## Null-hypothesis for a Chi-Square Goodness of Fit Test 2

### chi square lab report | Experiment | Null Hypothesis

The greater thecalculated chi-square value, the more likely the sample does notconform to the expected frequencies, and therefore you would reject thenull hypothesis.

### its Chi-Square value was used to prove the null hypothesis

Once data are collected, it is important to be able to determine whether they fall within the range of normal variation for the expected Mendelian ratios. To do this, a chi-square test is used. It will provide a guide as to whether to accept your null hypothesis (which will happen if the observed data fall within the normal variation for the expected ratios) or reject your null hypothesis (if the observed data do not fall within the range of normal variation). The chi-square value gives a measure of the extent to which your results differ from the expected - the larger the chi-square, the bigger the difference, and the less likely that the difference was due to random chance.

The significance level (also known as the "critical value" or "alpha") you should use depends on the costs of different kinds of errors. With a significance level of 0.05, you have a 5% chance of rejecting the null hypothesis, even if it is true. If you try 100 different treatments on your chickens, and none of them really change the sex ratio, 5% of your experiments will give you data that are significantly different from a 1:1 sex ratio, just by chance. In other words, 5% of your experiments will give you a false positive. If you use a higher significance level than the conventional 0.05, such as 0.10, you will increase your chance of a false positive to 0.10 (therefore increasing your chance of an embarrassingly wrong conclusion), but you will also decrease your chance of a false negative (increasing your chance of detecting a subtle effect). If you use a lower significance level than the conventional 0.05, such as 0.01, you decrease your chance of an embarrassing false positive, but you also make it less likely that you'll detect a real deviation from the null hypothesis if there is one.

## In a chi-square test, only the null hypothesis can be rejected.

In plant breeding and genetics research, plant breeders establish a hypothesis to explain how they think a particular trait is inherited, such as if it is due to one gene with complete dominance, an interaction of more than one gene, or quantitative inheritance, with many genes contributing, etc. Next the breeder sets up some crosses and observes the resulting progeny to test that inheritance hypothesis. However, when the data is collected, oftentimes the breeder discovers the number of plants observed in each class is not exactly what was expected from the hypothesis. The question then is how do plant breeders determine if the data supports their hypothesis or not? Following a tomato disease resistance example in this lesson, you will learn a simple statistical test that breeders can use to conclude if the experimental data supports their hypothesis.

This lesson is written for undergraduate and graduate students studying plant breeding, as well as agriculture professionals unfamiliar with the use of the chi-square analysis.

## Pearson's chi-squared test - Wikipedia

If you obtain a chi-square that requires you to reject yournull hypothesis for any of the boxed or bagged corn, try to derive another nullhypothesis to test. For example, a different phenotype may be dominantthan the one you expected, or both parents may not have been heterozygous. Some of your monohybrid bagged ears may have a ratio that appears to be closer to 1:1 than to 3:1, or a dihybrid might have a ratio that appears to be 1:1:1:1. What would account for a 1:1 or a 1:1:1:1 ratio? If you have an unexpected result, you should talk to members of another group and findout if they have the same result. Compare your results to determine whether the two results are similar, and if not, whichis more likely to be representative of all samples.

## can be rejected, and the alternative hypothesis ..

We would notreject our hypothesis, since is greater than0.05 (that is, >0.05).

You should note that many statistical packages for computerscan calculate exact -values for chi-square distributedtest statistics.