Spring2013_Lab5

=Data Collection and Analysis (Lab 5)=

Collective class data:
click on this link to get the class data: @https://docs.google.com/spreadsheet/ccc?key=0AvVyF7Sp08nJdE0wTmFTOTAzTFZaWXZUcXBWSlJhTGc&usp=sharing

Hints on worksheet
If you want to double-check our math, because maybe you're getting weird numbers, remember that the lab workbook has step-by-step instructions on how to calculate the variance, standard deviation, and average. If your work matches these calculations, you'll get it right every time. If you have any questions on what the lab book is saying, just email me or set up a time to talk. I have office hours from 9-11 on Wed.

Lecture topics and questions:
Average and Median are two ways to analyze a group of numbers. How are these calculations affected by different types of groups of numbers? When should you use median and when should you use average?

Your hypothesis is a statement about all the possible plants, ping-pong balls, or whatever it is that you are studying. You make an experiment to test your hypothesis, but you only experiment on a sample of the total possible data. This is a sample of the population of all possible data. When you run your experiment, you will get a result of a group of numbers, and from these numbers you can calculate statistics, such as average, median, etc. What happens if you re-run the experiment? Will you get the same numbers?

Most likely, if you re-run the experiment, you will get a different set of numbers. But these new numbers will probably be within a certain range of numbers. For example, you won't get a plant growth of 10,000 feet. That's crazy talk. So if you re-run the experiment, you will get a new set of numbers that reflect the biology of your experiment. In addition, if there is a relationship between the different experimental parameters (the independent and dependent variable), then if you re-run the experiment, you should see this relationship in the new numbers, too. So, if there is a relationship between the variables in your experiment, then you will see this every time you re-run the experiment. The trend that is present in the real-world population will always show up in your results.

So if these is going to be a certain range of numbers for your new results (in each of your re-run experiments), is there some way to calculate this range of numbers? And can you calculate how confident you should be in your numbers? This gets back to calculating a probability, based on your sample. If you grow plants in an experiment, and 7 out of 10 plants grow between 10 and 14 cm, then you can say that when you grow a plant in the same conditions as in your experiment, then 70% of the plants will grow between 10 and 14 cm.

But let's focus on the average. What if you wanted to predict what the average would be, if you re-run the experiment? By calculating the standard deviation, the standard deviation gives you the amount, above and below the average, that gives you the range of numbers (confidence intevral) which could predict the new average, if you re-ran the experiment. But, not all of your new averages (from re-running the experiment many times) will fall within this range. So don't be too confident in the interval you calculated.

The secret it, if you use calculate the range using 1.00 standard deviations (and then divide this number by the square root of the sample size), your range will predict the new averages in 67 out of 100 experiments (67% confidence interval). If you go 1.96 standard deviations, then the averages from each new re-run experiment will be within this range 95% of the time; in 5% of the re-run experiments, the average will fall outside this range.

When I calculate a confidence interval, I use the sample data that from my experiment. This confidence interval then predicts the average for future experiments. It doesn't talk about my current average, which will always fall within my confidence interval. In class, you analyzed the data from 20 ping-pong balls. The other groups used different sample sets. But also, these other groups essentially re-ran your experiment. In this way, you can compare your confidence interval with the average from the other groups. The confidence interval predicts the range of averages you would get, if you re-ran the experiment. If you re-ran the experiment, then you could observe these other averages and see if your confidence interval was worth its salt.

Quiz topic
Quiz 3 will be on Tue the 5th, and it will cover the Plant lab (this is old material, not many points), Animal Diversity (this is the last lab, the most points will cover this), and Digestion and Metabolism (future lab, not many points here).

Quiz 4 will be on Thurs. the 7th, and it will cover the Animal Diversity lab as the old material, Digestion and Metabolism as the current material. The questions will be over both of these topics in equal amount.