The chi-squared test is one of the most widely used techniques for hypothesis testing purposes. Whether you are analysing categorical data, testing variables, or seeing some good, this chi-square test will help you out.
It is the statistical process that will help in determining the difference between observed and expected data. It is mainly used to decide whether this data is correlated with our categorical variables. A chi-square test is also called a nonparametric test that requires a hypothesis regarding the distribution of our categorical variable. Categorical variables mean categories like plants, animals, or even countries. They should not have a normal distribution because they only have particular variables.
Here,
C = Degrees of freedom
O = Observed Value
E = Expected Value
The degree of freedom represents the number of variables that can vary. They are calculated to ensure that all these chi-square tests are quite statistically valid. Observed data is compared with expected data to determine if a particular hypothesis is true or not.
What are the Fundamentals of Hypothesis Testing?
Hypothesis testing is a technique used in interpreting and drawing inferences about sample data. There are two types of hypotheses:
What are the Types of Chi-Square Tests?
The two main types of Chi-square tests are :
Independence -This chi-square test of independence is one of the derivable statistics used that examines whether two sets are related or not. You can use this test when you have counts of values for two nominal or categorical variables, and also consider it as a non - non-parametric test. Large sample size and independence of criteria are some of the required criteria for conducting this test.
Example - Suppose in a movie theatre, we have a list of some movie genres. Now, let us consider this as the first variable. The second variable is whether or not people who came to watch this movie genre bought snacks at the theatre. So here the null hypothesis is that the genre of the film and whether those people bought snacks are unrelated. So if true, then it means that the movie genre doesn't impact snack sales.
Goodness-of-Fit - This will determine whether a variable is going to come from a distribution. A set of data values is required, and an idea of the distribution of this data. Using this test is good when you have value counts of categorical variables. This will help determine whether data values have a good fit for your idea or if it is a representative sample of the entire population set.
Example - We have bags of all's with 5 different colours in them. The condition is that bags should have an equal number of balls of each colour. The idea to test is that the proportion of each colour of ball in each bag must be exact.
Example - A researcher wants to analyse wants to find relation between gender ( male/female ) and preference for a new product ( like/dislike ). The test will help determine whether preferences are independent of gender or not.
Example - A dice manufacturer is interested in checking if a sided dice is fair or not. They then roll the dice 60 times and expect that each face should appear 10 times. This test will check whether observed frequencies match the expected frequencies or not.
Example - A fast food chain is interested in seeing whether preference for a particular item is consistent or not in different cities. So the test will compare the distribution of preferences in multiple cities to know if they are homogeneous or not.
Example - A study will investigate whether smoking status ( smoker/non-smoker ) is linked to the presence of lung disease ( yes/no ). So the test will evaluate the relationship between smoking and lung disease in the sample.
For this, let's consider like if a gender has anything to do with the preferences of people for the political party.
So the expected value for making a republican is :
=0.743 + 2.05 + 2.33 + 3.33 + 0.384 + 1
=9.837
Before concluding, determining critical statistics is essential for degrees of freedom. In this case, we can see that the degree of freedom is equal to the table's number of columns minus one multiplied by the table's number of rows minus one, or (r-1) (c-1). We have (3-1)(2-1) = 2.
Compare these critical ones in the chi-square table. As we can see, with an alpha level of 0.05 and two degrees of freedom, the critical statistic is 5.991, less than our obtained statistic of 9.83. So we will reject the null hypothesis here because we can see that the critical statistic is higher than the obtained statistic.
Now we have sufficient evidence that we can say that there is a relationship between gender and political party preference.
These categorical variables are a subset of all variables that will be divided into discrete categories. All these variables are qualitative because they will depict the quality pr characteristics of a variable. These variables are divided into two categories.
- Voting Patterns :
Problem - A researcher is interested in knowing whether voting preferences ( party A, party B, or party C ) and gender (male or female ) are related. So chi-square test is applied to the following set of data.
Solutions - To determine if the gender parameter influences voting preferences, a chi-square test for independence is used.
-Consumer Preferences :
Problem - A company will survey customers to determine age group (like under 20,20-40, over 40) and some of the preferred product categories ( food, apparel, or electronics ). The information gathered is mentioned below :
Solutions :
A chi-square test is used that will help in investigate a connection between product preferences and age group.
A chi-square test will help in determining whether the observed results correspond to the expected results. When you analyse the data, that should be from the random sample, while the variable used in the question should be categorical. In this scenario, choosing the chi-square test is right and accurate.
Most commonly, this chi-square test is used for analysing the data. Such a kind of analysis will help researchers in studying the survey response data. This research can easily range from customer to market research to other political science and economics disciplines.
This is a statistical value that will help in assessing the importance of your test results. Here, P simply means probability, so for calculating this p-value, the chi-square is of utmost importance. Different p-values simply mean different interpretations of the p-value.
Probability is the estimation of something that will likely happen. In simple words, it is the possibility of the outcome of a sample. This probability may represent a complicated or even bulky set of data. Statistics often involve collecting, organising, analysing, interpreting, and presenting the data.
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