Hypothesis Testing

Hypothesis vs Theory  Hypothesis  An educated guess about outcome of an experiment  Theory  An explanation of observed facts that is supported by a wide body of evidence and much experimental evidence

Null hypothesis  H 0  “no difference”  This is what is actually tested in experiment  We compare the known (primary observation) to the unknown sample (experimental observation)  We test whether sample is different from the known value or if there is “no difference”

Alternative hypothesis  H a  What will happen if there is a difference  Difference could be:  Less than (<)  Greater than (>)  Or ≠  This is what you think of when you normally write a hypothesis

Difference present?  Test the null  Is there a difference?  If there is a difference, is it significant?  How do we know it’s significant?  What is significant? How would you know that difference wasn ’ t random chance?

Tests for Significance  t test – interval or ratio data  Chi-square – categorical data  Obtain results from test and then compare to chart for significance

Difference determination  If significant: reject null hypothesis  If not significant: fail to reject null (accept null)  Sooo….if I reject null, what do I do with the alternative?  And if I fail to reject null, what do I do with alternative?

t test   X = mean of sample   population mean (comparison)  N = number in sample  s = standard deviation

Compare to table  df = degrees of freedom  df = number in sample -1  If t obs value is greater than t crit at.025 level, then reject null  If t obs value is less than t crit at.025 level, then fail to reject  level critical value

Chi-square  “good fit” with null hypothesis  Fail to reject null  “poor fit” with null hypothesis  Reject null

Compare to table  df = degrees of freedom  Number of categories - 1  level critical value If your number is greater than or equal to this number, reject null Reject Accept

Summary  If interval or ratio data, then use  If categorical data, then use Chi square t test

Examples  Experiment includes a student counting how many seeds are wrinkled and how many round  Experiment includes students determining how much oxygen was produced during a 30 minute period by plants during photosynthesis Chi square t test

Any Questions??

Let’s try an example of each…  A botanist is attempting to see if a certain soil composition would promote seedlings to sprout. She sowed the same amount of seeds in each container. Her results were as follows:  Trial 1 – 152 sprouts  Trial 2 – 162 sprouts  Trial 3 – 148 sprouts  Trial 4 – 127 sprouts  Control (normal soil) Which test do we use?

Second test...  A geneticist crossed Drosophila fruit flies in an attempt to determine if a certain trait was dominant or recessive. She sorted the offspring as follows:  Wild type eyes (red) – 404  Scarlet eyes – 400  Sepia eyes – 420  White eyes – 376  Which test is this? What do we do first?