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## Chi Square

Overview of Chi Square

The Chi-square statistic, also written as χ2, is commonly used for testing relationships between nominal (categorical) variables. The null hypothesis of the Chi-square test is that no relationship exists on the categorical variables in the population; they are independent. An example of research question that could be answered using a Chi-Square analysis would be:

Is there a significant relationship between variable A and variable B?

To make a conclusion about the hypothesis with 95% confidence, the value labeled Asymp. Sig. (which is the p-value of the Chi-Square statistic) should be less than .05 (which is the alpha level associated with a 95% confidence level)

Is the p-value (labeled Asymp. Sig.) less than .05? If so, we can conclude that the variables are not independent of each other and that there is a statistical relationship between the nominal variables.

In the following example, we illustrate how to do a step-by-step Chi-square analysis without any rigorous mathematical and statistical methods.

Example

A study is being done to examine the relationship between perceived competence in using social media outlets and the gender of students from a private tertiary institution. Use 5% level of significance to do a thorough analysis on the proposition that the perceived competence of private tertiary students in the use of social media outlets is not based on their gender.

##### Research Objective

To determine whether there is any statistically significant difference between perceived competence of private tertiary students in the use of social media outlets and their gender status.

##### Research Question

Is there is any statistically significant difference between perceived competence of private tertiary students in the use of social media outlets and their gender status?

##### Proposition

H0: there is no statistically significant difference between perceived competence of private tertiary students in the use of social media outlets and the gender status of students.

H1: there is statistically significant difference between perceived competence of private tertiary students in the use of social media outlets and the gender status of students.

##### Test Statistics

The results of SPSS cross tabulation procedure run on survey data is presented as:

• Chi-square value = 10.313
• N = 15
• DF = 2
• Likelihood (Asymptotic) value = 0.006
• Level of significance = 5% (0.05)
##### Criterion

We reject H0 if the likelihood value is less than the level of significance. Otherwise, we cannot reject the null hypothesis.

##### Decision

Since the p-value (0.006) is less than the level of significance (0.05), it suggests strong evidence against the null hypothesis, so we reject the null hypothesis the claim that there is no statistically significant difference between perceived competence of private tertiary students in the use of social media outlets and the gender status of students.

##### Conclusion

WeWean therefore conclude with 95% confidence that there is statistically significant difference between perceived competence of private tertiary students in the use of social media outlets and the gender status of students. Thus, we infer that perceived competence of private tertiary students in the use of social media outlets is influenced by their gender status.

##### NB

The formal language we use is to either reject the null hypothesis (in favor of the alternative) or to retain, or refuse to reject the null hypothesis. The word “accept” is not a good substitute for retain. The inferential conclusion to “reject or retain” the null hypothesis is simply a conjecture based on the evidence. But whichever inference we make, there is an underlying truth (null or alternative) that we can never know for sure, and there is always a chance that we will be wrong in our conclusion even if we use all of our statistical tools correctly.

##### Bibliography

Rumsey, D.J. (2019).What a p-value tells you about statistical data. Retrieved on November 30, 2019 from https://www.dummies.com/education/math/statistics/what-a-p-value-tells-you-about-statistical-data/

Sigma Plus Statistiek. (2018). Chi-Square Independence Test – What and Why?https://www.spss-tutorials.com/chi-square-independence-test/

Statistics Solution. (2009). Using Chi-Square Statistic in Research.https://wwew.statisticssolutions.com/using-chi-square-statistic-in-research/