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 variables2. 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

• http://www.bozemanscience.com/chi-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)

– Χ2 = 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 . . .

• X2 > c.v. – reject the null. i.e. data differences are more than you would expect by chance

• X2 < 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 true Null is false

Rejects the null Type I error (false positive)

correct

Fails to reject the null

correct Type 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