For goodness of fit test using Chisquare test, Expected frequency = Total number of observations * theoretical probability specified or Expected frequency = Total number of observations / Number of categories if theoretical frequencies are not given. For contingency tables (test for independence) Expected frequency = (Row total * Column total) / Grand total for each cell
The maximum likelihood estimate under the null hypothesis gives the best estimate for expected frequencies.
You first decide on a null hypothesis. Expected frequencies are calculated on the basis of the null hypothesis, that is, assuming that the null hypothesis is true.
The chi-square test is used to analyze a contingency table consisting of rows and columns to determine if the observed cell frequencies differ significantly from the expected frequencies.
Goodness of fit test is used to test a single population. The null hypothesis will be that the observed frequencies are equal to expected frequencies (based on computed intrinsic values given the extrinsic values). A good example would be comparing observed phenotype frequencies against expected frequencies calculated from the parental genotypes (Simple dominance gives rise to 1:2:1 ratio with two parental heterozygotes). Contingency test is used to see whether or not different populations are associated. The null hypothesis will be that that different populations are independent of one another. A good example would be comparing the effect of different host plants on different populations of insects. (Effect of Host A on Insect population 1, 2, 3; Effect of Host B on Insect population 1, 2, 3; etc)
For goodness of fit test using Chisquare test, Expected frequency = Total number of observations * theoretical probability specified or Expected frequency = Total number of observations / Number of categories if theoretical frequencies are not given. For contingency tables (test for independence) Expected frequency = (Row total * Column total) / Grand total for each cell
Expected frequencies are used in a chi-squared "goodness-of-fit" test. there is a hypothesis that is being tested and, under that hypothesis, the random variable would have a certain distribution. The expected frequency for a "cell" is the number of observations that you would expect to find in that cell if the hypothesis were true.
The maximum likelihood estimate under the null hypothesis gives the best estimate for expected frequencies.
You first decide on a null hypothesis. Expected frequencies are calculated on the basis of the null hypothesis, that is, assuming that the null hypothesis is true.
The chi-square test is used to analyze a contingency table consisting of rows and columns to determine if the observed cell frequencies differ significantly from the expected frequencies.
The null hypothesis in a chi-square goodness-of-fit test states that the sample of observed frequencies supports the claim about the expected frequencies. So the bigger the the calculated chi-square value is, the more likely the sample does not conform the expected frequencies, and therefore you would reject the null hypothesis. So the short answer is, REJECT!
Goodness of fit test is used to test a single population. The null hypothesis will be that the observed frequencies are equal to expected frequencies (based on computed intrinsic values given the extrinsic values). A good example would be comparing observed phenotype frequencies against expected frequencies calculated from the parental genotypes (Simple dominance gives rise to 1:2:1 ratio with two parental heterozygotes). Contingency test is used to see whether or not different populations are associated. The null hypothesis will be that that different populations are independent of one another. A good example would be comparing the effect of different host plants on different populations of insects. (Effect of Host A on Insect population 1, 2, 3; Effect of Host B on Insect population 1, 2, 3; etc)
It is often a "goodness of fit" test. This is a test of how well the observations match the frequencies that would have been expected on theoretical basis. The theoretical basis may simply be your hypothesis.
Because Chi-squares are used to analyze and compare observed frequencies to expected frequencies, they can help trace the probability of an offspring receiving a certain phenotype and genotype from their parents.
If the assumptions behind the chi-square test don't hold (e.g. more than 10% of your events have expected frequencies below 5) then consider using an exact test, such as Fisher's Exact Test for 2x2 contingency tables.
This is concerned with frequency. Can be used to test whether the observed frequencies in a particular case differ significantly from those which would be expected in the null hypothesis. source: analysis related lectures
It enables us to tell the difference between observed and expected frequencies objectively as it is practically impossible to tell the difference just by looking at the data.