Calculating the Value of Chi-Square Once you've defined the null hypothesis (and know what you're testing!), you can finally calculate the chi-square value based on your observed data and the expected distribution. There are many statistical software packages and free web-based applications that will automate the calculation for you, but it's important to understand the calculation to understand the meaning of the calculated value. Here, we'll walk through it using a calculation table. This is Mendel's historic data for the F2 generation of monohybrid cross for flower color. Recall that he expected to see in the F2 generation a ratio of 3 purple : 1 white. Chi-square calculation for data from a monohybrid cross with an expected 3 purple : 1 white ratio. (0-E)²/E Outcomes Observed (0) Expected (E) O-E Purple White Totals 705 224 929 (0-E)² X² = The first step is to calculate the expected (E) values for purple and white. Recall that E(purple) = P(purple) x n = 3/4 x 929 696.75. Similarly, E(white) = P(white) x n = 1/4 x 929 = 232.25. Do these expected values bother you? Is there such a think as 0.75 or 0.25 of an individual plant? No, but remember that expected values are theoretical. It's better in this analysis not to round off to whole values because doing so will introduce a high degree of error. Record the expected values in the table, and note that they should add up to n (or approximately n if you do round off at all). Chi-square calculation for data from a monohybrid cross with an expected 3 purple : 1 white ratio.
Calculating the Value of Chi-Square Once you've defined the null hypothesis (and know what you're testing!), you can finally calculate the chi-square value based on your observed data and the expected distribution. There are many statistical software packages and free web-based applications that will automate the calculation for you, but it's important to understand the calculation to understand the meaning of the calculated value. Here, we'll walk through it using a calculation table. This is Mendel's historic data for the F2 generation of monohybrid cross for flower color. Recall that he expected to see in the F2 generation a ratio of 3 purple : 1 white. Chi-square calculation for data from a monohybrid cross with an expected 3 purple : 1 white ratio. (0-E)²/E Outcomes Observed (0) Expected (E) O-E Purple White Totals 705 224 929 (0-E)² X² = The first step is to calculate the expected (E) values for purple and white. Recall that E(purple) = P(purple) x n = 3/4 x 929 696.75. Similarly, E(white) = P(white) x n = 1/4 x 929 = 232.25. Do these expected values bother you? Is there such a think as 0.75 or 0.25 of an individual plant? No, but remember that expected values are theoretical. It's better in this analysis not to round off to whole values because doing so will introduce a high degree of error. Record the expected values in the table, and note that they should add up to n (or approximately n if you do round off at all). Chi-square calculation for data from a monohybrid cross with an expected 3 purple : 1 white ratio.
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Transcribed Image Text:**Calculating the Value of Chi-Square**
Once you've defined the null hypothesis (and know what you're testing), you can finally calculate the chi-square value based on your observed data and the expected distribution.
There are many statistical software packages and free web-based applications that will automate the calculation for you, but it's important to understand the calculation to understand the meaning of the calculated value. Here, we'll walk through it using a calculation table.
This is Mendel's historic data for the F2 generation of monohybrid cross for flower color. Recall that he expected to see in the F2 generation a ratio of 3 purple: 1 white.
**Chi-square calculation for data from a monohybrid cross with an expected 3 purple: 1 white ratio.**
| Outcomes | Observed (O) | Expected (E) | O − E | (O − E)² | (O − E)² / E |
|----------|--------------|--------------|------|---------|-------------|
| Purple | 705 | | | | |
| White | 224 | | | | |
| **Totals** | **929** | | | | |
The first step is to calculate the expected (E) values for purple and white. Recall that E(purple) = P(purple) × n = 3/4 × 929 = 696.75. Similarly, E(white) = P(white) = n = 1/4 × 929 = 232.25. Do these expected values bother you? Is there such a thing as 0.75 or 0.25 of an individual plant? No, but remember that expected values are theoretical. It's better in this analysis not to round off to whole values because doing so will introduce a high degree of error. Record the expected values in the table, and note that they should add up to n (or approximately n if you do round off at all).
The explanation provided guides through the manual calculation of chi-square by using Mendel's data, emphasizing the theoretical nature of expected values.
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Step 1
Introduction
A chi-squared test, also known as a square test, is a type of statistical hypothesis test that can be used when the test statistic is distributed under the null hypothesis in a chi-squared manner. Pearson's chi-squared test and its variations fall under this category.
The expected frequencies and the observed frequencies in one or more categories of a contingency table are compared using Pearson's chi-squared test to see if there is a statistically significant difference.
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