Chi-Square Accustomator with Alternative Hypothesis

Using a Mendelian simple dominant example

Testing an Incorrect Hypothesis - You Choose Sample Size

Choose sample size to use:

Character Dominant Recessive Total
Observation
Ratio
Look at the Observations, and consider how close the Observed ratio is to the (incorrect) Expected 2:1 ratio used for this exercise. Is this a good fit? Is it a poor fit? Does this depend on the size of the sample? The "Goodness of Fit" can be calculated by the Chi-Square method.

While the "true" ratio in the data is a 3:1 (remember that we seldom, if ever, know the "true" ratio in real life problems) we might think that it something else. What happens if we think that the data arise from a 2:1 ratio and use this for our Expected entries in the Chi-Square analysis? This is done below:

          Result

Tally:   > 3.841         > 6.63         Samples

Interpreting the Calculated Chi-Square Value

How good a fit is shown by a calculated Chi-square value of this size? The closer the calculated value is to 0, the better the fit is between the Observed and Expected. If the calculated value for two categories is >3.841 then there is a statistically "significant" difference between the Observed and the Expected. If the value is >6.63, the difference is "highly significant."
Large differences do occur by chance and considerably more often when the observations result from a true ratio which is different than the one which is used for the Expected entries in the Chi-Square analysis (as is the case here.) How often does that occur? Note that significant or highly significant results do not occur for every sample, however the frequency of this depends on the sample size. The Tally shows the experience in this example. Compare how often this happens with different sample sizes.

Record of Tallies

Each set of samples is recorded in the text area below. You can review these at any time, and you can cut and past this information into your own records if you want to keep it.

Please send comments to hes@ncsu.edu   --henry schaffer
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Copyright © 1999 by Henry E. Schaffer