Transcript 9/21 or 22
Inquiry 1 written AND oral reports due Th 9/24 or M 9/28 During your presentation: •Look at your audience. •Project your voice. •Keep visuals simple and clear. •Explain completely and clearly but concisely (5-7 min). •Make sense. The written report for your inquiries will be formatted similarly to a scientific research article. •Title •Abstract •Introduction •Results •Discussion •Materials and Methods •References More stats... Chi2, R2, and sample size http://mathworld.wolfram.com/Chi-SquaredDistribution.html The Chi Square Test • A statistical method used to determine goodness of fit – Goodness of fit refers to how close the observed data are to those predicted from a hypothesis • Note: – The chi square test does not prove that a hypothesis is correct • It evaluates whether or not the data and the hypothesis have a good fit Two flies with different traits are bred together Out of 352 offspring 193 straight wings, gray bodies 69 straight wings, ebony bodies 64 curved wings, gray bodies 26 curved wings, ebony bodies Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display According to our hypothesis, there should be a 9:3:3:1 ratio of fly offspring Phenotype Expected probability Expected number straight wings, gray bodies 9/16 9/16 X 352 = 198 straight wings, ebony bodies 3/16 3/16 X 352 = 66 curved wings, gray bodies 3/16 3/16 X 352 = 66 curved wings, ebony bodies 1/16 1/16 X 352 = 22 Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display Apply the chi2 formula Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display Interpret the chi square value The calculated chi square value can be used to obtain probabilities, or P values, from a chi square table These probabilities allow us to determine the likelihood that the observed deviations are due to random chance alone If the chi square value results in a probability that is less than 0.05 (ie: less than 5%) The hypothesis is rejected Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display Interpret the chi square value Before we can use the chi square table, we have to determine the degrees of freedom (df) The df is a measure of the number of categories that are independent of each other df = n – 1 where n = total number of categories In our experiment, there are four categories Therefore, df = 4 – 1 = 3 Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display 1.06 Interpret the chi square value With df = 3, the chi square value of 1.06 is slightly greater than 1.005 (which corresponds to P= 0.80) A P = 0.80 means that values equal to or greater than 1.005 are expected to occur 80% of the time based on random chance alone Therefore, it is quite probable that the deviations between the observed and expected values in this experiment can be Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display Spreadsheet applications will compute chi2 Is the male:female ratio in the CNS different from the general population? What about relating 2 variables? What about relating 2 variables? R2 gives a measure of fit to a line. If R2 = 1 the data fits perfectly to a straight line If R2 = 0 there is no correlation between the data R2 gives a measure of fit to a line. birth month vs birth day 4 11 6 12 2 6 3 17 14 7 17 13 21 21 birth month vs birth day 30 R² = 0.01 25 Birth Day 20 15 10 5 0 1 3 5 7 Birth Month 9 11 Protein quantity vs absorbance Bradford Assay 3-7-05 0.160 2 R = 0.9917 0.140 0.120 0.100 0.080 OD595 0.060 0.040 0.020 0.000 0 0.5 1 1.5 ug protein 2 2.5 What about relating 2 variables? •To use R2 the data must be continually variable... R2 gives a measure of fit to a line. If R2 = 1 the data fits perfectly to a straight line If R2 = 0 there is no correlation between the data Samples vs populations Samples vs populations Population- everything or everyone about which information is sought Sample- a subset of a population (that is hopefully representative of the population) population sample Population- Sample- • U.S. census • Travis county • Dogs • Poodles • 1 – infinity • Prime numbers Why use a sample instead of a population? Why use a sample instead of a population? •Logistics Why use a sample instead of a population? •Logistics •Cost Why use a sample instead of a population? •Logistics •Cost •Time Samples: Random- each member of population has an equal chance of being part of the sample. or Representative- ensuring that certain parameters of your sample match the population. Replicates: Technical vs Experimental Technical replicate- one treatment is divided into multiple samples. Experimental replicate- different, replicate, treatments are done to different samples. Testing blood sugar levels after eating a Snickers: Testing blood sugar levels after eating a Snickers: Divide a participants blood into 3 samples and test blood sugar in each sample. Technical or Experimental replicate? Testing blood sugar levels after eating a Snickers: Test 3 different people. Technical or Experimental replicate? Testing blood sugar levels after eating a Snickers: Test the same person on 3 different days. Technical or Experimental replicate? What sample size do you need? What sample size do you need? It depends on the error you expect. To determine an appropriate sample size, you need to estimate a few parameters. •Means •Standard Deviation •Power: The probability that an experiment will have a significant (positive) result, that is have a p-value of less than the specified significance level (usually 5%). This calculator will help you determine the appropriate sample size: http://www.stat.ubc.ca/~rollin/stats/ssize/n2.html What sample size do you need? It depends on the error you expect. (So it is impossible to predict with 100% accuracy before the experiment is carried out.) Next lecture we will finish talking about setting appropriate sample sizes.