# 3.2.3 Sample Theory
**Sampling Distributions**
Sampling distributions describe the distribution for a specific statistic. That is, sampling distributions are a subset (sample) of the full data set, with which you can play, explore, and simulate statistics like averages, variance, and skew.
***Sampling distributions help us create conclusions using the statistics about a population. A sample population is the statistical representation of the actual population.***\
Before we dive into what and how to do sampling, let's understand a few key terms, that would help us calculate samples.
**I. Confidence Interval**\
Confidence intervals are ‘intervals’ that we can create to guess with a certain degree of accuracy where a parameter of interest lies.
Confidence Interval Width: The distance between the upper and lower bounds of the confidence interval.
**II. Method & Formula for Sampling**
In the real world, working with an entire population's data can be slow and heavy, but we can use sampling distributions to estimate what a population parameter most probably is. The general process is as follows:
* Get your data
* Figure out what you want to estimate(ex. Binary Classification/Regression)
* Bootstrap that parameter
* Create Confidence intervals.
It depends on the type of problem you want to address based on the distribution of the target on which the model is being built to predict.
* **Binary:**
For the other distributions, we use the Rule of thumb for minimum sample size
* **Multivariate:** n >= 100 + 50k
* **Regression:** n >= 104 + k\
\&#xNAN;*Note: Where k is the number of the independent variable*
**III. Implementation - Python function**\
We created our own function:
**Assumptions:**
* Error% = **1%**
* Confidence Interval = **95%**
* z = **1.95**
**IV. Sampling Theorem Script:**
We have used the [**H2O** ](https://www.h2o.ai/)library to operate and test the sampling to help us with the Interpretability and Evaluations of the Interpretable Models.
```python
class Sampling:
def __init__(self):
self.__error__ = 0.01
self.__zscore__ = 1.96
self.__binary__ = 2
self.__multivariate__ = 9
self.__addmultivariate__ = 200
self.__factormultivariate__ = 100
self.__addcontinous__ = 500
def sampling(self, df, y):
if len(df[y].unique()) == self.__binary__:
print('binary')
# values = have the binary category list from the target
values = list(df[y].unique().as_data_frame()['C1'])
# p0 = number of samples for category 1, p1 = number of samples for category 2
p0, p1 = len(df[df[y] == values[0]]), len(df[df[y] == values[1]])
# prob0 = probablity of category 1. prob1 = probability of category 2
prob0, prob1 = p0/(p0+p1), p1/(p0+p1)
# n_samples = number of samples to be computed
n_samples = prob0*prob1*(self.__zscore__/self.__error__)**2
if self.__binary__ < len(df[y].unique()) < self.__multivariate__:
print('multivariate')
# features = number of features the given dataset has
features = len(df.columns)
print('features', features)
# n_samples = number of samples to be computed
n_samples = self.__addmultivariate__ + (self.__factormultivariate__ * features)
if self.__multivariate__ < len(df[y].unique()):
print('continuous')
# features = number of features the given dataset has
features = len(df.columns)
print('features', features)
# n_samples = number of samples to be computed
n_samples = self.__addcontinous__ + features # first try = 104, second = 500
print('df', df.shape)
print('n_samples', n_samples)
# if the total population of the data is less than the sample calculated,
# we take the whole population as a sample
if n_samples/df.shape[0] < 1:
print('returning sampled_df')
sample_df, _, _ = df.split_frame(ratios=[n_samples/df.shape[0], 0.8 - n_samples/df.shape[0]])
return sample_df
else:
print('returning df')
return df
```