What is Chi square?

Chi square is a statistical test used to compare two outcomes in research, it compares the observed and expected results from a group of data collected and arranged in a table after a study. The essence of chi square in research is mainly to identify whether an existing difference between the Observed and Expected data is caused by chance (co-incident) or the difference is a result of a relationship between the variables being studied.

Furthermore, chi square helps the researcher determine if the observed outcomes in a study are what is expected of the outcome, this demonstrates how the variables (e.g. the effect of the malaria parasite on children’s health) are associated or related.

From the above, the malaria parasite represents the independent variable while children’s health represents the dependent variable.

Chi square helps in determining how the dependent and independent variables relate that is, the relationship between children’s health and the malaria parasite e.g. does the malaria parasite affect children’s health?

To get the test results that will enable a researcher to interpret and make a decision; six (6) main data are required, including;

Observed Frequencies:

These are the actual data which represent the groups’ scores. They are what the researcher observed in the data collected.

Expected Frequency:

These represent what the researcher anticipates or expects to find assuming the Null hypothesis is true where the variable(s) are dependent.

Level of Significance:

In the management and social sciences, the level of significance is usually 0.05 (that is, 5%), sometimes 0.1 or 10% can be applied in research.

LIMITATION OF CHI SQUARE

The Chi square test is frequently employed in research, even for 2 by 2 contingency tables. On the other hand, almost all statistics method textbooks advise against using the chi-square test if the anticipated frequency in any one cell is less than five. In such a scenario, we occasionally merge two or more samples so that none of the anticipated frequencies is lower than five. Because big sample theory is employed in the calculation of the chi square test, the probability generated from it is believed to be a poor approximation of the true probability with small cell frequencies.

CHI SQUARE TEST SOLVED

To test a hypothesis using chi square (also known as X² ) the following steps are to be followed. These steps are explained below:

Step 1

Extract the Data You Want to Test

This usually comes in a tabular format.

Response Variable	Frequency	Percentage frequency
Strongly agree	96	55.81%
Agree	56	32.56%
Disagree	12	6.98%
Strongly disagree	8	4.65%
Total	172	100.00%

Step 2

Identify The Relevant Hypothesis for the Study To Be Tested Using the Chi square (X²).

For example:

H_o: Cooperative societies do not provide cooperative education for their members to advance their entrepreneurship skills in Ebonyi State.

H₁: Cooperative societies provide cooperative education for their members to advance their entrepreneurship skills in Ebonyi State.

Step 3

Determine The Test Statistics Which In This Case is The Chi square Test Formula:

X² = Ʃ (Oi – Ei)/Ei

Where;

Oi = Observed frequency

Ei = Expected frequency

X² = Chi square

After determining the steps to take, you then proceed with the Test proper.

For easy understanding, we will follow the calculations step-by-step to the final results.

Step A

Call Up The Data That Will Be Tested.

Response Variable	Frequency	Percentage frequency
Strongly agree	96	55.81%
Agree	56	32.56%
Disagree	12	6.98%
Strongly disagree	8	4.65%
Total	172	100.00%

Step B

Determine the Expected Frequency (Ei)

The formula for determining Expected frequency in chi-square is Ei = Total Frequency/Number of Rows

Hence; total frequency = 96+56+12+8 =172

Number of Rows = 4

Therefore Ei = 172 ÷ 4 = 43

How is the No. of Rows determined?

	No. of Rows
Strongly agree	Row 1
Agree	Row 2
Disagree	Row 3
Strongly disagree	Row 4
Total Rows	4

Step C

Determine the Chi-Square Test Level of Significance:

The level of significance in this case is 5% that is, 5/100 = 0.05%

Step D

Calculate the Chi square Degree of Freedom (df)

This is given as:

Df = (Row total – 1)

Since the total Row is 4

Then, df = (4 – 1)

Df = 3

Step E

Determine the Critical Value

Determination of the critical value will require the use of a chi square table. To achieve this, you need to look up the critical value at the degree of freedom 3 and 5% level of significance. This will give you 7.81 on the statistical table.

Step F

State the Decision Rule or the test Criterion.

In this case, we will state the decision rule as follows;

“if the computed value of X² is more than or greater than the Critical Value of 7.81, the Null hypothesis (H_o) should be disregarded and rejected while the Alternate hypothesis (H₁) be upheld and accepted. But if the reverse is the case, then the Alternate hypothesis should be rejected while the Null hypothesis is accepted”.

Step G

Computation of Chi square Statistics using;

X² = Ʃ (Oi – Ei)/Ei

Recall, that the Observed frequencies are the figures that represent the frequencies on the table containing data collected from respondents based on the research objectives and hypothesis.

Also, remember that Ei = 43 as calculated earlier.

Let’s now continue.

Since

X² = Ʃ (Oi – Ei)/Ei

And Oi is the Observed frequency, hence the Observed frequencies are 96, 56, 12, and 8 respectively.

So, Ʃ (96 – 43)²/43 + (56 – 43)²/43 + (12 – 43)²/43 + (8 – 43)²/43

      Ʃ (53)²/43 + (13)²/43 + (-31)²/43 + (-35)²/43

      Ʃ 2,809/43 + 169/43 – 961/43 – 1,225/43

X²  = 65.33 + 3.93 – 22.35 – 28.49

X²  = 18.42

Therefore, the calculated value of X²   = 18.42

But the critical value earlier obtained = 7.81

Therefore, our decision will be as follows.

Decision:

Since the calculated value of X²   18.42 is greater than the critical value of 7.81, the null hypothesis (H_o) will be rejected while the alternate hypothesis (H₁) is accepted. Therefore, this study concludes that cooperative societies do provide cooperative education for their members to advance their entrepreneurial skills in Ebonyi state.