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# Some Basics You Need to Know Before Starting Your Chi-Squared Statistics Homework By Michelle Johnson
14 Jun, 2017
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Statistics generally deals with quantitative data, i.e., data that can be expressed numerically. However, even qualitative data can be analyzed with statistics. Data might not always be quantitative in nature, as far as real life situations are concerned. Therefore, there is a need for a method for analyzing qualitative date as well.

One such method that can be used for analyzing qualitative data is Chi-squared method. Students studying statistics are often given Chi-squared statistics homework. For doing this test, two or more attributes needs to be considered. Then, you have to check if these attributes are associated or not.

Need for Chi-square test

Different tests of significance like F, Z and t are mainly based on the assumption that the samples are drawn from a normal distribution. Since these tests need assumption about population parameters, they are called parametric tests. However, while drawing samples, there might be situations where making a firm assumption about distribution of population might not be possible. As a result of this, non-parametric tests have been developed. Chi-square test serves as a prominent example of a non-parametric test.

Defining Chi-Square

Chi-square test is amongst the most commonly used and simplest non-parametric test in statistics. This is why Chi-squared statistics homework is commonly given to students. This test is denoted by the Greek letter x2. This quantity describes discrepancy theory magnitude and observation.

Chi-squared test can be defined as a statistical hypothesis test where sampling distribution is a chi-squared distribution of test statistic when null hypothesis is true. Chi-squared tests are usually constructed from sample variance or sum of squared errors. Independent normally distributed data is assumed for tests statistics following chi-squared distribution, which is valid for a lot of cases because of central limit theorem.

Degrees of Freedom

When you are doing Chi-squared statistics homework, you will be required to determine degrees of freedom for comparing between the table value and calculated value of x2. This is why it is extremely vital what degree of freedom actually means. It basically means the number of classes to which arbitrary values can be assigned without the placed restriction being violated.

Distribution

X2, Chi-square statisticâ€™s sampling distribution can be approximated closely by chi-square distribution, which is a continuous curve. The number of degrees of freedom â€˜vâ€™ is the only parameter of this distribution. The probability function of this method depends on this â€˜v.’ With a change in the degrees of freedom, the probability function of Chi-square method also changes.

The distribution is skewed to right for small number of degree of freedom. With an increase in this number, the curve becomes more symmetrical on a rapid basis, until a large value is reached. At this point, the distribution can be approximated by normal distribution.

Applications of the test

Important applications of chi-squared test include:

• Test for independence of attributes
• Test of goodness of fit
• As a test for Homogeneity

Validity conditions for Chi-squared test

If you are given Chi-squared statistics homework, you need to know about the conditions which need to be satisfied for using Chi-square test. These include:

• Total number of frequencies â€˜Nâ€™ should be relatively large
• Independent sample observations need to be sued. This means that an individual item should not be included two or more times in the sample.
• Cell frequencies constrains must be linear.
• Theoretical cell frequencies must never be small.
• The distributions should never be replaced by relative frequencies. Instead, data should be provided in original units.

Steps involved in Chi-square test

The steps required to perform a Chi-squared test are rather simple, which is why it is a powerful statistical tool. This test can be used for analyzing a huge variety of data types. It is particularly useful when an analyst wishes to compare a percentage of items distributed among different categories. The steps mentioned below describes the method for computing Chi-square value and determining the statistical significance of that value:

• You need to start by organizing the data collected. The values acquired from the sample data should be placed in a two-way table. In the table, the data in the rows represent independent variable whereas data in columns represent dependent variable.
• Next, you need to calculate total frequencies for each column and row. You can do this by simply adding cell totals from the table.
• Now, the expected frequencies for every cell need to be calculated. For doing this, you need to multiply the column total from each cell by its row total. The resultant number then needs to be divided by overall total.
• Next, Chi-square value has to be calculated. For this, the squared difference between expected and observed cell frequencies needs to be calculated. Then, the obtained number needs to be divided by the number that represents the expected cell frequency. Once the first number for all cells are calculated, you have to add up all the values. You will then get the Chi-square value for the chosen sample data.
• Lastly, consulting the distribution table is required. It is done for determining whether the value has any statistical significance or not. The aim should be obtaining a p-value that is less than 0.05. This would be an indication that there is less than 5% chance that the results occurred by chance.

By simply following the steps mentioned above, you can use Chi-square test for analyzing certain changes that might have occurred. You can use the data for determining the reasons for these changes.