you previously copied will add missing values. Inserting cells

below the last value of the column will do as pasting cells: blank cells will not add data.

Clear Cells

Erases the contents of the selected cells, without moving other cells. This menu command is available

when at least one cell is selected in the Data window. To delete selected cells, see Delete Cells.

In a numeric column, ISSTATS inserts system missing values (*) in a cleared cell.

Delete Cells


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If you are deleting cells, other cells automatically shift up. If you click a cell and then press DELETE,

Excel deletes the cell contents.

Select All Cells

Click this button to select all cells on the worksheet.

Copy Columns

When you copy various columns, alternated selected columns will be joined together in a continuous

selection once you paste or insert them (as Excel does).

Paste Columns

On pasting, empty selected columns will not modify any existing variables. Not empty selected columns

will replace any existing variables.

Insert Columns

You can insert columns that previously copied in the worksheet.

To insert a single column, select the column in the column immediately to the right of where you want to

insert the new column. To insert multiple columns, select the columns immediately to the right of where

you want to insert columns.

If you insert columns, other columns automatically shift to the right.

On inserting, empty columns (no variable defined) will add new empty columns (no variable defined).

Clear Columns Content

Erases the contents of the selected column, without moving other columns. This menu command is

available when at least one column is selected in the Data window. To delete selected columns, see Delete

Columns.

The cleared cells remain as blank cells on the worksheet.

Delete Columns

If you are deleting columns, other columns automatically shift to the left.

Select All Columns

The Select All Columns command will create a new selection that includes every column with data.

As rows have not any structural meaning in the table, there is no copy/cut/paste/insert options for rows. If

you want to copy all cells of a row just select the rows and press COPY CELLS button.

4.3. – Options Menu


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Table Decimal Places

For numbers that are already entered on a worksheet, you can increase or decrease the number of places

that are displayed after the decimal point by using the Table Decimal Places buttons. By default,

ISSTATS displays 3 decimal places when you apply a built-in number format to the cells.

Table Columns

You can increase or decrease the number of columns that are available in the worksheet by using the

Table Columns buttons. By default, ISSTATS displays 10 columns.

To avoid memory problems, limit the number of table columns when operating with huge data. If you

want to handle variables with millions of values, set the number of table columns to minimum: if you are

using only 4 variables, set only 4 columns.

Table Rows

You can increase or decrease the number of rows that are available in the worksheet by using the Table

Rows buttons. By default, ISSTATS displays 100 rows.


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5. – Working in the Output window

New Document

Creating a new output document closes the current document. If your current document has been changed

since it was last saved, ISSTATS will prompt you to save the document before closing it.

Open Document

Opening a new document closes the current document. If your current document has been changed since

it was last saved, ISSTATS will prompt you to save the document before closing it.

The file format of the opened document must be ISSTAT XAML package (a XAML package file

produced by ISSTAT).

Save Document

Saves the current document in a ISSTAT XAML package file (a XAML package file produced by

ISSTAT). If the document has been saved before, Save Document saves the file with the current file

name without displaying a dialog box. If the document has not been saved before, Save Document opens

the Save Document As dialog box.

Use Windows Clipboard to copy and paste the document content in other applications, such as MS Word,

MS Excel, Notepad…

Save Document As

Saves the document in a file. Use this command if you want to rename your document or save it to a new

location.

Print Document

Prints the document.

Cut, Copy & Paste

The way to copy or move a selection is to use cut, copy, and paste operations.

Use this commands to copy a selection from Output window to other applications, such as MS Word, MS

Excel, Notepad…

Undo & Redo

To undo an action, click Undo Button on the Toolbar.

To redo an action that you undid, click Redo Button on the Toolbar.

Bold, Italic, Underline, Grow Font, Shrink Font, Bullets, Numbering, Align Left, Align Center,

Align Right, Align Justify, Increase Indent & Decrease Indent


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These are the formatting buttons, familiar to anyone who has used a word processor. These formats are

applied by selecting some text in the window and clicking the button in the editor toolbar.

Select All

The Select All command will create a new selection that includes everything on the document.


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6. – Descriptive Statistics

Overview

Produces descriptive statistics for each column. The data columns must be numeric and contain at least

one numeric value. The dialog box allows to choose the statistics that you wish to display.

Available Variables list shows numeric data columns containing at least one no-missing value.

Dialog box items

Mean: Choose to display the arithmetic mean.

Sample Variance: Choose to display the unbiased variance of the data. Estimates population variance

based on a sample. If your data represents the entire population, then compute the variance by using Total

Variance.

Sample Standard Deviation: Choose to display the standard deviation of the data. Estimates population

standard deviation based on a sample. If your data represents the entire population, then compute the Std.

Deviation by using Total Std. Deviation.

Sample Coefficient of variation: Choose to display the coefficient of variation.

Sample Skewness: Choose to display the skewness value. Estimates population skewness based on a

sample. If your data represents the entire population, then compute the skewness by using Total

Skewness.

Sample Kurtosis: Choose to display the kurtosis value. Estimates population kurtosis based on a sample.

If your data represents the entire population, then compute the kurtosis by using Total Kurtosis.


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Total Variance: Choose to display the variance of the data. Calculates variance based on the entire

population.

Total Standard deviation: Choose to display the standard deviation of the data. Calculates Std. Deviation

based on the entire population.

Total Coefficient of variation: Choose to display the coefficient of variation. Calculates coefficient of

variation based on the entire population.

Total Skewness: Choose to display the skewness value. Calculates skewness based on the entire

population.

Total Kurtosis: Choose to display the kurtosis value. Calculates kurtosis based on the entire population.

SEM: Choose to display the standard error of the mean.

Sum: Choose to display the data sum.

Minimum: Choose to display the data minimum.

Maximum: Choose to display the data maximum.

Range: Choose to display the data range. Data Range is the difference between the maximum and

minimum.

Quartiles: Choose to display the first quartile, the median and the third quartile.

Interquartile range: Choose to display the difference between the first and third quartiles.

Deciles: Choose to display the nine values that divide the sorted data into ten equal parts.

Percentiles: To request a percentile:

Enter the desired value in the box placed in Percentiles group box. For example, if you wanted the

7th

percentile, you would enter a 7 in the box.

Click the add button to add the percentile to the list of requested percentiles.

Repeat Step 1 and 2 to add additional percentiles as desired.

If you need to delete a percentile, select it in the list and click the remove button.

Mode: Choose to display the mode and the number of times it occurs. If multiple modes exist, Minitab

displays the smallest modes, up to a total of four, along with their frequency.

Sum of squares: Choose to display the sum of the squared data values. This is the uncorrected sums of

squares, without first subtracting the mean.

MSSD: Choose to display half the Mean of Successive Squared Differences.

N nonmissing: Choose to display the number of nonmissing column entries.

N missing: Choose to display the number of missing column entries.

N total: Choose to display the total (nonmissing and missing) number of column entries.


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Cut–Points: Divide the data into a number of equal groups. For example, to create deciles, you would

enter 10 in the box .Enter 3 to divide the data into tertiles.

Check statistics

Check None: Choose to clear all check boxes and then individually check the statistics to display.

Check All: Choose to check all boxes. You can uncheck statistics as needed.


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7. – One Sample Test

Overview

In the box Test Type, choose the test to perform:

Z Test

T Test

Variance Test

Hypothesis Test

To perform a hypothesis test, check the box Perform Hypothesis Test and choose the alternative

hypothesis of the test:

Less than: Perform a level test of H0: ≥ 0 against the one-sided alternative H1: < 0

Not Equal: Perform a level test of H0: = 0 against the two-sided alternative H1: ≠ 0

Greater than: Perform a level test of H0: ≤ 0 against the one-sided alternative H1: > 0

Significance level of the test () derive from the 1- value set in the Confidence Level text box.

If you choose a lower-tailed hypothesis test, an upper confidence bound will be constructed. If you

choose an upper-tailed hypothesis test, a lower confidence bound will be constructed.

Available Variables list shows numeric data columns containing at least one no-missing value.

7.1. – Z Test

Use 1-Sample Z to compute a confidence interval or perform a hypothesis test of the mean when the

standard deviation of the population σ is known. The samples should come from a normal population if n

is low; if however n>30 the distribution of the population does not have to be normal.


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Dialog box items

Data: Choose the origin of the data.

Samples in columns: Choose if you have entered raw data in columns. Enter the columns

containing the sample data in the list Computing Variables. Move these variables from Available

Variables list to Computing Variables list using Add and Remove buttons. Enter the value for the

population standard deviation in the text box. Entering multiple columns, ISSTATS performs

separate one-sample analyses on each column.

Summarized data: Choose if you have summary values for the sample size and mean.

o Sample size: Enter the value for the sample size.

o Mean: Enter the value for the sample mean.

o Population Standard deviation: Enter the value for the population standard deviation.

Confidence level: Enter the level of confidence desired. Enter any number between 0 and 1. Entering 0,9

will result in a 90% confidence interval. The default is 0,95 = 95%.

Perform hypothesis test: Check to perform the hypothesis test.

Hypothesized mean: Enter the test mean 0.

Alternative hypothesis: Choose the alternative hypothesis of the test.

7.2. – T Test

Performs a one-sample t-test or t-confidence interval for the mean.

Use T Test for one sample to compute a confidence interval and perform a hypothesis test of the mean

when the population standard deviation, σ, is unknown. Use this test when samples come from a normal

population or n > 30.

Dialog box items




Variables list to Computing Variables list using Add and Remove buttons. Entering multiple

columns, ISSTATS performs separate one-sample analyses on each column

Summarized data: Choose if you have summary values for the sample size and mean.


o Mean: Enter the value for the sample mean.

o Sample Standard deviation: Enter the value for the sample standard deviation.




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Hypothesized mean: Enter the test mean 0.


7.3. – Variance Test

This procedure calculates confidence intervals for the variance of a population, and performs a hypothesis

test to determine whether the population variance equals a specified value. Use this test when samples

come from a normal population.

Dialog box items




Variables list to Computing Variables list using Add and Remove buttons. Entering multiple

columns, ISSTATS performs separate one-sample analyses on each column.

Summarized data: Choose if you have summary values for the sample size and variance.


o Sample Variance: Enter the value for the sample variance.




Hypothesized variance: Enter the test variance σ2

0.



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8. – Two-Sample Test


2-Sample t-Test

Paired t-Test

2 Variances F-Test

Hypothesis Test

To perform a hypothesis test, check the box Perform Hypothesis Test and choose the Alternative

Hypothesis of the test:

Less than: Perform a level test of H0: ≥ d against the one-sided alternative H1: < d

Not Equal: Perform a level test of H0: = d against the two-sided alternative H1: ≠ d

Greater than: Perform a level test of H0: ≤ d against the one-sided alternative H1: > d

Significance level of the test () derive from the 1- value set in the Confidence Level text box.

If you choose a lower-tailed hypothesis test, an upper confidence bound will be constructed. If you

choose an upper-tailed hypothesis test, a lower confidence bound will be constructed.

Available Variables list shows numerical and text columns containing at least one no-missing value.

Text columns may be used as Subscripts.

8.1. – 2 Sample t-Test

Performs an independent 2-sample t-test and generates a confidence interval.


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When you have dependent samples, use 8.2. – Paired t-Test.

Use 2-Sample t-Test to perform a hypothesis test and compute a confidence interval of the difference

between two population means when the population standard deviations, σ's, are unknown.

Dialog box items


Samples in one column: Choose if the sample data are in a single column, differentiated by

subscript values (group codes) in a second column.

o Computing Variables: Enter the columns containing the sample data in the list

Computing Variables. Move these variables from Available Variables list to Computing

Variables list using Add / Remove buttons.

o Grouping Variable: Enter the column containing the sample subscripts to define the

groups. It may be a numerical or text column.

o Group 1/Group 2: Enter the subscripts that define both groups.

o Automatic Grouping: Check to let the application define automatically both groups. It

will identify the first two different subscripts in the grouping variable.

Samples in different columns: Choose if the data of the two samples are in separate columns.

o First Sample: Enter the column containing one sample from Available Variables list.

o Second Sample: Enter the column containing the other sample from Available Variables

list.

Summarized data: Choose if you have summary values for the sample size, mean, and variance

for each sample.

o First Sample

Sample size 1: Enter the sample size for the first sample.

Mean 1: Enter the value for the mean of the first sample.

Sample Variance 1: Enter the value for the variance of the first sample.

o Second Sample

Sample size 2: Enter the sample size for the second sample.

Mean 2: Enter the value for the mean of the second sample.

Sample Variance 2: Enter the value for the variance of the second sample.

Assume Population equal variances: Check to assume that the populations have equal variances.




Hypothesized mean: Enter the hypothesized difference between the two population means 1-2.


A difference of 0 suggests in the null hypothesis the equality between mean populations; H0: 1-2 = 0

against an alternative H1: 1-2 ≠ 0


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A difference equal or less than 0 suggest in the null hypothesis that the first mean is equal or less than the

second; H0: 1-2 ≤ 0 against an alternative H1: 1-2 > 0

A difference equal or greater than 0 suggest in the null hypothesis that the first mean is equal or greater

than the second; H0: 1-2 ≥ 0 against an alternative H1: 1-2 < 0

Optionally, test ratios other than 0 (equality) can be specified. A difference of 2 suggests in the null

hypothesis the first mean is the second mean plus 2.

8.2. – Paired t-Test

Performs a paired t-test. This is appropriate for testing the mean difference between paired observations

when the paired differences follow a normal distribution.

Use the Paired t command to compute a confidence interval and perform a hypothesis test of the mean

difference between paired observations in the population. A paired t-test matches responses that are

dependent or related in a pairwise manner. A typical example of the repeated measures t-test would be

where subjects are tested prior to a treatment, say for high blood pressure, and the same subjects are

tested again after treatment with a blood-pressure lowering medication. Paired samples t-tests are often

referred to as "dependent samples t-tests". When the samples are drawn independently from two

populations, use 8.1. – 2 Sample t-Test.

Dialog box items


Sample in columns: Choose if you have entered raw data in two columns.

o First sample: Enter the column containing the first sample from Available Variables list.

o Second sample: Enter the column containing the second sample from Available Variables

list.

Pairs must have two numerical values. Pairs that have a missing data in any of the

members are ignored.

Summarized data: Choose if you have summary values for the sample size, mean, and variance

of the difference.


o Mean of Differences: Enter the value for the mean of differences .

o Variance of Differences: Enter the value for the variance of differences s2

d.




Hypothesized mean: Enter the hypothesized population mean of the paired differences d.


8.3. – 2 Variances F-Test


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The 2 Variances F-Test procedure performs hypothesis tests and computes confidence intervals for the

ratios between two populations' variances. Use this test to determine if one treatment condition has more

variability than the other. Each population must follow the normal distribution.

Dialog box items


Samples in one column: Choose if you have entered data into a single column with a second

column of subscripts that identify the samples.

o Computing Variables: Enter the columns containing the sample data in the list

Computing Variables. Move these variables from Available Variables list to Computing

Variables list using Add and Remove buttons. Entering multiple columns, ISSTATS

performs separate analyses on each column.

o Grouping Variable: Enter the column containing the sample subscripts to define the

groups. It may be a numerical or text column.

o Group 1/Group 2: Enter the subscripts that define both groups.

o Automatic Grouping: Check to let the application define automatically both groups. It

will identify the first two different subscripts in the grouping variable.

Samples in different columns: Choose if you have entered the data for the two samples into

separate columns.

o First Sample: Enter the column that contains the data for the first sample from Available

Variables list.

o Second Sample: Enter the column that contains the data for the second sample from

Available Variables list.

Summarized data: Choose if you have summary values for the sample sizes and variances.

o First Sample

Sample size 1: Enter the sample size for the first sample.

Sample Variance 1: Enter the variance for the first sample.

o Second Sample

Sample size 2: Enter the sample size for the second sample.

Sample Variance 2: Enter the variance for the second sample.




Hypothesized ratio: Enter the hypothesized ratio between two population’s variances σ2

1/σ22.


A ratio of 1 suggests in the null hypothesis the equality between variance populations; H0: σ21/σ

22 = 1

against an alternative H1: σ2

1/σ22 ≠ 1.

A ratio equal or less than 1 suggest in the null hypothesis that the first variance is equal or less than the

second; H0: σ21/σ

22 ≤ 1 against an alternative H1: σ

21/σ

22 > 1.


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A ratio equal or greater than 1 suggest in the null hypothesis that the first variance is equal or greater than

the second; H0: σ2

1/σ22 ≥ 1 against an alternative H1: σ

21/σ

22 < 1.

Optionally, test ratios other than 1 (equality) can be specified. A ratio of 2 suggests the first variance is

double the second variance.


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9. – One-Way ANOVA

Performs a one-way analysis of variance. You can also perform multiple comparisons. The response

variable must be numeric. The factor level column (grouping variable) may be numeric or text.

Dialog box items


Groups in different Columns

o Computing Variables: Enter the columns containing the response. Each column must

contain the data for one of the groups.

Groups in 1 Column

o Computing Variables: Enter the column or columns containing the response. ISSTATS

performs a ANOVA test for each of these columns.

o Grouping Variable: Enter the column containing the factor levels.

Confidence level: Enter the confidence level.

For further details, see ANOVA Test.

Multiple Comparisons: Use to generate grouping information tables and confidence intervals for the

differences between means, by different methods. Check to obtain confidence intervals for all pairwise

differences between level means using any of these methods.

Scheffe

Tukey HSD: Tukey's Honestly Significant Difference test.

Sidak


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Fisher LSD: Fisher's Least Significant Difference test.

Bonferroni

For further details, see ANOVA Multiple Comparisons.

Include Brown-Forsythe Test for equality of Means

Use to test the equality of means when distribution violates the assumption of equal variances.

The Brown-Forsythe test cannot be computed if all groups have zero variance. To take part into Brown–

Forsythe test, a group must have at least two elements. In the situation that some groups have zero

standard deviations, the statistic can be computed but the approximation may not work.

For further details, see Brown–Forsythe Test for equality of means.

Include Welch’s Test for equality of Means

Use to test the equality of means when distribution violates the assumption of equal variances.

To take part into Welch’s test, a group must have non zero variance. Moreover, sample sizes of a group

have to be greater than or equal to 2.

For further details, see Welch’s Test for equality of means.

Remark: ISSTATS does not cancel a test if any of the groups does not fulfill the conditions. It simply

rejects the group. To take part into a ANOVA test, a group must have at least one element. To take part

into a Welch’s Test, a group must have at least two elements; moreover, the group must have a non-zero

variance. Thus, ISSTATS may use 4 of the groups to perform ANOVA Test but only 2 of the groups to

perform a Welch’s Test. It depends on the number of elements of each group. You should read the

Descriptive Statistics information to check the Rejected Groups and also should read the Total Groups

info of each test to check the number of groups being used in that test.

Outputs

Outputs include:

Descriptive statistic for every level of the factor’s variable.

Total mean.

Degrees Of Freedom: DFTotal, DFInter and DFIntra

The Sum Of The Squares: SSTotal, SSInter and SSIntra

The Mean Square: MSTotal, MSInter and MSIntra

The F ratio

The p-value

R-squared

R-squared adjusted

Inter is also referred as Between Groups or Between Treatments. Intra is also referred as Within Groups

or Error Term.


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R-squared represents the percentage of variation in a response variable that is explained by its relationship

with one predictor variable.

R-squared adjusted is a version of r-squared that has been adjusted for the number of predictors in the

model. R-squared tends to overestimate the strength of the association, especially when there are more

than one independent variables.


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10. – Homoscedasticity Tests

These tests are used to test if k samples are from populations with equal variances. The response variable

has to be numeric. The factor level column (grouping variable) may be numeric or text.

Dialog box items


Levene's Test

Brown–Forsythe Test for equality of variances

Bartlett's Test

For further details, see Homoscedasticity Tests.

Remark: ISSTATS does not cancel a test if any of the groups does not fulfill the conditions. It simply

rejects the group. To take part into a Levene or Brown–Forsythe test, a group must have at least one

element. To take part into a Bartlett's Test, a group must have at least two elements; moreover, the group

must have a non-zero variance. Thus, ISSTATS may use 4 of the groups to perform Levene's Test but

only 2 of the groups to perform a Bartlett's Test. It depends on the number of elements of each group.

You should read the Descriptive Statistics information to check the Rejected Groups and also should read

the Total Groups info of each test to check the number of groups being used in that test.


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11. – Methods and Formulas Help

Mean

The arithmetic mean is the sum of a collection of numbers divided by the number of numbers in the

collection.

Sample Variance

The estimator of population variance, also called the unbiased sample variance, is:

∑ ( )

Source: http://en.wikipedia.org/wiki/Variance

Sample Kurtosis

The estimators of population kurtosis is:

( )

( )( )( )

∑ ( )

( )

( )( )

The standard error of the sample kurtosis of a sample of size n from the normal distribution is:

√ ( ) ( )

( )( )( )( )( )

Source: http://en.wikipedia.org/wiki/Kurtosis#Estimators_of_population_kurtosis

Sample Skewness

Skewness of a population sample is estimated by the adjusted Fisher–Pearson standardized moment

coefficient:

( )( ) ∑(

)

where n is the sample size and s is the sample standard deviation.

The standard error of the skewness of a sample of size n from a normal distribution is:

√ ( )

( )( )( )

Source: https://en.wikipedia.org/wiki/Skewness#Sample_skewness

Total Variance

http://en.wikipedia.org/wiki/Variance

http://en.wikipedia.org/wiki/Kurtosis#Estimators_of_population_kurtosis

https://en.wikipedia.org/wiki/Skewness#Sample_skewness


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Variance of the entire population is:

∑ ( )

Source: http://en.wikipedia.org/wiki/Variance

Total Kurtosis

Kurtosis of the entire population is:

∑ ( )

where n is the sample size and σ is the total standard deviation.

Source: http://en.wikipedia.org/wiki/Kurtosis

Total Skewness

Skewness of the entire population is:

∑ ( )

where n is the sample size and σ is the total standard deviation.

Source: https://en.wikipedia.org/wiki/Skewness

Quantiles of a population

ISSTATS uses the same method as R–7, Excel CUARTIL.INC function, SciPy–(1,1), SPSS and Minitab.

Qp, the estimate for the kth

q–quantile, where p = k / q and h = (N–1)*p + 1, is computing by

Qp =

Linear interpolation of the modes for the order statistics for the uniform distribution on [0,1]. When p = 1,

use xN.

Source: http://en.wikipedia.org/wiki/Quantile#Estimating_the_quantiles_of_a_population

MSSD (Mean of the squared successive differences)

It is calculated by taking the sum of the differences between consecutive observations squared, then

taking the mean of that sum and dividing by two.

∑ ( )

( )

The MSSD has the desirable property that one half the MSSD is an unbiased estimator of true variance.

http://en.wikipedia.org/wiki/Variance

http://en.wikipedia.org/wiki/Kurtosis#Estimators_of_population_kurtosis

https://en.wikipedia.org/wiki/Skewness

http://en.wikipedia.org/wiki/Quantile#Estimating_the_quantiles_of_a_population


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Confidence Bounds and One-Sided Tests

Suppose you are testing the null hypothesis H0: ≥ 0 against the one-sided alternative H1: < 0. Rather

than give a two-sided confidence interval for , the more appropriate procedure is to give an upper

confidence bound in this setting. This upper confidence bound has a direct relationship to the one-sided

test, namely:

1. A level test of H0: ≥ 0 against the one-sided alternative H1: < 0 rejects H0 exactly when

the value 0 is above the 1–α upper confidence bound.

2. A level test of H0: ≤ 0 against the one-sided alternative H1: > 0 rejects H0 exactly when

the value 0 is above the 1–α lower confidence bound.

ANOVA Test

∑∑( )

∑ ( )

∑∑( )

DFTotal = N – 1

DFInter = k – 1

DFIntra = N – k

where

F is the result of the test

k is the number of different groups to which the sampled cases belong

∑ is the total sample size

ni is the number of cases in the i-th group

yij is the value of the measured variable for the j-th case from the i-th group


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is the mean of all yij

is the mean of the yij for group i.

The test statistic has a F-distribution with DFInter and DFIntra degrees of freedom. Thus the null

hypothesis is rejected if ( )

ANOVA Multiple Comparisons

Difference of Means

Standard Error of the Difference of Means Estimator

√ (

)

Scheffe’s Method

Confidence Interval for Difference of Means

( ) √ ( ) (

)

Source: http://en.wikipedia.org/wiki/Scheff%C3%A9%27s_method

Tukey's range test HSD


( ) ( ) √

(

)

Where q is the studentized range distribution.

Source: https://en.wikipedia.org/wiki/Tukey%27s_range_test

Fisher's Method LSD

If overall ANOVA test is not significant, you must not consider any results of Fisher test, significant or

not.


( ) ( ⁄ )

√ (

)

Where t is the student distribution.

http://en.wikipedia.org/wiki/Scheff%C3%A9%27s_method

https://en.wikipedia.org/wiki/Tukey%27s_range_test


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Bonferroni's Method

The family-wise significance level (FWER) is α = 1 - Confidence Level. Thus any comparison flagged by

ISSTATS as significant is based on a Bonferroni Correction:

( )

( )

Where k is the number of groups.


( ) (

⁄ )

√ (

)


Sidak's Method

The family-wise significance level (FWER) is α = 1 - Confidence Level. So any comparison flagged by

ISSTATS as significant is based on a Sidak Correction:

( )

( )

( ) ( )

Where k is the number of groups.


( ) (

⁄ )

√ (

)


Welch’s Test for equality of means

The test statistic, F*, is defined as follows:

∑ ( )

( )

∑

where


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F* is the result of the test



∑ ∑

∑

(

)

The test statistic has approximately a F-distribution with k-1 and

∑

degrees of freedom. Thus

the null hypothesis is rejected if ( )

Brown–Forsythe Test for equality of means

The test statistic, F*, is defined as follows:

∑ ( )

∑ (

)

where

F* is the result of the test


ni is the number of cases in the i-th group (sample size of group i)


∑

is the overall mean.

The test statistic has approximately a F-distribution with k-1 and df degrees of freedom. Where df is

obtained with the Satterthwaite (1941) approximation as

∑

with

(

)

∑ (

)

Thus the null hypothesis is rejected if ( )

Homoscedasticity Tests

Levene's Test

The test statistic, F, is defined as follows:


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∑ ( )

∑ ∑ ( )

where





Yij is the value of the measured variable for the j-th case from the i-th group

| | where is a mean of i-th group

is the mean of all Zij

is the mean of the Zij for group i.

The test statistic has a F-distribution with k-1 and N-k degrees of freedom. Thus the null hypothesis is

rejected if ( )

Source: http://en.wikipedia.org/wiki/Levene%27s_test

Brown–Forsythe Test for equality of variances

The test statistic, F, is defined as follows:

∑ ( )

∑ ∑ ( )

where





Yij is the value of the measured variable for the j-th case from the i-th group

| | where is a median of i-th group

is the mean of all Zij

is the mean of the Zij for group i.

The test statistic has a F-distribution with k-1 and N-k degrees of freedom. Thus the null hypothesis is

rejected if ( )

Source: http://en.wikipedia.org/wiki/Levene%27s_test

Bartlett's Test

Bartlett's test is used to test the null hypothesis, H0 that all k population variances are equal against the

alternative that at least two are different.

If there are k samples with size ni and sample variances S2

i then Bartlett's test statistic is

http://en.wikipedia.org/wiki/Levene%27s_test

http://en.wikipedia.org/wiki/Levene%27s_test


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( ) (

) ∑ ( ) ( )

( ) (∑ (

)

)

where


∑ ( )

is the pooled estimate for the variance

The test statistic has approximately a chi-squared distribution with k-1 degrees of freedom. Thus the null

hypothesis is rejected if ( ).

Source: http://en.wikipedia.org/wiki/Bartlett%27s_test

http://en.wikipedia.org/wiki/Bartlett%27s_test

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