Statistical Significance

[Terik Daly]

Beka,

I'm not sure that I understand your question. The Pearson Product-Moment Correlation Coefficient is generally referred to as r, but there are many different types of correlation and the symbols used sometimes vary from text to text. What text are you using? Perhaps you could post the formula that you are using as well as a detailed description of the process you went through to calculate the statistic in question.

I'm also a bit confused about what you mean by "I feel I have enough to explain with the chi-square and p-values!" The Chi-square is a test that produces a p-value. Do you mean that you have enough to explain about how and why you used a Chi-square and then the interpretation of the p-value produced? Or are you using another method in addition to Chi-square to get an additional p-value. You need to be careful that you aren't doing lots and lots of different kinds of statistical tests lots and lots of times because then you get into issues associated with multiple testing. It's a bit much to explain two days before the fair, but if you go on, we can discuss this more.

Your conclusion should be short, sweet, and to the point. Nothing is more unhelpful than a lengthy conclusion. I would say something along the lines of "I found strong evidence that [population description here] [insert conclusion here]." You can discuss the sampling issues in your discussion.

[Beka]

Terik,

Thanks for your quick reply!

Yes, I feel I have enough to explain about how and why I used a Chi-square and the interpretation of the p-value produced. (This has been a crash course in statistics for me!)

I am using the following website for the statistical tests, I did not do the math myself.
http://faculty.vassar.edu/lowry/odds2x2.html
It does chi-square for data where all the expected cell values are over 5 or Fisher Exact Probability if one of the expected cell values are under 5. Most of my 'frustrated' tests use chi-square and my 'distracted' tests use Fisher, is that okay? Also, the website gave the p-values for Yates and Pearson. Is that okay that I listed both p-values on my display board?

One of the values the website produces the a 'phi coefficient'. I spent a long time trying to track down what this meant and if it is part of the data for the Chi-square or a totally different test, and I am still confused.

The main questions are
If p-values are <.05, does the chi-square test show correlation? Or do I need the phi coefficient to be in a certain range as well? Or is that a different test all together (Pearson Product-Moment Correlation Coefficient)?

There is an empty spot on my display waiting for my conclusion. I'm really having trouble with the wording. Which of these do you think is best?

My data provide convincing evidence that women over 30 years old in Washington State, who responded by saying store music was loud or had a strong rhythmic beat, tended to be more frustrated and distracted.

or

My data provide convincing evidence of a strong correlation between music with a strong, rhythmic beat and customer frustration and distraction, for women over 30 in Washington State.

or

I found a strong correlation that women over 30 in Washington State tended to be more frustrated and distracted when they described the store music as loud or having a strong beat.

Thanks again,
Beka

[ChrisG]

Hi Beka,
I don't want to butt in, but I see this is a time sensitive issue for you. In general, simplicity in presentation is good. You will want to make sure that your audience sees the main points of your experiment, and having multiple sets of statistical results can distract them from your more important conclusions. I recommend reporting only the Fisher test, which I believe will be reported for all your comparisons (and not just when one or more expected values are <5). You should also double check the chi-square results (when available) to satisfy yourself that the two tests give the same results in terms of whether a relationship is significant or not. You can keep this in mind in case it comes up in questions, but there's no need to confuse people with two types of tests.

Here is a page that describes the phi-coefficient:
http://www.andrews.edu/~calkins/math/edrm611/edrm13.htm
and another with some general rules about how to interpret them:
http://www.childrensmercy.org/stats/definitions/phi.htm
The phi-value will show you what sort of correlation you have (positive, negative, or none) and the p-value will tell you whether this correlation is statistically significant (and whether it is worth reporting). You can report your phi-values with accompanying interpretation (positive correlation, no correlation, negative correlation) but make sure that you keep in mind that it is possible to have a strong correlation that is not statistically significant (p is large; could result from random error) due to a small number of samples, and it is possible to have a relatively weak correlation that is statistically significant (p is small; is highly unlikely to result from random error) when the number of samples is large.

All 3 versions of your conclusions sound fine to me. Another possibility, if you prefer to avoid using the first person, would be something like "A strong correlation exists between music with a strong, rhythmic beat and customer frustration and distraction for women over 30 surveyed in Washington State." You might want to substitute "significant" for "strong".
Good luck!
Chris

[Terik Daly]

Beka,

I echo what Chris said completely.

Chris,

Thanks for jumping in!

--Terik

[Beka]

Terik & Chris,

Thank you for all of your help! I did not have time to redo the discussion section on my display and you were right about the multiple tests distracting the judges!

I did not make it to Intel ISEF this year. The competition at our state fair is very tough and I do not have a regional fair that I can go to, but I have two more years to try!

I am very happy about all of the things I learned through this process and know it will help me in college.

Thanks again,

Beka

[Terik Daly]

Beka,

I'm glad that you're feeling comfortable with the outcome of the fair. We wish you'd gone on to ISEF, too, but I'm glad that you are ready to keep trying. You've learned a lot this year, both about science and about how to present it, and all of that experience will help you be able to do an even better project next year. Congratulations on a job well done, on your dedication, your hard work, and your tenacity.

Terik