Quantitative statistics
Most of the statistical functions can be also applied directly to the mdadata objects. Besides that, a few of additional methods have been implemented, including for example, summary(), which is an analogue of the same function in R. The default functions include: mean(), std(), min(), max(), var(), cov() and corr().
The functions calculate statistics for each column. The result of calculations is also an object of dataset class.
load people
% take only first six columns
data = people(:, [1:2 4:6]);
% calculate simple statistics and show result
show(mean(data))
show(std(data))
Variables
Height Weight Shoesize Age Income
------- ------- --------- ----- ---------
Mean 173 64.5 39.9 34.4 2.74e+04
Variables
Height Weight Shoesize Age Income
------- ------- --------- ----- ---------
Stdev 10.1 15.2 3.9 9.52 8.93e+03
The results of calculation can be concatenated into a single dataset:
show([mean(data); std(data); var(data); min(data); max(data)])
Variables
Height Weight Shoesize Age Income
------- ------- --------- ----- ---------
Mean 173 64.5 39.9 34.4 2.74e+04
Stdev 10.1 15.2 3.9 9.52 8.93e+03
Variance 101 231 15.2 90.6 7.97e+07
Min 157 46 34 18 1.1e+04
Max 198 92 48 55 4.5e+04
Calculation of covariance and correlation always results in a matrix.
show(cov(data))
Covariance:
Variables
Height Weight Shoesize Age Income
-------- --------- --------- --------- ---------
Height 101 147 37.7 23.1 2.7e+04
Weight 147 231 57.4 36.8 4.55e+04
Shoesize 37.7 57.4 15.2 12 1.23e+04
Age 23.1 36.8 12 90.6 7.52e+04
Income 2.7e+04 4.55e+04 1.23e+04 7.52e+04 7.97e+07
show(corr(data(:, [1 3])))
Correlation:
Variables
Height Shoesize
------- ---------
Height 1 0.961
Shoesize 0.961 1
The additional methods include calculation of percentiles:
show(percentile(data, 5))
Percentiles:
Variables
Height Weight Shoesize Age Income
------- ------- --------- ---- ---------
5% 158 46.5 34.5 19 1.12e+04
standard errors:
show(se(data))
Variables
Height Weight Shoesize Age Income
------- ------- --------- ----- ---------
Std. error 1.78 2.69 0.689 1.68 1.58e+03
confidence intervals:
show(ci(data))
Confidence intervals (95%):
Variables
Height Weight Shoesize Age Income
------- ------- --------- ----- ---------
Lower 169 59 38.5 31 2.42e+04
Upper 177 69.9 41.3 37.9 3.07e+04
show(ci(data, 0.01))
Confidence intervals (99%):
Variables
Height Weight Shoesize Age Income
------- ------- --------- ----- ---------
Lower 168 57.1 38 29.8 2.31e+04
Upper 178 71.8 41.8 39.1 3.18e+04
one-sample t-test:
show(ttest(data))
P-values for t-test (mu = 0):
Variables
Height Weight Shoesize Age Income
------- ------- --------- ---- -------
Left tail 1 1 1 1 1
Both tails 0 0 0 0 0
Right tail 0 0 0 0 0
show(ttest(data(:, 'Height'), 170))
P-values for t-test (mu = 170):
Height
-------
Left tail 0.956
Both tails 0.0887
Right tail 0.0443
and summary statistics for a dataset:
show(summary(data))
Summary statistics:
Variables
Height Weight Shoesize Age Income
------- ------- --------- ----- ---------
Min 157 46 34 18 1.1e+04
Q1 164 50 36 26.5 1.95e+04
Median 174 64.5 40 34 3e+04
Mean 173 64.5 39.9 34.4 2.74e+04
Q3 180 80.5 43 41 3.4e+04
Max 198 92 48 55 4.5e+04