Standards of reporting the findings of "Chi-Square test of goodness-of-fit” and “Chi-Square test of independence” in original articles

Presenting Chi-Square test results in an original article or thesis requires following a standard procedure. Here, I have prepared a simple approach or template that helps the author to present the findings of Chi-Square test in an appropriate way. I am sure, after reading this guideline, readers will agree with me that the findings of such a simple statistical analysis as Chi-Square test are reported wrongly in more than 95% of published papers! If you think that statistic is exaggerated, spend a few minutes of your time here and you may change your mind.

First, I should remind you that there are two types of Chi Square test, and reporting their findings are completely different:
1. Chi-Square test of goodness-of-fit
2. Chi-Square test of independence

The authors need to ask themselves which type of Chi-Square they used. The first one examines one categorical variable, but the second one examines two non-metric variables, and the way we should present their findings, and indeed the way we should write the specific objective, research question, and hypothesis are very different.

1- Presenting the Chi-Square test of goodness-of-fit:
Chi-Square test of goodness-of-fit is used to test certain assumptions on the distribution of a categorical variable. For example, to examine the hypothesis of “The proportion of people with obesity differs by age group”, we can use the Chi-Square test of goodness-of-fit. In this hypothesis, the researcher wants to know whether obesity is distributed in different age groups equally or not. Although “Age” is a metric variable, the “age group” is a categorical variable as we may categorize the people in age groups of <10 years old, 10-20 years, 20-30 years, 30-40 years, and so on. So, in this type of Chi-Square test we have only one variable, and that is a categorical variable.

Here, I will present the scientific method in writing the research question, the specific objective, the hypothesis, and the written report of the statistical findings of the Chi-Square test of goodness-of-fit:

1-1- Research question:
Is the proportion of people with obesity different by age group?
An alternative for this research question might be:
Is obesity distributed equally among the age groups?

1-2- Specific objective:
To determine the difference between the proportion of obesity in different age groups.

1-3- Hypothesis:
H0 (Null hypothesis): The proportion of people with obesity is the same for all age groups
HA (Alternative hypothesis / research hypothesis): The proportion of people with obesity is different by age group (The proportion of people with obesity differs by age group).

1-4- Reporting the statistics:
According to the study, the proportion of people with obesity is different by age group at 0.05 level of significance.

Or better to say:
According to the study, the proportion of people with obesity is significantly different by age group (p=0.032).

Reporting the p-value should be in exactly the same way as the above example. In this example, the calculated p-value is 0.032, it might be 0.04 or 0.01. Authors should present the exact p-value, and not simply say p≤0.05. However, in some certain cases, it may be presented as p<0.001.

2- Presenting the Chi-Square test of independence:
The second type of Chi-Square test, the Chi-Square test of independence, is used to determine association between two nonmetric variables. So, in this type of Chi-Square test we have two variables: a dependent variable (DV), and an independent variable (IV), and both of them are either Nominal or Ordinal variables. For example, if the researcher is going to examine whether the academic performance is dependent on gender, they should use the Chi-Square test of independence. In this example, gender is a bimodal variable and acts as the independent variable, and the academic performance is a categorical variable and could be high, moderate, or low.

Here, I will present the scientific method in writing the hypothesis and the report of statistical findings of the Chi-Square test of independence:

2-1- Hypothesis:
The hypothesis of such tests could be in this format:
H0 (Null hypothesis): Academic performance is independent of gender
HA  (Alternative hypothesis / research hypothesis): Academic performance is dependent on gender

2-2- Reporting the statistics:
When reporting the statistical findings of Chi-Square test of independence, we should report two items:
2-2-1- The result of test of independence
2-2-2- Measure of Association

If the Chi-Square test does not show enough evidence to conclude that gender and academic performance are dependent, we can present it as the following statement:
According to the Chi-Square test of independence, the academic performance was independent of gender (p=0.12).

An important statistic to be presented in the results of the Chi-Square test of independence is the “Measure of Association”. In the above example, the statement of measure of association could be as follows:

According to the Chi-Square test of independence, there was no significant association between gender and academic performance (p=0.12).

Or:

According to the Chi-Square test of independence, there was negligible association between gender and academic performance (p=0.12, v = 1.6).

As it is shown, when reporting the statistical findings of the Chi-Square test of independence, authors should also report the “Measure of Association”, and that is something to be calculated using Phi Coefficient, Contingency Coefficient, or Cramer’s V Coefficient. In the above example, the “v=1.6” refers to Cramer’s V Coefficient.

Note:

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