BOLD Educational Software
Writing Hypotheses

Getting Started

Hypotheses are derived from the purpose statement.
If you do not have a clear vision of your problem and purpose statements, you cannot write your hypotheses.
While the problem is something to be solved, the purpose addresses the problem, and the hypotheses address the purpose.

A hypothesis is the researcher's prediction, derived from a theory or speculation, about how two or more measured variables will be related to each other.

The two variables can be from two groups, or comparing the group to a predetermined parameter. For example, if you know the mean score of all students who took the SATs BEFORE this year’s group, you can compare this year’s group to the population.

Quantitative studies are designed to test hypotheses.

Qualitative studies are often designed to develop theories and hypotheses to be tested using quantitative analysis.

Beliefs/Predictions

A hypothesis is the researcher's belief about a population parameter, or a comparison of two population parameters (e.g., male vs. female)
A parameter is the population (true) mean

Before Analysis

The hypothesis must be stated before analysis. Scientific research cannot be conducted without following a set process (i.e., gathering data and then data snooping is not permitted)

Null Hypothesis

A hypothesis comes in a number of different ‘flavors’:
The null hypothesis states that there is no significant difference, or that the means are equal.
If the null indicates a direction, as in the mean is equal to OR LESS THAN 3, then the null hypothesis will be accepted ANYTIME the test mean is equal to or less than 3.

Alternative Hypothesis

The alternative hypothesis states that there is a significant difference or relationship or that the means are NOT equal.
If the null indicates a direction, as in the mean is equal to OR LESS THAN 3, then the ALTERNATIVE hypothesis is the opposite: the mean is GREATER THAN 3.
The ALTERNATIVE never has ‘equal’ in it.

Directional Hypotheses

Alternative hypotheses MAY specify direction:

The alternative hypothesis (non-directional): there is a significant difference
The alternative hypothesis (directional): Mean one is significantly greater than mean two
The alternative hypothesis (directional): Mean one is significantly smaller than mean two

The alternative hypothesis (non-directional): there is a significant relationship
The alternative hypothesis (directional): There is a significant and positive relationship
The alternative hypothesis (directional): There is a significant and negative relationship

If the statistical analysis is significant but NOT in the predicted direction,
the null hypothesis CANNOT BE REJECTED.

If the alternative hypothesis DOES NOT specify direction, then the null hypothesis is rejected regardless of the direction if the analsyis is significant.

For example, if the alternative hypothesis is that men will score significantly higher than women in math, but the results indicate women are significantly higher, then the null hypothesis cannot be rejected.

By contrast, if the alternative hypothesis is that there is a significant difference in math scores by genderand the results are significant, you reject the null regardless of WHICH gender's mean is higher.

Significance Level

Just because two means are different does not mean they are SIGNIFICANTLY different!
Use the SIGNIFICANCE LEVEL (the level set by the researcher prior to conducting the study) and compare it to the test statistic’s significance level (p-value)

The significance level defines unlikely values of a sample statistic if the null hypothesis is true
The significance level is called the rejection region of the sampling distribution
The significance level is a probability
The significance level, or alpha, is selected by researcher before beginning analysis
Typical values are .05, .01, .001

Critical Value

The critical value is the dividing point between the region where the null hypothesis is rejected and the region where it is not rejected.
The critical value is determined by the the p-value.
If alpha is set at .05 by the researcher, and p = .04, reject the null hypothesis that there is no significant difference or relationship.

Read more at http://bold-ed.com/barrc/hyptest.pdf

Reject/Fail to Reject

We reject or fail to reject the null hypothesis.

Theory Behind
Hypothesis Testing

Hypothesis testing is based on the theory that, in a distribution of sample means, if the TRUE POPULATION MEAN is the center point, then the odds of finding a mean too far away from that center get less as you move to the side.
So, if you have a normal population of 100 people with a true mean 75 on their test scores, if you randomly select two people, the odds are greater that you will find a mean close to 75, say 73 or 77, than you will find a mean of 99 or 31.
If you DO find a mean of 31, it is possible, even probable, that the people in that sample belong to ANOTHER POPULATION who’s true score is closer to 31 – say 35 – than it is to the original population whose true mean is 75.

Example 1

Research Question: What is the effect of a radio ad on weekly sales?
Null Hypothesis: A radio ad has no significant effect on weekly sales.
Alternative Hypothesis: A radio ad has a significant positive effect on weekly sales.

Example 2

Research Question: Is there a significant diference in employee job satisfaction based on type of leadership (transformational vs. transactional) of the supervisor?
Null Hypothesis: There is no significant difference in level of employee job satisfaction in employees who work for transformational leaders compared to transactional leaders.
Alternative Hypothesis: Employees who work for transformational leaders will have significantly higher job satisfaction than employees who work for transactional leaders.