Comparative Physiology BIO 112
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This 6 page Class Notes was uploaded by Hilda Schumm on Wednesday October 28, 2015. The Class Notes belongs to BIO 112 at Wake Forest University taught by Staff in Fall. Since its upload, it has received 10 views. For similar materials see /class/230718/bio-112-wake-forest-university in Biology at Wake Forest University.
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Date Created: 10/28/15
Statistics for Bio 112 lab Background Did my treatment affect the measured variable When you are trying to determine if your independent variable has an effect on your dependant variable you will often do so by comparing two sets of data your control and your experimental data Remember you are using only a sample of the experimental universe 7 the situation is equivalent to if I wanted to see if giving lab students candy increases their performance on the quiz and took 3 students from the lab and gave them the quiz and 3 others to which I gave candy and the quiz There are two possibilities 1 Your control data is not di erent from your experimental data It means there was no effect of the independent variable on the dependant variable and that any difference that is observed is due to chance only 0 If I randomly picked 3 students out of the class the mean quiz grade of these students by chance could be higher or lower than the mean of the entire class 0 As a result the means of two groups containing 3 students each can be different by chance only Note as the sample size increases the sample mean gets closer to the class or population mean 2 Your control data is di erent from your experimental data It means there has been an effect of the independent variable on the dependant variable 0 Maybe candy does affect student performance on the quiz In this case one would expect the difference between means to re ect an effect How can we make the difference between the two options Statistics are a tool scientists use to assign a probability or likelihood to each of these two possible outcomes and therefore to make the strongest possible conclusions from limited amounts of data Statistics provide an output or P value that corresponds to the probability that the two data sets are not di erent in other words the probability that the difference between data sets that is observed is due to chance alone If you remember probabilities since only two outcomes are possible it means that the probability of a signi cant effect is equal to lP o The way it works is that if case 1 is true one can expect the difference between means to be most often within a certain range As an extreme example one can be sure that this difference will be smaller than the highest minus the lowest grade in the class 0 If the difference between means falls outside the range that is likely to contain most of the differences then it is likely that something other than chance has caused it Scientists agree that in most cases if the probability of the outcome being due to chance only is less than 5 or P lt 005 then it is acceptable to state that there is a signi cant di erenee between data sets or a significant effect of the treatment Note Statistics never give you a yes or no answer but a probability for yes and for no Bottomline If plt005 you can say that the data sets are significantly different If pgt005 they are not The lowest the pvalue the highest your confidence that data sets are different Delphine Masse Wake Forest University Bio 112 Lab Fall 2004 2 There are many types of statistical tests but in this lab we will limit ourselves to T tests Ttests are simple tests used to compare two sets of data points and see if they are different There are two types of ttests we will use the names here are the names used by Excel a T test Two sample assuming unequal variances This is the basic type of ttest also called Student s ttest It usually applies to data where each study subject is measured only once If you were to put your data in two columns you could shuf e the data in one column without altering your data group group Equivalent to b T test paired two samplefor means This test is a special case of the test above and is typically used to compare two measures of the SAME individuals at different times for example in a beforeafter study In other words the measurements are paired two by two hence the name In this case shuf ing one column of your data would break up the pans Student Heart rate before Heart rate after NOT Student Heart rate Heart rate after caffeine bpm caffeine bpm Equivalent before caffeine bpm to caffeine bpm 1 90 1 90 2 m 60 2 60 3 95 3 95 Be very careful when you choose which test to use If you are in doubt always choose the regular ttest Working examples i You want to determine if Wake Forest Undergraduates have higher blood pressure than Duke Undergraduates You will have two groups one with Wake undergrads and one with Duke undergrads and will measure their blood pressure To determine if blood pressure of Wake undergrads is signi cantly different from blood pressure of Duke undergrads will you use a regular or a paired ttest ii You want to determine if being in school increases blood pressure of Wake undergrads You could measure blood pressure of a group of students while they are on holiday then measure blood pressure of the SAME students when they are back in school In order to compare these values will you need to use a regular or a paired ttest iii Now if you want to address the same question as in ii and you measured the blood pressure for one group of students that were away from school and of one group of students that were in school Which test would you use Delphine Masse Wake Forest University Bio 112 Lab Fall 2004 How to use MS Excel to run ttests Go to Tools then select Data Analysis Note this option is not present select AddIns and check the Analysis Toolpack option then go to data analysis xamvl lnr qravh mg g Mew lnsevt ngmat m mggg 1 1753211in F7 Was 6 Enmthetbnq a 7 E U 1K v Speech 39 Shale wkaan hack Changes Aft EWIEEUW gt Treatment 1 391 mg anvevsmn owing allahmatmn 1 1 Sally 1 7 2 1 1 2 ngmgg mm gdllmq Yuals an the Web ii Mann 14 4 MKSheetl cm 5mm ReadY an Ins ammm Options v0 guszame Ojtmns ganamanai Sum Lamp gate Analysis l The following window will pop up Data Analysis 7 31g nalysis Tuuls Anuva Twu Facluv Wlthuut Replitatlnn A thin Cancel unela ovavlance Jescnptiv Statistlcs I Help Test TwoSample for Vaviances ouHer Analysis Delphine Masse Wake Forest University Bio 112 Lab Fall 2004 A 1 Student Hes assummg unequal vanances your data could look like the example below Treatment 1 Treatment B 1 Paved Hest Your data could look like the example below Subject number Before A er L bML L m lmludwd autumn A2 Select retest Twu 51le assuming unequal Vanances and click OK note Analylls Aquot 55 Tank mayquot veraue dam Numbav Sensualon B2 Select T4252 paved twn Samplefm means and click OK nnzn Anulyns Analsis Yuols e cells containing the data for your first treatment to select them Do the same thing with variable 2 and the data for your second treatment lfyou selected the labels too check the labels box ill p vstsuieirsue 3 Vavtahle 2 Fame la Camel Winthgslzed Mean DWEYSKE If Lleb 39 gs els glut nus nah new assure n teens it s le Agsurmn E al Vanish tr wasample 7 i milieu one We Sample Vus Ywu Sample fur Means zleak on Sample Fm Means A3 The following window appear B 3 the following window appears In the variable 1 field click on then click In the variable 1 field click on then click on the cells containing your before datato select them Do the same thing with variable 2 and your A er data lfyou selected the labels too check the labels box l Its no Twn Snmvh39nr Mums Input Valabe tusnge Valarie Range Hluotheslzed Mean oilreienre I Labels Erma u us A4 The window would look like this Click OK B 4 the window would look like this Click OK Delphlne Masse Wake Forest Univ ersity Bio 112 Lab Fall 2004 B5 The output looks like this 1 5 c trTesl Palm 1 1m 1 it 51 H T I 591019 men 795 me 1 ZESNMEE 2 Mean 1 555557 2333333 am 5 235595235 5 555555557 quot3quot 3355557 U 555557 555 7 7 Ohservatluns E E quotHyputhesizei Mean 515212an 5 Peavsun Curvelalmn U 857722 1 Hypothesized Mean 55512055 5 9 1 St 71 955795535 1 5 1 7124511 5 537559554 1 Stat A7 1 cyitirai unetaii 1512451555 7 15Tltt twurta 5 575519355 F39Tlt0 WENquot U 005405 E Cutirai twurta 2 225139235 1 CYIUEaI 00571311 2 E55049 lt1 tw5 tail U DDUBW t Cutlcal 75435 2 57U578 A6 Interpretation you are interested in the B6 Inlelpraa on you are interested in the PTlt4 twotail This is your Pvalue pug twotail This is your PValue o prlt005 the mean for treatment 1 is o IfPlt005 like here the mean for Before Szgm camly dz mm from the mean for is Szgm camly dszzmmfrom the mean for treatment 2 0 IfPgt005 the mean for before is no 515005 like here the mean for tr ment 39 from the mean for treatment after A A Test TwnSawie A2515quot 50 that m va mm nest patienmn Samnietheans r I 2 7 51mm 15 3 Before ARer 39 I 555557 2 533333 Mgan A 5 Vanancs 5555557 5555557 5 Observations 5 5 7 Pearscm Cnnzlalmn 5 557722 8 Hypothesizeu Mean 515mm 5 797 5 15 t5tat e7 Lima 5524311 5 555455 12 tcnieain 4311 2515549 13 i 1 1 2mmm Delphine Masse Wake Forest University B10 112 Lab Fall 2004 My t test results don t make sense what should I do During this semester you may run into an odd situation You would intuitively see a large difference in each of your test samples but then the test would say there is no signi cant difference Here is why Statistical tests are not fool proo There are two risks associated with statistical tests 1 The risk of having a quotsigni cant difference according to the test when nothing happened a We call that quotType I errorquot b The probability of making that mistake is the same as your Pvalue For example if p 001 there is a 1 chance that you are making a type I error 2 The risk of having no quotsigni cant difference when there was actually an effect a We call it a quotType II errorquot b Its probability depends on two things i The type of test you are using not a concern here ii Your sample size When your sample size is small it is much more difficult for the test to detect effectschanges There is a tradeoff between the two risks most likely if your test has a low risk of Type I error it will often have a higher risk of Type 11 error Scientists think it is preferable to have a type 11 error rather than a type I error so often tests will have a very high type II error risk when sample size is small Usually statistics are used with sample sizes of at LEAST 10 or 15 Because of the limitations of this lab you ll often have to deal with sample sizes of3 The bottomline 1 Run the statistics and report the results 2 Describe the trends shown by your graphs You can mention a high risk of type 11 error in case the trends and statistics do not seem to agree Delphine Masse Wake Forest University Bio 112 Lab Fall 2004
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