Researchers also need to remember that the chi-square test does not give much information about the strength of the relationship. For example one cannot say that a tomato plant height is correlated with its leaf size simply by running a chi-square statistic. While chi-square does have limitations, it also has a number of strengths.
One of the largest strengths of chi-square is that it is easier to compute than some statistics. Also it can be used with data that has been measured on a nominal categorical scale. For example one could see if there is an association between the size of a tomato fruit and the number of fruit produced on a single plant. Another strength is that chi-square makes no assumptions about the distribution of the population. Other statistics assume certain characteristics about the distribution of the population such as normality.
We could gather a random sample of baseball cards and use a chi-square goodness of fit test to see whether our sample distribution differed significantly from the distribution claimed by the company. The sample problem at the end of the lesson considers this example. The chi-square goodness of fit test is appropriate when the following conditions are met:.
This approach consists of four steps: 1 state the hypotheses, 2 formulate an analysis plan, 3 analyze sample data, and 4 interpret results. Every hypothesis test requires the analyst to state a null hypothesis H o and an alternative hypothesis H a. The hypotheses are stated in such a way that they are mutually exclusive.
That is, if one is true, the other must be false; and vice versa. Typically, the null hypothesis H o specifies the proportion of observations at each level of the categorical variable. The alternative hypothesis H a is that at least one of the specified proportions is not true. Practice: Expected counts in a goodness-of-fit test.
Practice: Conditions for a goodness-of-fit test. Practice: Test statistic and P-value in a goodness-of-fit test. Practice: Conclusions in a goodness-of-fit test. Next lesson. Current timeTotal duration Google Classroom Facebook Twitter. Video transcript - [Instructor] In the game rock-paper-scissors, Kenny expects to win, tie, and lose with equal frequency.
Kenny plays rock-paper-scissors often, but he suspect his own games were not following that pattern. So he took a random sample of 24 games and recorded their outcomes. Here are his results. So out of the 24 games, he won four, lost 13, and tied seven times. He wants to use these results to carry out a chi-squared goodness-of-fit test to determine if the distribution of his outcomes disagrees with an even distribution. What are the values of the test statistic, the chi-squared test statistic, and P-value for Kenny's test?
So pause this video and see if you can figure that out. Okay, so he's essentially just doing a hypothesis test using the chi-squared statistic. Because it's a hypothesis that's thinking about multiple categories. So what would his null hypothesis be? Well, his null hypothesis would be that he has that all of the outcomes are equal probability.
Outcomes equal equal probability. And then his alternative hypothesis would be that his outcomes have not equal not equal probability. Remember we assume that the null hypothesis is true. And then assuming if the null hypothesis is true, the probability of getting a result at least this extreme is low enough, then we would reject our null hypothesis.
Another way to think about it is if our P-value is below threshold, we would reject our null hypothesis. And so what he did is he took a sample of 24 games, so n is equal to And then this was the data that he got. Now before we even calculate our chi-squared statistic, and figure out what's the probability of getting a chi-squared statistic that large or greater, let's make sure we meet the conditions for inference for a chi-squared goodness-of-fit test.
So you've seen some of them, but some of them are a little bit different.
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