Chi-square test Hypothesis testing

Null hypothesis- The status quo– AKA no change/difference. Alternative hypothesis- What you want to prove/show with experiment.

Examples: Ex 1: Question: Is Drug A better than a placebo? Null: No, it is not more effective. (assumes no difference). Alternative hypothesis: Yes, drug is more effective than a placebo. (significantly better?): Ex 2: In court case, assume innocent until proven guilty (no change/ no wrongdoing) until enough evidence to say otherwise. One widely-used type of evidence in scientific studies is the Chi-square test.

The null hypothesis refers to a general statement or default position that there is no relationship between two measured phenomena. OR that there is no statistically significance difference between the two measured phenomena. If the null hypothesis is rejected or the data does not support it, we can conclude there is a statistically significant difference between variables, meaning there is an association between those variable. To answer the question of statistical significance, we will use the Chi- square test.

Chi-square χ 2 = chi-square test statistic o= observed value e= expected value Σ = the sum of.

Homozygous green peas were crossed with homozygous yellow peas. All the offspring were phenotypically yellow. A test cross was performed with one of the offspring from the F 1. A. Using Y as the symbol for pea color, what are the genotypes of the parents used in this cross? B. If the F 2 generation consisted of 20 offspring, how many would you expect to be green and how many would you expect to be yellow?

Degrees of Freedom and Chi-square table Look at your Chi-square table. How do we determine which row to use? We have to use the degrees of freedom in the experiment. df= (number of groups being compared – 1) df for our example = ????

Using the Chi-square table Move across correct df row until you find your X2 value. Look at corresponding P-value. If there is a P-value< 0.05 it demonstrates that there is a statistically significant difference. If your χ 2 falls between values you must infer the p-value from the table and should be able to determine statistical significance. When p < 0.05 it is very unlikely that you observed your data by “chance”– so it is considered statistically significant.

So what is a p-value anyway? P= the probability of observing data as extreme or more extreme than the data you observed in your experiment given the null hypothesis is true. OR if those are the correct expected values, then the p-value is how likely it is to observe your data (or data that is more extreme)

More practice!! Problems: 1-5