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## Testing PhilosophyIn every hypothesis test we have to chose between the null hypothesis and the
alternative hypothesis. But there is no level playing field between the two. One of them (H - The alternative hypothesis
- The null hypothesis
- Test design and test statistic
- Distribution as predicted by the null nulhypothesis
- Significance levels
- Conclusion
- Errors
## The alternative hypothesisThe alternative is the interesting part of the story behind a test. Situation 1: Testing a research hypothesis. Situation 2: Testing the validity of a claim. Situation 3: Testing in decision-making situations. ## The null hypothesisIn statistics, the null hypothesis proposes an
established model for the world. Then we look at the data.
If the data is consistent with that model, we have no reason
to disbelieve H We know what to expect according to H ## Test design and test statisticNow we have to set up our research. We specify what and how we will measure.
These measurements will be summed up in a single number, the
## Distribution as predicted by the null nulhypothesisGiven the setup and the specifications of H We have one sample that results in a single value for the test
statistic T. We would like to know if this result is
"Something" or "Nothing At All". Yes, then H “Fitting in nicely” is translated into a probability about
likelihood of occurrence given the null hypothesis. We call
this the sample significance = P( T = sample result or more extreme | the distribution for T
as predicted by H A large significance is consistent with the null
hypothesis, while a small significance is (very) unlikely
given H In many cases the alternative hypothesis states that
there is some difference between groups or between a
population (parameter) and a given number or distribution.
If we stick to the null hypothesis we have found
insufficient evidence against it.
If in a court case an accused person is acquitted due to lack
of evidence, because there are doubts regarding
the evidence, that does by no means implicate we have
proven that this person is innocent. He or she might be, but
that was not the issue. Not enough evidence
against H ## Significance levelsThe explanation above tells us that the choice between "stick
to H - Smaller than 0.10: some suspicion, but nowhere near conclusive evidence for H
_{A} - Smaller than 0.05: considerable evidence for H
_{A} - Smaller than 0.01: very strong evidence for H
_{A} - Smaller than 0.001: practically conclusive evidence for H
_{A}
In marketing research the default setting is that when the significance drops below 0.05 we will reject the null hypothesis. Please note that significances vary on a continuous scale and that the value of 0.05 is not written in stone. It was settled on when significances were hard to compute and so some specific values needed to be provided in tables. Nowadays calculating exact significances is easy (thank you SPSS) and so an investigator can report "sign. = 0.06" and leave it to the reader to decide how significant it is. Referring to outcomes where sign. < 0.05 as significant and where sign. > 0.05 as nonsignificant is problematic when the significance is close to 0.05. We are not dealing with an all-or-nothing situation, where 0.049 means everything and 0.051 means nothing. Ask yourself whether the effect is interesting enough for further research. ## ConclusionHow do we proceed when H - Are the results
**meaningful**? For example do they indicate market segments that can be targeted individually? - Are the results
**stable**? If our H_{A}shows only short-term or transitory differences it is not good enough to act on it. - Are the results
**actionable**? This means we can focus various marketing strategies and tactics on the different groups we found.
## Errors"Statistics is the only profession that demands the right to make mistakes five percent of the time." We base our conclusions on sample data. No matter how good the test design was and how well it was executed, a sample can never give you absolute centainty about the properties of the underlying population. The possibility of errors is inherent to any test. There are two types of errors we can make:
Note that we know the probability of a Type I error. It is equal to the significance. We can control this and impose a maximum (like 0.05) before we start the research. The probability whether a test will correctly decide that the null hypothesis is false is far harder to handle. It is called the power of the test. This topic is beyond this website. If you are interested start with searching on "power of a test". It gave over 75,000 hits on Google when I wrote this page. |

Last modified
30-10-2012
© Jos Seegers, 2009; English version by Gé Groenewegen. |