Using sci-analysis¶
From the python interpreter or in the first cell of a Jupyter notebook, type:
import numpy as np
import scipy.stats as st
from sci_analysis import analyze
This will tell python to import the sci-analysis function analyze()
.
Note
Alternatively, the function analyse()
can be imported instead, as it is an alias for analyze()
. For the case of this documentation, analyze()
will be used for consistency.
If you are using sci-analysis in a Jupyter notebook, you need to use the following code instead to enable inline plots:
%matplotlib inline
import numpy as np
import scipy.stats as st
from sci_analysis import analyze
Now, sci-analysis should be ready to use. Try the following code:
np.random.seed(987654321)
data = st.norm.rvs(size=1000)
analyze(xdata=data)
Statistics
----------
n = 1000
Mean = 0.0551
Std Dev = 1.0282
Std Error = 0.0325
Skewness = -0.1439
Kurtosis = -0.0931
Maximum = 3.4087
75% = 0.7763
50% = 0.0897
25% = -0.6324
Minimum = -3.1586
IQR = 1.4087
Range = 6.5673
Shapiro-Wilk test for normality
-------------------------------
alpha = 0.0500
W value = 0.9979
p value = 0.2591
H0: Data is normally distributed
A histogram, box plot, summary stats, and test for normality of the data should appear above.
Note
numpy and scipy.stats were only imported for the purpose of the above example. sci-analysis uses numpy and scipy internally, so it isn’t necessary to import them unless you want to explicitly use them.
A histogram and statistics for categorical data can be performed with the following command:
pets = ['dog', 'cat', 'rat', 'cat', 'rabbit', 'dog', 'hamster', 'cat', 'rabbit', 'dog', 'dog']
analyze(pets)
Overall Statistics
------------------
Total = 11
Number of Groups = 5
Statistics
----------
Rank Frequency Percent Category
--------------------------------------------------------
1 4 36.3636 dog
2 3 27.2727 cat
3 2 18.1818 rabbit
4 1 9.0909 hamster
4 1 9.0909 rat
Let’s examine the analyze()
function in more detail. Here’s the signature for the analyze()
function:
from inspect import signature
print(analyze.__name__, signature(analyze))
print(analyze.__doc__)
analyze (xdata, ydata=None, groups=None, labels=None, alpha=0.05, order=None, dropna=None, **kwargs)
Automatically performs a statistical analysis based on the input arguments.
Parameters
----------
xdata : array-like
The primary set of data.
ydata : array-like
The response or secondary set of data.
groups : array-like
The group names used for location testing or Bivariate analysis.
labels : array-like or None
The sequence of data point labels.
alpha : float
The sensitivity to use for hypothesis tests.
order : array-like
The order that categories in sequence should appear.
dropna : bool
Remove all occurances of numpy NaN.
Returns
-------
xdata, ydata : tuple(array-like, array-like)
The input xdata and ydata.
Notes
-----
xdata : array-like(num), ydata : None --- Distribution
xdata : array-like(str), ydata : None --- Frequencies
xdata : array-like(num), ydata : array-like(num) --- Bivariate
xdata : array-like(num), ydata : array-like(num), groups : array-like --- Group Bivariate
xdata : list(array-like(num)), ydata : None --- Location Test(unstacked)
xdata : list(array-like(num)), ydata : None, groups : array-like --- Location Test(unstacked)
xdata : dict(array-like(num)), ydata : None --- Location Test(unstacked)
xdata : array-like(num), ydata : None, groups : array-like --- Location Test(stacked)
analyze()
will detect the desired type of data analysis to perform based on whether the ydata
argument is supplied, and whether the xdata
argument is a two-dimensional array-like object.
The xdata
and ydata
arguments can accept most python array-like objects, with the exception of strings. For example, xdata
will accept a python list, tuple, numpy array, or a pandas Series object. Internally, iterable objects are converted to a Vector object, which is a pandas Series of type float64
.
Note
A one-dimensional list, tuple, numpy array, or pandas Series object will all be referred to as a vector throughout the documentation.
If only the xdata
argument is passed and it is a one-dimensional vector of numeric values, the analysis performed will be a histogram of the vector with basic statistics and Shapiro-Wilk normality test. This is useful for visualizing the distribution of the vector. If only the xdata
argument is passed and it is a one-dimensional vector of categorical (string) values, the analysis performed will be a histogram of categories with rank, frequencies and percentages displayed.
If xdata
and ydata
are supplied and are both equal length one-dimensional vectors of numeric data, an x/y scatter plot with line fit will be graphed and the correlation between the two vectors will be calculated. If there are non-numeric or missing values in either vector, they will be ignored. Only values that are numeric in each vector, at the same index will be included in the correlation. For example, the two following two vectors will yield:
example1 = [0.2, 0.25, 0.27, np.nan, 0.32, 0.38, 0.39, np.nan, 0.42, 0.43, 0.47, 0.51, 0.52, 0.56, 0.6]
example2 = [0.23, 0.27, 0.29, np.nan, 0.33, 0.35, 0.39, 0.42, np.nan, 0.46, 0.48, 0.49, np.nan, 0.5, 0.58]
analyze(example1, example2)
Linear Regression
-----------------
n = 11
Slope = 0.8467
Intercept = 0.0601
r = 0.9836
r^2 = 0.9674
Std Err = 0.0518
p value = 0.0000
Pearson Correlation Coefficient
-------------------------------
alpha = 0.0500
r value = 0.9836
p value = 0.0000
HA: There is a significant relationship between predictor and response
If xdata
is a sequence or dictionary of vectors, a location test and summary statistics for each vector will be performed. If each vector is normally distributed and they all have equal variance, a one-way ANOVA is performed. If the data is not normally distributed or the vectors do not have equal variance, a non-parametric Kruskal-Wallis test will be performed instead of a one-way ANOVA.
Note
Vectors should be independent from one another — that is to say, there shouldn’t be values in one vector that are derived from or some how related to a value in another vector. These dependencies can lead to weird and often unpredictable results.
A proper use case for a location test would be if you had a table with measurement data for multiple groups, such as test scores per class, average height per country or measurements per trial run, where the classes, countries, and trials are the groups. In this case, each group should be represented by it’s own vector, which are then all wrapped in a dictionary or sequence.
If xdata
is supplied as a dictionary, the keys are the names of the groups and the values are the array-like objects that represent the vectors. Alternatively, xdata
can be a python sequence of the vectors and the groups
argument a list of strings of the group names. The order of the group names should match the order of the vectors passed to xdata
.
Note
Passing the data for each group into xdata
as a sequence or dictionary is often referred to as “unstacked” data. With unstacked data, the values for each group are in their own vector. Alternatively, if values are in one vector and group names in another vector of equal length, this format is referred to as “stacked” data. The analyze()
function can handle either stacked or unstacked data depending on which is most convenient.
For example:
np.random.seed(987654321)
group_a = st.norm.rvs(size=50)
group_b = st.norm.rvs(size=25)
group_c = st.norm.rvs(size=30)
group_d = st.norm.rvs(size=40)
analyze({"Group A": group_a, "Group B": group_b, "Group C": group_c, "Group D": group_d})
Overall Statistics
------------------
Number of Groups = 4
Total = 145
Grand Mean = 0.0598
Pooled Std Dev = 1.0992
Grand Median = 0.0741
Group Statistics
----------------
n Mean Std Dev Min Median Max Group
--------------------------------------------------------------------------------------------------
50 -0.0891 1.1473 -2.4036 -0.2490 2.2466 Group A
25 0.2403 0.9181 -1.8853 0.3791 1.6715 Group B
30 -0.1282 1.0652 -2.4718 -0.0266 1.7617 Group C
40 0.2159 1.1629 -2.2678 0.1747 3.1400 Group D
Bartlett Test
-------------
alpha = 0.0500
T value = 1.8588
p value = 0.6022
H0: Variances are equal
Oneway ANOVA
------------
alpha = 0.0500
f value = 1.0813
p value = 0.3591
H0: Group means are matched
In the example above, sci-analysis is telling us the four groups are normally distributed (by use of the Bartlett Test, Oneway ANOVA and the near straight line fit on the quantile plot), the groups have equal variance and the groups have matching means. The only significant difference between the four groups is the sample size we specified. Let’s try another example, but this time change the variance of group B:
np.random.seed(987654321)
group_a = st.norm.rvs(0.0, 1, size=50)
group_b = st.norm.rvs(0.0, 3, size=25)
group_c = st.norm.rvs(0.1, 1, size=30)
group_d = st.norm.rvs(0.0, 1, size=40)
analyze({"Group A": group_a, "Group B": group_b, "Group C": group_c, "Group D": group_d})
Overall Statistics
------------------
Number of Groups = 4
Total = 145
Grand Mean = 0.2049
Pooled Std Dev = 1.5350
Grand Median = 0.1241
Group Statistics
----------------
n Mean Std Dev Min Median Max Group
--------------------------------------------------------------------------------------------------
50 -0.0891 1.1473 -2.4036 -0.2490 2.2466 Group A
25 0.7209 2.7543 -5.6558 1.1374 5.0146 Group B
30 -0.0282 1.0652 -2.3718 0.0734 1.8617 Group C
40 0.2159 1.1629 -2.2678 0.1747 3.1400 Group D
Bartlett Test
-------------
alpha = 0.0500
T value = 42.7597
p value = 0.0000
HA: Variances are not equal
Kruskal-Wallis
--------------
alpha = 0.0500
h value = 7.1942
p value = 0.0660
H0: Group means are matched
In the example above, group B has a standard deviation of 2.75 compared to the other groups that are approximately 1. The quantile plot on the right also shows group B has a much steeper slope compared to the other groups, implying a larger variance. Also, the Kruskal-Wallis test was used instead of the Oneway ANOVA because the pre-requisite of equal variance was not met.
In another example, let’s compare groups that have different distributions and different means:
np.random.seed(987654321)
group_a = st.norm.rvs(0.0, 1, size=50)
group_b = st.norm.rvs(0.0, 3, size=25)
group_c = st.weibull_max.rvs(1.2, size=30)
group_d = st.norm.rvs(0.0, 1, size=40)
analyze({"Group A": group_a, "Group B": group_b, "Group C": group_c, "Group D": group_d})
Overall Statistics
------------------
Number of Groups = 4
Total = 145
Grand Mean = -0.0694
Pooled Std Dev = 1.4903
Grand Median = -0.1148
Group Statistics
----------------
n Mean Std Dev Min Median Max Group
--------------------------------------------------------------------------------------------------
50 -0.0891 1.1473 -2.4036 -0.2490 2.2466 Group A
25 0.7209 2.7543 -5.6558 1.1374 5.0146 Group B
30 -1.0340 0.8029 -2.7632 -0.7856 -0.0606 Group C
40 0.1246 1.1081 -1.9334 0.0193 3.1400 Group D
Levene Test
-----------
alpha = 0.0500
W value = 10.1675
p value = 0.0000
HA: Variances are not equal
Kruskal-Wallis
--------------
alpha = 0.0500
h value = 23.8694
p value = 0.0000
HA: Group means are not matched
The above example models group C as a Weibull distribution, while the other groups are normally distributed. You can see the difference in the distributions by the one-sided tail on the group C boxplot, and the curved shape of group C on the quantile plot. Group C also has significantly the lowest mean as indicated by the Tukey-Kramer circles and the Kruskal-Wallis test.