# MEASURABLE HYPOTHESES (testable predictions)

### Measurable hypotheses express predictions that can be experimentally tested.

DEFINITION: A "Measurable Hypothesis" is a tentative, specific prediction that can be rejected by experimental data.

Measurable Hypotheses typically have a consistent form: Measurable Hypotheses involve a prediction that can be directly compared to an experimental outcome to result in a conclusion.

An example of a Measurable Hypothesis is:

MH1: "We hypothesize that students who serially practice math skills (alternating among algebra, geometry, and word problems) will have significantly higher performance on retention and transfer tests than students who use blocked practice of each math skill."

Can you think of an experiment that would be able to test MH1?

Strong Measurable Hypotheses predict the outcome of experiments or other observations.

Simply reading MH1 suggests that it could be tested using a controlled design, where one group of students use serial practice and one group of students use blocked practice of math skills (algebra, geometry, and word problems). Average performance on two tests (retention and transfer) could be compared between the two groups using a statistical test (e.g. a t-test).

There are still quite a few areas that need to be specified. For example, the appropriate student population to recruit, the amount of practice (e.g. how much practice per day for how many days), the degree of interleaving (e.g. how much time to practice each subject before moving on to the next), whether practice will be spaced with rest breaks or not, the specific type of retention and transfer tests to use, and many others. The approaches chosen for each area, and the reasons for choosing each approach, can be specified and justified in the Methods section of the paper. Therefore, although Measurable Hypotheses cannot express all details of an experiment, strong Measurable Hypotheses predict an experimental design and outcome that depend on a limited number of the most relevant variables.

Measurable Hypotheses are Predictions.

A rule of thumb for writing Measurable Hypotheses is note that Measurable Hypotheses are predictions. Therefore, it should be easy to write a Measurable Hypothesis as a prediction. For example, if we simply change the word "hypothesis" to "prediction" in MH1, the statement should still make sense:

MH1: "We predict that students who serially practice math skills (alternating among algebra, geometry, and word problems) will have significantly higher performance on retention and transfer tests than students who use blocked practice of each math skill."

One approach to writing strong Measurable Hypotheses is simply to begin writing with the words "We predict," and revise the prediction until it is specific enough to be compared directly to the outcome of an experiment that you can actually perform. Once a statement makes a prediction specific enough to directly test, then the statement is ready to be a hypothesis, and you can simply replace the word "predict" with "hypothesize."

Measurable Hypotheses are based on General Hypotheses.

Although the distinction between General and Measurable Hypotheses is important, General and Measurable Hypotheses are closely linked. Specifically, Measurable Hypotheses are predictions that come from specific General Hypotheses. For example, let's re-visit our third General Hypothesis:

GH3: "Non-repetitive study results in lower performance during practice, but more learning, than blocked study of mathematics skills."

GH3 is a reasonably specific General Hypothesis, but still does not make predictions that we can directly compare to the outcomes of experiments. To make testable predictions, we can specify that serial study is one specific approach (out of many possible ways) to make study non-repetitive. We can also specify that retention and transfer tests are techniques for assessing learning. Therefore, we can create at least 3 Measurable Hypotheses from GH3: Useful Measurable Hypotheses use variables that we can directly measure.

To an extent, Measurable Hypotheses are operational: strong Measurable Hypotheses are expressed in terms of measurements sufficient to test the hypothesis. Three common ways of testing Measurable Hypotheses are:

1) Significant differences among groups (requires STATISTICAL comparisons, t-tests, ANOVA, etc.).

2) Significant differences over time (requires STATISTICAL comparisons, paired t-tests, repeated-measures ANOVA, etc.).

3) Significant correlations (requires STATISTICAL comparisons, coefficients of determination, etc.).

Although it is not necessary to include details of which statistical tests will be performed, writing Measurable Hypotheses that clearly lead to statistical comparisons (or other objective criteria) is helpful.

Measurable Hypotheses do not need to be one sentence.

Similar to General Hypotheses, Measurable Hypotheses can be as many sentences as necessary to explain the Measurable Hypothesis. For example, we may choose to clarify Measurable Hypothesis 2 (above):

"MH 2: Serial study will result in significantly higher scores on algebra, geometry, and word problem tests than blocked study during retention tests. We will test for retention one day following practice and 10 days following practice."

Additional clarification may require additional sentences. However, all clarifications are part of the same Measurable Hypothesis. 