Explain Chi-Square in your own words, including what it is and how it works
A Chi-Square test is used to test relationships between two nominal variables. When testing the relationship between two variables, the null hypothesis as per the Chi-Square test is that there is no relationship between the two variables. Researchers typically have an assumption often expressed in the hypothesis even before testing the variables. A Chi-Square test shows if there is a difference between the observed value and the expected value.
An example given in the video illustrates what Chi-Square is. When a coin is tossed 100 times, it is expected that the coin will land 50 times on the head and 50 times on the tail (Bozeman Science, 2011). However, the video shows that the coin landed on the head 62 times and 38 times on the tail. Therefore, Chi-Square is a test of independence that evaluates whether there is an association between the two variables. It does so by comparing the observed patterns against a pattern that would be expected for two independent variables.
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A Chi-Square test is not complete without understanding the concept of the degree of freedom and the critical value. When testing the null hypothesis, the Chi-Square test can exceed or not exceed the critical value (Gaunt et al., 2017). The critical value is determined by the degree of freedom, which involves a comparison of the outcomes. When tossing a coin 100 times, there can only be two outcomes; hence the degree of freedom will be 2-1, making it one. The degree of freedom is on the left side of the Chi-Square table, which is compared against the different levels of significance, and in most cases, 0.05 level of significance is often used. 0.05 level of significance is a 95% chance of accepting or rejecting the null hypothesis.
Take 30 coins and follow the instructions of the 2nd video of how to figure out Chi-Square.
By flipping the coin 30 times, it is expected that there will be 15 heads and 15 tails based on 50/50 probability. While 50/50 probability is expected, this is not the case. After flipping the coin, there were 17 heads and 13 tails. Thus, the question is how far the observed value is from the null hypothesis. How far are the observed values without significantly being different from the expected value? The Chi-Square test will answer the question, as demonstrated below:
The formula for Chi Square test is:
| Side of the coin | Observed (O) | Expected (E) | O-E | (O-E) 2 | (O-E) 2 /E |
| Heads | 17 | 15 | 2 | 4 | 0.267 |
| Tail | 13 | 15 | -2 | 4 | 0.267 |
The X 2 value is 0.534.
The next step is identifying the critical value from the Chi-Square table. The first step is identifying the degree of freedom, which is N-1. There are categories and two rows and two columns for the heads and tails; thus, the degree of freedom is 1. From the Chi-Square table, we use the significance of 0.05 (95% significance).
Since the P-value is 0.05, the critical value is 3.841. The next step is to compare the X2 value of 0.534 against the critical value of 3.841. If the X2 is greater than the critical value, you reject the null hypothesis. In this case, the X2 is lower than the critical value; hence the null hypothesis is accepted. The null hypothesis is that there is no significant difference between the observed and the expected frequencies.
Explain the value of using the Chi-Square tool.
According to Sharpe (2015), a Chi-Square test is useful for analyzing the participant response data's cross-tabulations. Cross tabulations often show the frequency and percentage of responses to questions from various groups such as age groups and genders. A Chi-Square tests whether the variables are independent, but it does not show the extent of difference among the categories.
A Chi-Square test is a valuable statistical tool. First, it makes it possible to establish the relationship between categorical variables. Researchers often make assumptions or use available tools to make predictions of the expected relationships between variables. For example, it is assumed that education reduces poverty levels, but the Chi-Square test attempts to find out if there is a relationship (Gaunt et al., 2017). The test also tests for deviation of differences from the expected and observed, often expressed in one-way tables. The Chi-Square test allows it to evaluate the relationship between two variables on different levels of significance, either at 0.01, 0.05, or 0.025.
A Chi-Square test is also known as a goodness-of-fit test because it shows if the observed distribution is aligned with what is expected or it is up to chance. The test is also useful because it is used to analyze categorical data, which cannot be analyzed by parametric tests such as T-tests and Anova. A Chi-Square test makes it possible to assess whether the relationship between nominal values is normal or not.
References
Bozeman Science. (2011, November 13). Chi-squared Test. [Video file].YouTube Video. https://www.youtube.com/watch?reload=9&v=WXPBoFDqNVk
Gaunt, R. E., Pickett, A. M., & Reinert, G. (2017). Chi-square approximation by Stein’s method with application to Pearson’s statistic. The Annals of Applied Probability , 27 (2), 720-756.
Sharpe, D. (2015). Chi-Square Test is Statistically Significant: Now What? Practical Assessment, Research, and Evaluation , 20 (1), 8.
