# 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.

## Contents

## Sampling

Create a table with data sampled from another table.

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. |

### Data

**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.

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. |

### Data

**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

Choose **Data - Statistics - Analysis of Variance (ANOVA)**

ANOVA is the acronym for **AN**alysis **O**f **VA**riance. This tool produces the analysis of variance of a given data set

For more information on ANOVA, refer to the corresponding Wikipedia article. |

### Data

**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.

### Type

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 |

Between Groups | 1876.5683284457 | 2 | 938.2841642229 | 4.3604117704 | 0.0224614952 |

Within Groups | 6025.1090909091 | 28 | 215.1824675325 | ||

Total | 7901.6774193548 | 30 |

## Correlation

Calculates the correlation of two sets of numeric data.

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. |

### Data

**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.

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. |

### Data

**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

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. |

### Data

**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

Choose **Data - Statistics - Moving Average**

For more information on the moving average, refer to the corresponding Wikipedia article. |

### Data

**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 |

## t-test

Calculates the t-Test of two data samples.

Choose **Data - Statistics - t-test**

A **t-test** is any statistical hypothesis test that follows a Student's t distribution.

For more information on t-tests, refer to the corresponding Wikipedia article. |

### Data

**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 t-Test:

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

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.

Choose **Data - Statistics - F-test**

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

For more information on F-tests, refer to the corresponding Wikipedia article. |

### Data

**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.

Choose **Data - Statistics - Z-test**

For more information on Z-tests, refer to the corresponding Wikipedia article. |

### Data

**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.

Choose **Data - Statistics - Chi-square Test**

For more information on chi-square tests, refer to the corresponding Wikipedia article. |

### Data

**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 |