Hypotheses and Hypothesis Testing

Hypothesis An educated prediction about the outcome of an investigation A statement explaining that a causal relationship exists between an underlying factor (variable) and an outcome Sometimes called a “working hypothesis” Created after making an observation

Hypothesis ≠ guess Hypotheses are testable in quantifiable ways, not simply guesses about what might happen

Why create hypotheses? Helps in the design of an investigation The design process also requires identification of a few other elements

Variables Factors that affect the outcome of an event

Manipulated variable The one thing that you intentionally change in an investigation

Responding variable What you are measuring as an outcome of an investigation.

Controlled variable Everything else that you keep the same during an investigation

Format of working hypothesis Written in the “If...then...because” format If (manipulated variable), then (responding variable) because (prior knowledge).

Let’s practice Seniors from the same math class were tested to compare their speed working math problems. Each group was given the same problems. One group used calculators and the other computed without calculators. 1.Identify all variables 2.Create a working hypothesis

Dr. Ack wanted to find the ideal spot in her yard for planting tomatoes. She wanted to know if the amount of sun the plants received made a difference in how tall the plants would grow.

Problems with using hypotheses While the working hypothesis helps you to frame the question and design your investigation, it is impossible to prove absolutely.

Null hypothesis Scientist often use another type of hypothesis called the null hypothesis. The null hypothesis is sometimes called the “no difference” hypothesis. It is a statement that says that there is no causal relationship between the manipulated variable and the outcome.

For example We would like to know if the amount of sleep students get impact their performance on tests Hypothesis: If students get at least 6 hours of sleep, then they will do better on tests. Null hypothesis: There is no difference in test scores between students who get more than 6 hours of sleep and those who get fewer.

Let’s practice... With your table group, look back at the hypotheses we created and rework them into null hypotheses.

Why the null? Because you cannot prove a hypothesis absolutely, statistical hypothesis testing focuses on rejecting the null hypothesis. That is, if you can say that the null hypothesis (that there is no relationship between variable and outcome) is not true, then you provide evidence that your initial hypothesis might be true. It doesn’t prove that your initial is true.

Back to the sleep study... If our null hypothesis is that there is no difference in test scores, but we find a difference in our data, we have rejected the null. We have not proven that getting more sleep improved the test scores, that there was a causal relationship, but we certainly have some evidence that there might be a causal relationship.

Chi square squared-test squared-test

Chi square = – A way to compare data to determine if the variation in your data is due to the change in one of your variables (as opposed to chance) – Χ 2 = Σ (o-e) 2 / e

Degrees of freedom= – Possible outcomes – 1 – For example, you need 5 classes to graduate and 5 semesters in which to take them. – The first 4 semesters you have a choice, but the last semester you get whichever class is left. No “freedom”

Critical value = 0.05 means you are 95% sure that you can either accept or reject the null

Once you’ve determined the degrees of freedom and have calculated the chi square value... X 2 > c.v. – reject the null. i.e. data differences are more than you would expect by chance X 2 < c.v. – accept or “fail to reject” the null. i.e. the data differences could simply be chance

Possible outcomes in hypothesis testing Investigator action Null is trueNull is false Rejects the null Type I error (false positive) correct Fails to reject the null correctType II error (false negative)

A well written procedure: Has numbered steps written in the order that they should occur Is detailed enough that someone who is not familiar with the investigation could easily perform the investigation exactly like you Includes at least 3 trials Describes exactly how to measure the responding variable Describes all controlled variables