Quantitative Skills 3: Hypothesis Testing

A hypothesis is a statement explaining that a causal relationship exists between an underlying factor (variable) and an observable phenomenon. Example Hypothesis: If gravity is related to root growth, then roots will always grow toward the earth regardless of a seed's orientation.

A hypothesis is not a prediction. A hypothesis is a testable statement explaining some relationship between cause and effect. A prediction is a statement of what you think will happen given certain circumstances.

Because science cannot prove anything, it is impossible to prove a working hypothesis. Instead, statistical hypothesis testing focuses on trying to reject a null hypothesis.

After making an observation, you might propose some sort of tentative explanation for the phenomenon; this is called a working hypothesis. “If ladybugs are added to aphid- infected plants, then infected plants will have less aphids after a week of exposure to ladybugs than plants that are left untreated.”

A null hypothesis (H 0 ) is a statement explaining that there is no relationship between the observed phenomenon and the independent variable being manipulated in the study. “If ladybugs are added to aphid- infected plants, then infected plants will have the same number of aphids after a week of exposure to ladybugs than plants that are left untreated

Establishing a null hypothesis (H 0 ) and an alternative hypothesis (H A ) A null hypothesis states that there is no relationship between two variables. The finding probably occurred by chance. A null hypothesis states that there is no relationship between two variables. The finding probably occurred by chance. An alternative hypothesis states that there is a relationship between two variables. The finding probably did not occur by chance. An alternative hypothesis states that there is a relationship between two variables. The finding probably did not occur by chance.

Example null hypothesis (H 0 ): If cheese is kept at room temperature for a week, then it will have the same amount of mold on it as the same amount of cheese kept in a refrigerator for a week. Example alternative hypothesis (H A ): If cheese is kept at room temperature for a week, then it will have more mold on it than the same amount of cheese kept in a refrigerator for a week. Example : “ I think my cheese will mold if I leave it out on the counter too long.”

It is important to understand that hypothesis testing does not allow proof, or even acceptance, of the alternative to the null hypothesis. The best thing we can do is find support for the alternative hypothesis by rejecting the null hypothesis.

If a null hypothesis is rejected, it is usually a good practice in hypothesis testing to develop a second working hypothesis and to perform a statistical test for that option. What if it is a difference in humidity, and not temperature, that is causing the cheese to mold more quickly?

Occam's razor: If two hypotheses can account for observations equally well, scientists normally prefer the simpler hypothesis. The object in the sky is a UFO. The object in the sky is a cloud. or

Four possible outcomes of hypothesis testing:

Correlation: interpreting a scatterplot by regression analysis

A best-fit line (regression line) is created by calculating how far each point is from the mean x value and from the mean y value. This is typically done with a spreadsheet or other graphing program.

Regression analysis provides a measure of how the two variables are related to each other. The r-value, also known as the correlation coefficient, can range from -1.0 to The closer r is to +1 or -1, the more closely the two variables are related.

A positive r-value is a positive correlation, which means that as one variable increases, so does the other. Remember: “Correlation does not imply causation!”

A negative r-value is a negative correlation, which means that as one variable increases, the other decreases.

An r-value of 0 indicates that there is no correlation between the two variables – they are not related.

References AP Biology Quantitative Skills Manual