1. Chapter 16: Sample Size
“See what kind of love the Father has given to us, that we should be called children of God; and so we are. The reason why the world does not know us is that it did not know him. Beloved, we are God's children now, and what we will be has not yet appeared; but we know that when he appears we shall be like him, because we shall see him as he is.
1 John 3: 1-2

2. How many subjects should you test?
Introduction
How many subjects should you test?
When comparing groups to each other, it is impossible to compare all the subjects in a group to all the possible subjects in another group. We call all the possible subjects in a group the group population.
For example: if you were trying to find out which variety of tomato had the most acid it in, you would never be able to get all the beefsteak tomatoes in the world to compare to all the Roma tomatoes and all the cherry tomatoes in the world.
Vocabulary!
Sample size - this is a calculation that helps you decide how many subjects you need to test to find out an accurate answer to your question.
Group Population - all possible subjects in a group. Often includes
all the subjects that exist in the world.

3. Sample Size
Here’s a fun exercise that will show you that you need to test more than one subject to find out the answer to scientific questions. This works well if you know how to find an average. If not, simply compare the packages.
Procedure:
Open each of the 24 packages and count out the number of green M&Ms in each one.
2) Record the number in each bag.
3) Calculate the average from each bag and observe how it changes between each bag.
4) Note the point at which the average becomes more stable. Point out that this is the number of bags that would need to be tested to get a fairly accurate idea of the number of green M&Ms in a bag.
Get 24 small bags of M&Ms
Question: How many green M&Ms are in a personal size package of M&Ms on average?
Hypothesis: Make your hypothesis based on opening ONLY 2 packages and comparing the number in each package.
Write down your hypothesis:

4. m&m Sample Size
Compare the average you found for all 24 bags to your initial hypothesis and to each individual bag.
Can you see how it is important to look at more than one package?
If you only looked at 1 package, you might think that that package represented the number of green M&Ms in all packages.
You can see they are different and it is necessary to look at more than one bag.
Now consider your project:
Make a guess as to how many subjects do you think you should test? ____

5. Finding the right number
When you aren’t sure, it is a good idea to begin with a minimum of 10 subjects. Remember, the more you test, the more certain you are you have the right answer to your question. The judges will be looking to see if you really answered your question. They are looking for A LOT of tests.
One way you can determine how many subjects you need to test is to do a practice experiment. How many trials did it take before you could see a difference in your groups? Was it a meaningful difference?
Vocabulary!
Meaningful Difference - This term is used when we find differences between groups that really matter. For example, if you brushed the teeth on 10 dogs for 1 year and then did not brush the teeth on 10 other dogs for one year and you found that the dogs that had their teeth brushed only needed to have 1 tooth pulled from the entire group, but the dogs that were not brushed had 15 teeth pulled overall, that would be an important difference. However, if the group that was brushed only had one tooth pulled and the group that was not brushed only had 2 teeth pulled, that could have occurred just by chance alone.

6. Statistical Analysis Vocabulary!
This is for high school students or advanced middle school students!
If you will not be using statistical analysis, continue to the end of the PowerPoint
Vocabulary!
Type 1 Error - rejects a null hypothesis when it should have been accepted
Type 2 Error - accepts a null hypothesis when it should have been rejected.

7. Sample Size Calculations
How many subjects should I test? This is always a critical question to ask.
There is a mathematical calculation that will answer this question, but in order to understand it, it helps to have studied more advanced mathematics, especially statistics. You should not use calculations you do not really understand because you will not be able to explain it to the science fair judge should they ask. If you do use it, study it enough to really understand what you are doing.
Keep in mind testing too few subjects will not give you a wide enough range of participants to see results. If your sample size is too large, the costs of doing your project could be too high and you won’t be able to finish.
Here’s the formula:
Sample Size = (Z²) P (1 -- P) I²

8. Using the Sample Size Calculation Equation – Step One
Here is how to use the formula:
Step 1: Determine the confidence interval of your study.
Sample Size = (Z²) P (1 -- P) I²
The confidence interval also describes the amount of uncertainty associated with a sample estimate of a population. People often state things like, “there is a 90% confidence interval in this study”. That means that there is a 10% chance your answer is wrong.
Vocabulary!
Confidence Interval - the amount of percentage points above and below the mean that you find in your study where real true data should lie. For example, if you were studying how much practice time improves a 10 year old player’s ability to catch a football, might find that 60 minutes daily for 1 week improved the number of times they caught the ball by 53% on average. You might find the data ranged from 51% to 55%. Your confidence interval would then be +/-2%. It would be correctly written as 53% +/- 2%. This would be expressed as a decimal of 0.02 in your equation.

9. Using the Sample Size Calculation Equation – Step Two
Step 2: Determine the confidence level of your study.
Sample Size = (Z²) P (1 -- P) I²
Vocabulary!
Confidence Level - describes how certain you are that the true answer lies within your confidence interval. For example, if you choose a 95% confidence interval for the football practice question, that says that you are 95% sure that for the entire population of 10 year old football players, 60 minutes of daily practice for 1 week would truly improve their catching ability by 53%. You are willing to accept a 5% chance of being wrong. The 5% comes from = 100%.

10. Using the Sample Size Calculation Equation – Step Three
Step 3: Convert your confidence level to a Z-score by using a Z-score table.
Sample Size = (Z²) P (1 -- P) I²
Vocabulary!
Z value is taken from a Z value chart available on the internet and at the back of any statistics text book. Z scores are measures of standard deviation. For example, if a tool returns a Z score of +2.5 it is interpreted as "+2.5 standard deviations away from the mean". The Z score is a test of statistical significance that helps you decide whether or not to reject the null hypothesis.
Standard Deviation - shows how much variation exists from the average.

11. Using the Sample Size Calculation Equation – Step Four
Sample Size = (Z²) P (1 -- P) I²
Step 4: Predict the proportion of the study.
The standard bell curve follows the rule.
Approximately 99.7% of the data is between -3 and 3.
Approximately 68% of all of the data is between -1 and 1.
Approximately 95% of all the data is between -2 and 2.
Vocabulary!
P or proportion is amount of respondents you think will respond positively to the treatment in your study or your survey. For example in the football practice example, your proportion would be 53% expressed as 0.53 in your equation.

12. Using the Sample Size Calculation Equation – Step Five
Step 5: Compute the needed sample size by plugging your values into the formula, where:
Z is the Z-score,
P is the proportion, &
I is the confidence interval.
Sample Size = (Z²) P (1 -- P) I²

13. Using the Sample Size Calculation Equation to Calculate Your Sample Size
Try to get an idea of what your result should be when calculating sample size.
You can do that by looking at previous studies that were similar and finding out what their results were. For example, if you predicted a 53% percent improvement in catching the football but you only got a 20% percent improvement, you will not have tested enough people in your study. You will then have to go back and recalculate your sample size using the 20%. It is possible you will have to add subjects to your study to come out with a good result.
The bigger your positive response, the smaller the number of subjects you will have to test. The smaller the difference, the larger the number of subjects you will have to test.

14. Calculating Yours
Read more about calculating Sample Size here: How to Calculate Sample Size Formula | eHow.com sample-size-formula.html#ixzz21ZoVOFAE
There are many sample size calculators available on the internet to do the math for you. However, you still must understand the values you are entering in the machine in order to get a good result.
If this calculation is beyond what you are able to understand, choose a reasonable number of subjects to test. It is not appropriate to test just one because your experiment must be repeatable. You should likely test a minimum of ten subjects in each arm, but more is probably going to be much better.

15. Remember to write in your prayer journal and scientific notebook!!
Write in your notebook how you are going to determine how many subjects to test?
How many subjects do you really think you can reasonably get?