Read this article to learn about the applications of Chi-Square test in analyzing statistical data.
Goodness of Fit: Habitat Use:
If you are looking for habitat selection or avoidance in a species (e.g., black bear), you can use a goodness of fit test to see if the animals are using habitat in proportion to its availability.
If you have collected 100 radio-locations on a bear or bears, you would expect that, if the species were not selecting or avoiding habitat, you would find the radio-locations spread in each habitat type depending on its general availability (If 90% of the area was lowland conifer, you would expect 90% of the locations to occur in that habitat type). Imagine you generate the following data from your spring bear study.
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Ho: The bears are using habitat in proportion to its availability.
1. Fill in the expected number of radio-locations in each cover type.
2. Calculate the chi-square value for these bears.
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3. Given that the degrees of freedom are (r-1)*(c-1) = 4, the critical value for chi-square (at alpha = 0.05) is anything greater than 9.49. Would you accept or reject the null hypothesis? What does that mean in layman’s terms?
Survival:
Let you are investigating the population dynamics of the deer herd at Sand hill and hypothesize that a constant death rate of 50% per year has existed over the past several years with a stable herd.
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You sample the population at random and classify deer into age groups as indicated:
The expected value, (X), of the first age group is obtained from the formula:
X + (d + d2 + … dn-1) X = T
X + (.5 + .52 + … .55) X = 253
X + (.96875) X = 253
1.96875 X = 253
X = 129
Subsequent expected values are computed by applying the expected 50% death rate (d) for each succeeding year.
1. State the null hypothesis.
2. Calculate the Chi-square value.
3. Knowing the critical value for 5 degrees of freedom (* = 0.05) is 11.0705, what do you conclude about the “fit” between the observed and hypothesized death rates? Are there significant differences?
Model Selection:
Many programs develop predictive equations for data sets. A common test for the “fit” of a model to the data is chi-square goodness-of-fit test. For example, program DISTANCE, which develops curves to estimate probabilities of detection, uses discrete distance categories (e.g., 0-5m, 5-10m, etc.) to see how well the model predicts the number of objects that should be seen in each distance category (Expected) versus what the data actually show (Observed). II)