Hypothesis testing and variables
Hypothesis Testing
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Research Hypothesis and Null Hypothesis
Research hypothesis is what we are theorizing we will find (in other words what we want to find)
Null hypothesis is the exact opposite of the research hypothesis. The null hypothesis is what you are testing statistically.
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Research Hypothesis and Null Hypothesis: Example
Research Hypothesis: College students who take a freshmen writing course will earn better grades in upper-level courses with an emphasis on written work.
Null Hypothesis: There is no difference in the grades for students who took a freshmen writing course and those that did not.
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Why a null hypothesis?
If the null hypothesis is not rejected, then we can never know if our research hypothesis is correct.
We MUST reject the null in order to be certain of our results.
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Hypothesis Testing
Researchers want to draw conclusions about a particular population.
e.g., babies in general
Conclusions will be based on results of studying a sample.
e.g., one baby
Copyright © 2011 by Pearson Education, Inc. All rights reserved
The Core Logic of Hypothesis Testing
Researchers must spell out in advance what would have to happen in order to allow them to conclude that their hypothesis was supported. (Null hypothesis and level of significance)
They then conduct their study
Then they figure the probability of getting their particular experimental result if their hypothesis was not true.
If we reject the opposite prediction, we can accept our prediction.
Copyright © 2011 by Pearson Education, Inc. All rights reserved
The Hypothesis-Testing Process
Step 1: Restate the question as a research hypothesis and a null hypothesis about the population.
Step 2: Determine the characteristics of the comparison distribution.
Step 3: Determine the cutoff sample score on the comparison distribution at which the null hypothesis should be rejected.
Step 4: Determine your sample’s score on the comparison distribution.
Step 5: Decide whether to reject the null hypothesis.
Copyright © 2011 by Pearson Education, Inc. All rights reserved
Hypothesis Testing: Step 1
Restate the question as a research hypothesis and a null hypothesis about the populations.
Population 1: students who participate in a reading program
Population 2: students in general (who do not participate in the reading program)
research hypothesis
Students who participate in this reading program (Population 1) will be able to read at a higher level than students in general (Population 2).
null hypothesis
There is no difference in reading level between students in the reading program and students not in the reading program.
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Copyright © 2011 by Pearson Education, Inc. All rights reserved
Hypothesis Testing: Step 2
Determine the characteristics of the comparison distribution.
comparison distribution
distribution used in hypothesis testing
represents the population distribution if the null hypothesis is true
Find out the key information about the comparison distribution.
e.g., population mean, population SD, shape of the distribution (does it follow a normal curve?)
If the null hypothesis is true:
Population 1 and Population 2 are the same.
Copyright © 2011 by Pearson Education, Inc. All rights reserved
Hypothesis Testing: Step 3
Set a cutoff sample score or critical value.
This is a target against which you will compare the results of your study.
By setting a cutoff score, you are deciding how extreme a sample score would need to be in order to be too unlikely to get such an extreme score if the null hypothesis were true.
Researchers use Z scores and percentages to set the cutoff scores.
Copyright © 2011 by Pearson Education, Inc. All rights reserved
Hypothesis Testing: Step 4
Determine your samples score on the comparison distribution.
Figure the Z score for the sample’s raw score based on the comparison distribution’s mean and standard deviation (the population mean and the population standard deviation).
Implications of Rejecting of Failing to Reject the Null Hypothesis
When you reject the null hypothesis, all you are saying is that your results support the research hypothesis.
The results never prove the research hypothesis or show that your hypothesis is true.
When the results are not extreme enough to reject the null hypothesis, you do not say that the results support the null hypothesis.
You say that the results are not statistically significant, or that the results are inconclusive.
Let’s complicate things...
One-tailed and two-tailed hypothesis tests
Directional (one-tailed) hypothesis: predicts a specific direction of difference. For example, that the sample mean is higher than the population in general.
Nondirectional (two-tailed) hypothesis: makes no assumption at the direction of the difference.
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One-Tailed and Two-Tailed Cutoff Z-scores
| One-Tailed | Two-Tailed | |
| .05 Significance Level | -1.64 or 1.64 | -1.96 or 1.96 |
| .01 Significance Level | -2.33 or 2.33 | -2.58 or 2.58 |
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One-Tailed Test
The benefit to a one-tailed test is that you can establish statistical significance with a less extreme score
BUT you risk having to ignore possibly important results
Because we are testing null hypotheses, we are always conducting a two-tailed test.
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Decision Errors in Hypothesis Testing
Decision Errors: The right procedures lead to the wrong decisions.
Why do decision errors happen?
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Type 1 Error
You reject the null hypothesis when in fact it is true.
Your chance of making a Type 1 error is determined by your significance level – either 5% chance or 1% chance.
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Type 1 Error
What are the implications for making a Type 1 error?
How do you lessen your chance of making a Type 1 error?
Why not just set the significance level at p=0 and eliminate any chance of Type 1 error....
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Type II Error
Because lowering your chance of Type I error increases your chance for Type II error.
Retaining the null hypothesis when it is false.
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Type II Error
What are the implications for making a Type II error?
How do you lessen your chance of making a Type II error?
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Decision Error
Remember, you cannot know if you have made a Type I or Type II error!
But, how can you attempt to lessen the chance of making both types of errors??
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Conventional Levels of Significance
Two conventional levels:
p<.05
The probability (p) of getting a sample score this extreme if the null hypothesis is true is less than 5%.
p<.01
The probability (p) of getting a sample score this extreme if the null hypothesis is true is less than 1%.
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Copyright © 2011 by Pearson Education, Inc. All rights reserved
Hypothesis Tests about Means of Samples in Research Articles
Z tests are not often seen in research articles because it is rare to know a population’s mean and standard deviation.
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Hypothesis Tests as Reported in Research Articles
In research articles, for each result of interest, the researcher usually says whether the result was statistically significant.
The researcher gives the symbol for the specific method used in figuring out the probabilities.
There will be an indication of significance level (e.g., p < .05 or p < .01).
Usually a two-tailed test is used; if this is not the case, the researcher will generally specify that a one-tailed test was used.