CHI-SQUARE TEST (χ²):
Chi-square is a statistical test commonly used to compare observed data with data we would expect to obtain according to a specific hypothesis. For example, if, according to Mendel's laws, you expected 10 of 20 offspring from a cross to be male and the actual observed number was 8 males, then you might want to know about the "goodness to fit" between the observed and expected. Were the deviations (differences between observed and expected) the result of chance, or were they due to other factors. How much deviation can occur before you, the investigator, must conclude that something other than chance is at work, causing the observed to differ from the expected. The chi-square test is always testing what scientists call the null hypothesis, which states that there is no significant difference between the expected and observed result. The formula for calculating chi-square (χ²) is:

2= (o-e) ²/e
That is, chi-square is the sum of the squared difference between observed (o) and the expected (e) data (or the deviation, d), divided by the expected data in all possible categories.

INTERPRETATION OF CHI-SQUARE TEST
1. Determine degrees of freedom (DF). Degrees of freedom can be calculated as the number of categories in the problem minus 1. 2. Determine a relative standard to serve as the basis for accepting or rejecting the hypothesis. The relative standard commonly used in biological research is p > 0.05. The p value is the probability that the deviation of the observed from that expected is due to chance alone (no other forces acting). In this case, using p > 0.05, you would expect any deviation to be due to chance alone 5% of the time or less. 3. Refer to a chi-square distribution table Using the appropriate degrees of 'freedom, locate the value closest to your calculated chi-square in the table. Determine the closest probability(p) value associated with your chi-square and degrees of freedom. Step-by-Step Procedure for Testing Your...

...Chisquaretest for independence of two attributes. Suppose N observations are considered and classified according two characteristics say A and B. We may be interested to test whether the two characteristics are independent. In such a case, we can use Chisquaretest for independence of two attributes.
The example considered above testing for independence of success in the English...

...Chi-square requires that you use numerical values, not percentages or ratios.
Then calculate 2 using this formula, as shown in Table B.1. Note that we get a value of 2.668 for 2. But what does this number mean? Here's how to interpret the 2 value:
1. Determine degrees of freedom (df). Degrees of freedom can be calculated as the number of categories in the problem minus 1. In our example, there are two categories (green and yellow); therefore, there is I degree...

...CHI-SQUARE AND TESTS OF CONTINGENCY TABLES
Hypothesis tests may be performed on contingency tables in order to decide whether or not effects are present. Effects in a contingency table are defined as relationships between the row and column variables; that is, are the levels of the row variable diferentially distributed over levels of the column variables. Significance in this hypothesis test means that interpretation of...

...Chi-SquareTestChi-square is a statistical test commonly used to compare observed data with data we would expect to obtain according to a specific hypothesis. For example, if, according to Mendel's laws, you expected 10 of 20 offspring from a cross to be male and the actual observed number was 8 males, then you might want to know about the "goodness to fit" between the observed and expected. Were the...

...THE CHI-SQUARE GOODNESS-OF-FIT TEST
The chi-square goodness-of-fit test is used to analyze probabilities of multinomial distribution trials along a single dimension. For example, if the variable being studied is economic class with three possible outcomes of lower income class, middle income class, and upper income class, the single dimension is economic class and the three possible outcomes are the three...

...Chi-squaretests
1. INTRODUCTION
1.1 χ2 distribution and its properties
A chi-square (χ2) distribution is a set of density curves with each curve described by its degree of freedom (df). The distribution have the following properties:
- Area under the curve = 1
- All χ2 values are positive i.e. the curve begins from 0 (except for df=1) increases to a peak and decreases towards 0 as its asymptote
- The...

...A chi-squared test, also referred to as chi-squaretest or χw² test, is any statistical hypothesis test in which the sampling distribution of the test statistic is a chi-squared distribution when the null hypothesis is true. Also considered a chi-squared test is a test in which this is asymptotically true, meaning that the...

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