# Data Statistics in Calc

Use the data statistics in Calc to perform complex data analysis

To work on a complex statistical or engineering analysis, you can save steps and time by using Calc Data Statistics. You provide the data and parameters for each analysis, and the set of tools uses the appropriate statistical or engineering functions to calculate and display the results in an output table.

## Sampling

Create a table with data sampled from another table.

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Choose Data - Statistics - Sampling

Sampling allows you to pick data from a source table to fill a target table. The sampling can be random or in a periodic basis. Sampling is done row-wise. That means, the sampled data will pick the whole line of the source table and copy into a line of the target table.

### بيانات

Input Range: The reference of the range of the data to analyze.

Results to: The reference of the top left cell of the range where the results will be displayed.

### Sampling Method

Random: Picks exactly Sample Size lines of the source table in a random way.

Sample size: Number of lines sampled from the source table.

Periodic: Picks lines in a pace defined by Period.

Period: the number of lines to skip periodically when sampling.

### Example

The following data will be used as example of source data table for sampling:

 A B C 1 11 21 31 2 12 22 32 3 13 23 33 4 14 24 34 5 15 25 35 6 16 26 36 7 17 27 37 8 18 28 38 9 19 29 39

Sampling with a period of 2 will result in the following table:

 12 22 32 14 24 34 16 26 36 18 28 38

## Descriptive Statistics

Fill a table in the spreadsheet with the main statistical properties of the data set.

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Choose Data - Statistics - Descriptive Statistics

The Descriptive Statistics analysis tool generates a report of univariate statistics for data in the input range, providing information about the central tendency and variability of your data. For more information on descriptive statistics, refer to the corresponding Wikipedia article.

### بيانات

Input Range: The reference of the range of the data to analyze.

Results to: The reference of the top left cell of the range where the results will be displayed.

### Grouped By

Select whether the input data has columns or rows layout.

### Example

The following data will be used as example

 A B C 1 Maths Physics Biology 2 47 67 33 3 36 68 42 4 40 65 44 5 39 64 60 6 38 43 7 47 84 62 8 29 80 51 9 27 49 40 10 57 49 12 11 56 33 60 12 57 13 26

The following table displays the results of the descriptive statistics of the sample data above.

 Column 1 Column 2 Column 3 Mean 41.9090909091 59.7 44.7 Standard Error 3.5610380138 5.3583786934 4.7680650629 Mode 47 49 60 Median 40 64.5 43.5 Variance 139.4909090909 287.1222222222 227.3444444444 Standard Deviation 11.8106269559 16.944681237 15.0779456308 Kurtosis -1.4621677981 -0.9415988746 1.418052719 Skewness 0.0152409533 -0.2226426904 -0.9766803373 Range 31 51 50 Minimum 26 33 12 Maximum 57 84 62 Sum 461 597 447 Count 11 10 10

## Analysis of Variance (ANOVA)

Produces the analysis of variance (ANOVA) of a given data set

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Choose Data - Statistics - Analysis of Variance (ANOVA)

ANOVA is the acronym for ANalysis Of VAriance. This tool produces the analysis of variance of a given data set ### بيانات

Input Range: The reference of the range of the data to analyze.

Results to: The reference of the top left cell of the range where the results will be displayed.

### Grouped By

Select whether the input data has columns or rows layout.

### نوع

Select if the analysis is for a single factor or for two factor ANOVA.

### Parameters

Alpha: the level of significance of the test.

Rows per sample: Define how many rows a sample has.

### Example

The following data will be used as example

 A B C 1 Maths Physics Biology 2 47 67 33 3 36 68 42 4 40 65 44 5 39 64 60 6 38 43 7 47 84 62 8 29 80 51 9 27 49 40 10 57 49 12 11 56 33 60 12 57 13 26

The following table displays the results of the analysis of variance (ANOVA) of the sample data above.

 ANOVA - Single Factor Alpha 0.05 Groups Count Sum Mean Variance Column 1 11 461 41.9090909091 139.4909090909 Column 2 10 597 59.7 287.1222222222 Column 3 10 447 44.7 227.3444444444 Source of Variation SS df MS F P-value F-critical Between Groups 1876.5683284457 2 938.2841642229 4.3604117704 0.0224614952 3.340385558 Within Groups 6025.1090909091 28 215.1824675325 Total 7901.6774193548 30

## Correlation

Calculates the correlation of two sets of numeric data.

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Choose Data - Statistics - Correlation

The correlation coefficient (a value between -1 and +1) means how strongly two variables are related to each other. You can use the CORREL function or the Data Statistics to find the correlation coefficient between two variables.

A correlation coefficient of +1 indicates a perfect positive correlation.

A correlation coefficient of -1 indicates a perfect negative correlation For more information on statistical correlation, refer to the corresponding Wikipedia article.

### بيانات

Input Range: The reference of the range of the data to analyze.

Results to: The reference of the top left cell of the range where the results will be displayed.

### Grouped By

Select whether the input data has columns or rows layout.

### Example

The following data will be used as example

 A B C 1 Maths Physics Biology 2 47 67 33 3 36 68 42 4 40 65 44 5 39 64 60 6 38 43 7 47 84 62 8 29 80 51 9 27 49 40 10 57 49 12 11 56 33 60 12 57 13 26

The following table displays the results of the correlation of the sample data above.

 Correlations Column 1 Column 2 Column 3 Column 1 1 Column 2 -0.4029254917 1 Column 3 -0.2107642836 0.2309714048 1

## Covariance

Calculates the covariance of two sets of numeric data.

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Choose Data - Statistics - Covariance

The covariance is a measure of how much two random variables change together. For more information on statistical covariance, refer to the corresponding Wikipedia article.

### بيانات

Input Range: The reference of the range of the data to analyze.

Results to: The reference of the top left cell of the range where the results will be displayed.

### Grouped By

Select whether the input data has columns or rows layout.

### Example

The following data will be used as example

 A B C 1 Maths Physics Biology 2 47 67 33 3 36 68 42 4 40 65 44 5 39 64 60 6 38 43 7 47 84 62 8 29 80 51 9 27 49 40 10 57 49 12 11 56 33 60 12 57 13 26

The following table displays the results of the covariance of the sample data above.

 Covariances Column 1 Column 2 Column 3 Column 1 126.8099173554 Column 2 -61.4444444444 258.41 Column 3 -32 53.11 204.61

## Exponential Smoothing

Results in a smoothed data series

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Choose Data - Statistics - Exponential Smoothing

Exponential smoothing is a filtering technique that when applied to a data set, produces smoothed results. It is employed in many domains such as stock market, economics and in sampled measurements. For more information on exponential smoothing, refer to the corresponding Wikipedia article.

### بيانات

Input Range: The reference of the range of the data to analyze.

Results to: The reference of the top left cell of the range where the results will be displayed.

### Grouped By

Select whether the input data has columns or rows layout.

### Parameters

Smoothing Factor: A parameter between 0 and 1 that represents the damping factor Alpha in the smoothing equation.

### Example

The following table has two time series, one representing an impulse function at time t=0 and the other an impulse function at time t=2.

 A B 1 1 0 2 0 0 3 0 1 4 0 0 5 0 0 6 0 0 7 0 0 8 0 0 9 0 0 10 0 0 11 0 0 12 0 0 13 0 0

The resulting smoothing is below with smoothing factor as 0.5:

 Alpha 0.5 Column 1 Column 2 1 0 1 0 0.5 0 0.25 0.5 0.125 0.25 0.0625 0.125 0.03125 0.0625 0.015625 0.03125 0.0078125 0.015625 0.00390625 0.0078125 0.001953125 0.00390625 0.0009765625 0.001953125 0.0004882813 0.0009765625 0.0002441406 0.0004882813

## Moving Average

Calculates the moving average of a time series

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Choose Data - Statistics - Moving Average For more information on the moving average, refer to the corresponding Wikipedia article.

### بيانات

Input Range: The reference of the range of the data to analyze.

Results to: The reference of the top left cell of the range where the results will be displayed.

### Grouped By

Select whether the input data has columns or rows layout.

### Parameters

Interval: The number of samples used in the moving average calculation.

### Example

The following table has two time series, one representing an impulse function at time t=0 and the other an impulse function at time t=2.

 A B 1 1 0 2 0 0 3 0 1 4 0 0 5 0 0 6 0 0 7 0 0 8 0 0 9 0 0 10 0 0 11 0 0 12 0 0 13 0 0

### Results of the moving average:

 Column 1 Column 2 #N/A #N/A 0.3333333333 0.3333333333 0 0.3333333333 0 0.3333333333 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 #N/A #N/A

## Paired t-test

Calculates the paired t-Test of two data samples.

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Choose Data - Statistics - Paired t-test

A paired t-test is any statistical hypothesis test that follows a Student's t distribution. For more information on paired t-tests, refer to the corresponding Wikipedia article.

### بيانات

Variable 1 range: The reference of the range of the first data series to analyze.

Variable 2 range: The reference of the range of the second data series to analyze.

Results to: The reference of the top left cell of the range where the test will be displayed.

### Grouped By

Select whether the input data has columns or rows layout.

### Example

The following table has two data sets.

 A B 1 28 19 2 26 13 3 31 12 4 23 5 5 20 34 6 27 31 7 28 31 8 14 12 9 4 24 10 0 23 11 2 19 12 8 10 13 9 33

### Results for paired t-test:

The following table shows the paired t-test for the data series above:

 paired t-test Alpha 0.05 Hypothesized Mean Difference 0 Variable 1 Variable 2 Mean 16.9230769231 20.4615384615 Variance 125.0769230769 94.4358974359 Observations 13 13 Pearson Correlation -0.0617539772 Observed Mean Difference -3.5384615385 Variance of the Differences 232.9358974359 df 12 t Stat -0.8359262137 P (T<=t) one-tail 0.2097651442 t Critical one-tail 1.7822875556 P (T<=t) two-tail 0.4195302884 t Critical two-tail 2.1788128297

## F-test

Calculates the F-Test of two data samples.

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Choose Data - Statistics - F-test

A F-test is any statistical test based on the F-distribution under the null hypothesis. ### بيانات

Variable 1 range: The reference of the range of the first data series to analyze.

Variable 2 range: The reference of the range of the second data series to analyze.

Results to: The reference of the top left cell of the range where the test will be displayed.

### Grouped By

Select whether the input data has columns or rows layout.

### Example

The following table has two data sets.

 A B 1 28 19 2 26 13 3 31 12 4 23 5 5 20 34 6 27 31 7 28 31 8 14 12 9 4 24 10 0 23 11 2 19 12 8 10 13 9 33

### Results for F-Test:

The following table shows the F-Test for the data series above:

 Ftest Alpha 0.05 Variable 1 Variable 2 Mean 16.9230769231 20.4615384615 Variance 125.0769230769 94.4358974359 Observations 13 13 df 12 12 F 1.3244637524 P (F<=f) right-tail 0.3170614146 F Critical right-tail 2.6866371125 P (F<=f) left-tail 0.6829385854 F Critical left-tail 0.3722125312 P two-tail 0.6341228293 F Critical two-tail 0.3051313549 3.277277094

## Z-test

Calculates the z-Test of two data samples.

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Choose Data - Statistics - Z-test ### بيانات

Variable 1 range: The reference of the range of the first data series to analyze.

Variable 2 range: The reference of the range of the second data series to analyze.

Results to: The reference of the top left cell of the range where the test will be displayed.

### Grouped By

Select whether the input data has columns or rows layout.

### Example

The following table has two data sets.

 A B 1 28 19 2 26 13 3 31 12 4 23 5 5 20 34 6 27 31 7 28 31 8 14 12 9 4 24 10 0 23 11 2 19 12 8 10 13 9 33

### Results for z-Test:

The following table shows the z-Test for the data series above:

 z-test Alpha 0.05 Hypothesized Mean Difference 0 Variable 1 Variable 2 Known Variance 0 0 Mean 16.9230769231 20.4615384615 Observations 13 13 Observed Mean Difference -3.5384615385 z #DIV/0! P (Z<=z) one-tail #DIV/0! z Critical one-tail 1.644853627 P (Z<=z) two-tail #DIV/0! z Critical two-tail 1.9599639845

## Chi-square test

Calculates the Chi-square test of a data sample.

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Choose Data - Statistics - Chi-square Test For more information on chi-square tests, refer to the corresponding Wikipedia article.

### بيانات

Input range: The reference of the range of the data series to analyze.

Results to: The reference of the top left cell of the range where the test will be displayed.

### Grouped By

Select whether the input data has columns or rows layout.

### Example

The following table has two data sets.

 A B 1 28 19 2 26 13 3 31 12 4 23 5 5 20 34 6 27 31 7 28 31 8 14 12 9 4 24 10 0 23 11 2 19 12 8 10 13 9 33

### Results for Chi-square Test:

 Test of Independence (Chi-Square) Alpha 0.05 df 12 P-value 2.32567054678584E-014 Test Statistic 91.6870055842 Critical Value 21.0260698175