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.
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.
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.
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.
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.
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
ANOVA is the acronym for ANalysis Of VAriance. This tool produces the analysis of variance of a given data set
For more information on ANOVA, refer to the corresponding Wikipedia article.
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.
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.
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.
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.
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.
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
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.
Parameters
Smoothing Factor: A parameter between 0 and 1 that represents the damping factor Alpha in the smoothing equation.
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
For more information on the moving average, refer to the corresponding Wikipedia article.
Parameters
Interval: The number of samples used in the moving average calculation.
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.
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.
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.
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.
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.
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.
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.
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.
For more information on chi-square tests, refer to the corresponding Wikipedia article.
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 |