Python Z Test

Updated May 6, 2023

Introduction to Python Z Test

The following article provides an outline for Python Z Test. In the vast field of statistics, the process of hypothesis testing plays a very major role. Hypothesis testing helps to decide on a statistics assumption. When a hypothesis is formed, hypothesis testing is used to confirm how close the assumption is to reality. This is the key characteristic of hypothesis-based testing. The Z test is a method or a type of testing used in hypothesis testing.

The Z test involves determining the P-value and then verifying how close the determined P-value is to the significant value. Usually, the significance value is around 0.05. The P value stands for the representation of the probability value identified. The probability value mentions how possible the determined assumption is a null hypothesis or an alternative hypothesis. So based on the P value determined, the reality of the hypothesis assumption is validated. This is the critical process of the Z test.

Z Test Syntax

Given below is the syntax mentioned:

statsmodels.stats.weightstats.ztest(x1, x2=None, value=0, alternative='two-sided', usevar='pooled', ddof=1.0)

• The Z test model can take two independent samples to process and determine the p-value. The x1 will be the first independent sample used in the above syntax. Therefore, the x1 must be keyed as an array in one dimensional or two-dimensional format.
• The x2 will be the second independent sample used in the above syntax. The x2 must be keyed as an array in a one-dimensional or two-dimensional format.
• The value will hold the mean of X1, which forms the alternative hypothesis. When more than one independent variable is used, this value will be the mean of the difference between X1 and X2.
• The user holds the value pooled, meaning the samples’ standard deviation is the same.
• H1 refers to the alternative hypothesis.
• ddof is used for mean estimate calculation.

When to Perform Z Test in Python?

• First, the sample size determines when the Z test needs to be performed. This means whenever the sample size is more significant than 30 records, the Z test is preferred. So the sample size plays a key in Z test determination. When the number of sample records involved is lesser than 30, then the t-test is preferred over the Z test.
• Every data point involved needs to be independent of each other. This means both the data points involved in the Z test need to be self-governing, then the data used must be suitable for the Z test. This is another key functionality for considering the Z test in Python.
• The normal distribution of the data is expected. Especially for smaller sample sizes, this needs to be strictly followed. The normal distribution of the sample sizes is a critical factor for this Z test selection. When the sample size exceeds 30 records, it can be considered without the normal distribution.
• The method of sampling is another crucial factor used. This determines how precise the hypothesis is calculated. Here we need to ensure the data selected in the sample is well distributed and chosen randomly. So from a large set of population, it is necessary to ensure the data is well shuffled and selected from this large set so that all aspects of the population can be covered in the sample set.

Examples of Python Z Test

Given below are the examples of the Python Z Test:

Data Used ( BP.csv ):

patient_name	patient_ sex	patient_agegrp	patient_bp_before	patient_bp_after
1	Male	30-45	142	153
2	Male	30-45	163	170
3	Male	30-45	143	168
4	Male	30-45	153	142
5	Male	30-45	146	141
6	Male	30-45	150	147
7	Male	30-45	158	133
8	Male	30-45	153	141
9	Male	30-45	153	131
10	Male	30-45	158	125
11	Male	30-45	169	164
12	Male	30-45	173	159
13	Male	30-45	165	135
14	Male	30-45	145	159
15	Male	30-45	133	153
16	Male	30-45	152	126
17	Male	30-45	141	162
18	Male	30-45	176	134
19	Male	30-45	143	136
20	Male	30-45	162	150
21	Male	46-59	149	168
22	Male	46-59	156	155
23	Male	46-59	151	136
24	Male	46-59	159	132
25	Male	46-59	164	160
26	Male	46-59	154	160
27	Male	46-59	152	136
28	Male	46-59	142	183
29	Male	46-59	162	152
30	Male	46-59	155	162
31	Male	46-59	175	151
32	Male	46-59	184	139
33	Male	46-59	167	175
34	Male	46-59	148	184

Example #1

Code:

import pandas as pd
from statsmodels.stats import weightstats as stests
dataframe = pd.read_csv(r"C:\Users\ANAND\Desktop\BP.csv")
dataframe[['patient_bp_before','patient_bp_after']].describe()
ztest ,propability_value = stests.ztest(dataframe['patient_bp_before'], x2=None, value=146)
print(float(propability_value))
if propability_value<0.05:
    print("Null hyphothesis rejected , Alternative hyphothesis accepted")
else:
    print("Null hyphothesis accepted , Alternative hyphothesis rejected")

Output:

Explanation:

• In this first example, the following assumptions are made.
• Alternative Hypothesis: All patients’ average BP ranges around 146 in before.
• Null Hypothesis: All patients’ average BP does not provide a range in the given mean value.
• When the probability value is determined, and the hypothesis is evaluated, the probability values lie somewhere around -1.91, less than the 0.05 significance level; hence, this is considered an Alternative hypothesis. Therefore the assumption is successful.

Example #2

Code:

# The Mean value is alone manipulated as 78
ztest ,propability_value = stests.ztest(dataframe['patient_bp_before'], x2=None, value=146)

Output:

Explanation:

• In this second example, the following assumptions are made.
• Alternative Hypothesis: All patients’ average BP ranges around 78 in before.
  Null Hypothesis: All patients’ average BP does not provide a range in the given mean value.
• When the probability value is determined, and the hypothesis is evaluated, the probability values lie somewhere around +0.78, more significant than the 0.05 significance level; hence, this is considered a Null hypothesis. Thus the assumption has failed.

Conclusion

Among the different methods for hypothesis testing, the Z test is one of the most stable methods used. This method offers much flexibility in determining the p-value involved and identifying the type of hypothesis happening. So, the presence of the Null hypothesis or alternative hypothesis can be flexibly calculated.

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