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# Biometry BIO 2801

Florida Tech

GPA 3.97

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This 9 page Class Notes was uploaded by Annette Leannon on Monday October 12, 2015. The Class Notes belongs to BIO 2801 at Florida Institute of Technology taught by Ralph Turingan in Fall. Since its upload, it has received 9 views. For similar materials see /class/221685/bio-2801-florida-institute-of-technology in Biological Sciences at Florida Institute of Technology.

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Date Created: 10/12/15

What doesthe r2 value mean This value indicates how much ofthe variation in the dependent variable quotyquot is explained bythe variation in the independent variable quotxquot in the model In this case study the regression model indicatesthat about 94 r2 0939 ofthe variation in heart rate ofthe snakes under investigation is explained bythe variation in temperature In otherwords we are confidentthat temperature affected heart rate in this case study Pearson Correlation Analysis Case Study Asample of 10 fish is randomly selected from a normally distributed population of Indian River Lagoon fishes Eachfish is weighed and measured and then dissected to remove the otoliths which are also measured The distribution of otolith length measurements is approximately normal Ho rho0 H1 rho 0 RQ Is there a significant correlation between otolith length and mass of fish in the Indian River Lagoon under investigation Test Stat r 08386 A strong correlation Ho Rejection region If r 2 critical r then reject H0 ifr 5 critical r then we failto reject H0 STAT Conc Since calculated r 08386 gt critical r 0632 we reject H0 BIO We conclude that there is a significant strong correlation between otolith length and mass of fish in the Indian River Lagoon r 08386 df 8 P lt 005 A niinimi usefulness of Samplesfrom 3 L 39 J b di mat in 39 aier hardne Ii 9 39 39 39 39 fromthe localwater authority Isthere a significant correlation between water hardness and number of Plecoptera nymphs Ho rS 0 H1 r5 1 0 RQ Is there a significant correlation between water hardness and number of Plecoptera nymphs Test Stat rs 087 A strong negative correlation Ho rej region If p lt 005 reject Ho if p gt 005 we fail to reject Ho STAT Conc Since p lt 005 we reject Ho Blo We conclude that there is a significant negative correlation between water hardness and numberof Plecoptera nymphs r5 087 n 13 P lt 005 REGRESSION ANALVSIS Case A snake physiologist wishes to investigate the effect of temperature on the heartarate of pythons These animals were approximately the same age and size and were allthe same sex Nine specimens were subjectedto nine different temperature regimes Ho 3 0 H1 3 0 RQ Generic Isthere a statistically significant linear relationship betweenthe two variables x and y Ex Isthere a significant causeaeffect relationship between heart rate and temperature Test statt 10421 Ho rejection reg If p lt 005 reject Ho if p gt 005 we fail to reject Ho STAT CONCL Since P 005 we reject Ho that the slope ofthe line that relates temperature with heart rate is zero BIO Concl We conclude thatthere is a significant linear relationship between heart rate and temperature t 10421 df 7 P ltltlt 005 REDUCED MAJOR AXISRMA OR MODEL 2 REGRESSION This is used when bothx and y variables are random iethe dependent variable x is not underthe control ofthe investigator This isthe case in Model 2 Regression recall Model 2 ANOVA Case Study Asample of9fish is randomly selected from a normally distributed fish population Each fish is weighed and measured and then dissected to remove the otoliths or ear stones which are also measured Isthere a significant linear relationship between otolith length and weight offish HVPOTHESIS TESTING IN REGRESSION ANALVSIS USING ANOVA THE ONLY WAVTO USE IN MODEL2 REDUCED MAJORAXIS REGRESSION Hypotheses Ho 3 0 p20 RQ Isthere a significant linear relationship between mass offish and otolith length Teststatistic F as inANOVA F Regression MS Variance Residual MS Variance calculated F 37211793 2366776 15729 STAT Concl Since Plt 005 we reject the H0 that B 0 BIO Concl We conclude that there is a significant linear relationship between otolith length and weight offish F 15729 df 1 7 P lt 005 Chisquare tests address questions about the distribution of discrete variables and observations on the nominal scale eg species color habitat Various forms ofthe Chisquare test 1 Test for GOODN ESS OF FIT 2 Test forASSOCIATION Test for Heterogeneity orTest for Independence Chisquare goodness offit Example The number of 39 q 39 are as follows L Poisson distribution Ho Observed Frequency Expected Frequency H1 Observed Frequency 1 Expected Frequency RQ Does the observed frequency of nematodes agree with the expected frequency based on random distribution ie Poisson Model Teststatistic 168 chi squared Ho Rejection If calculated 12 gt critical 12then we reject Ho If calculated 12lt critical 12thenwe do not reject Ho STATS Since calculated 12168 lt critical 12 1107 then we do not reject Ho BIO We conclude that the distribution of nematodes in L 39 aglee illl llle expected J J39 39L 39 it 39 q 39 bythe 39 df 1105 Pgt005 The ChiSquare test forASSOCIATION is used when TWO nominal levels Ul 39 quot J 39 39 F g 39 quot gender 39 found in running water The mobile larvae pupate independently on emergent stones vegetation etc wherethey may be collected A biologist investigating habitat preferences of four 39 39 pupae L 39 r 39 39 39 39 mesotrophic and eutrophic Ho Observed Frequency Expected Frequency H1 Observed Frequency 3 Expected Frequency RQ L L L J 39 39 r 39 39 their aquatic habitat Teststatistic 3098 12 Ho Rej Region 12 gt critical 12 then we reject Ho Ifcalculated 12 lt critical 12 then we do not reject HoSTATS Since calculated 12 3096 gt critical 12 1259 then we reject HoBIO We conclude that there is a significant association between the abundance of Dixa species and the state ofeutrophication of their aquatic habitat of 3098 Plt005 Normality test Ho 39 39L 39 L J39 39L 39 39 normal RQ Did L 39 from r r 39 Statistic 0976 Ho Rejection If p lt 005 reject Ho if p gt 005 we fail to reject Ho Stat Concl Since pgt005 fail to reject null hypothesis Bio Concl The samples came from populationswith normal distributions Test CORRELATION IS USED To DETERMINEIf an association between two variables exist and If so how strong is such an association By association we mean that if one variable changes the other variable changes in some consistent way In Regression Analysis a quotcauseaandaeffectquot relationship between the two variables is determined Pearson Correlation Coef cientused when both variables come from normally distributed 39 39 39 39 39 y 39 39 10 positive correlation r0 no correl r710 neg correl REQUIREMENTS OF PEARSON CORRELA ON ANALVSIS The sample is a random sample fromthe population of interest Both variables are approximately normally distributed Measurement of UUII 39 39 ratio scaleThe 39 L39r L the two variables if it exists is linear REGRESSION ANALVSIS How doyou draw a line through a scattergramTHE METHOD OF LEAST SQUARES Fittinga regression line to a scattergram involves placing it through the points so that the sum ofthe vertical distances deviations of all the points from the line is minimized REQUIREMENTS OF LEAST SQUARE REGRESSION There is a linear relationship between a dependent yavariable and the independent xavariable which is implied to be functional or causalThe xavariable is not a random variable but is underthe control ofthe observer RECALL MODEL I ANOVA FIXED EFFECTS MODELFor any single defined observation ofxavariable there is a theoretical population ofyavalues that is normally distributedThe variances of different populations of yavalues corresponding to different 39 39I39 39d 39 39 39 quot 39 39 39 39 1 quantifies the proportion ofthe variance in the y dependent variable that is explained by its dependence on the xaindependent variable 100r2 the residual or quotunexplainedquot variance ie the variance in ythat is not explained by its relationship withx Homogeneity ofVariance Ho The variance of sample 1the variance of sample 2 Ha The variance of sample 1 does not equalthe variance of sample 2 RO Did the samples come 39 39 39 39 ariaiice 39 39 39 If p lt 005 reject Ho if p gt 005 we fail to reject Ho StatConcl Since pgt005fail to reject null hypothesis Bio Concl The samples came from populations BIO 2801 FINAL EXAM page 1 NAME Lab Section PART 1 Short Questions Short Answers Use only the space provided 1 What does the r2 value mean in the following figure B I u u u u 875 n 26 p lt 0001 091 BodyTemp I I I 2m in AU Eanemp Figure Y Relationship between environmental temperature Eanemp C and body temperature BodyTemp C of a coldblooded vertebrate BIO 2801 FINAL EXAM page 2 PART 2 Hypothesis Tests Please use only the space provided In the following case studies test all the hypotheses that are necessary to address the main goal or objective ofthe study Follow the guidelines we used in class to select the appropriate statistical test Copy is attached in your examination booklet Make sure that tests for normality homogeneity of variances and differences in average are clearly stated following these logical steps in testing a hypothesis Hypotheses including the research question Test Statistic Null Hypothesis Rejection Region Conclusions statistical and biological conclusions IMPORTANT NOTE Your test of hypothesis SHOULD look like this Test of hypothesis comparing the means of two populations Carbin and Panal 1 Hypotheses Ho Meancarbin Meanpanal H1 MeanCarbin T Meanpanal Research Question Is the length of fish different between Carbin and Panal reefs 2 Test Statistic t 3697 3 Ho rejection region If p lt 005 reject Ho if p gt 005 we fail to reject Ho 4 Conclusions Statistical Conclusion Since p lt 005 we reject Ho Biological ConclusionThe body length of fish differs between Carbin and Panal reefs t 3697 df 16 p lt 005 BIO 2801 FINAL EXAM page 3 Case Study 1 A sample of 10 fish is randomly selected from a normally distributed population of Indian River Lagoon fishes Each fish is weighed and measured and then dissected to remove the otoliths or ear stones which are also measured The distribution of otolith length measurements is approximately normal A statistical analysis of this case study shows the following results r 08386 P lt 005 E m E V 5 a U 5 O l O c 8 39 o 2 o O 7 39 a C e so 100 150 200 250 300 Fish Mass 9 Figure 2 A scatter plot showing the correlation between mass 9 and otolith length mm of fish in the Indian River Lagoon BIO 2801 FINAL EXAM page 4 Case Study 2 Twenty fish traps were randomly set in each of six lakes to collect fish The objective of the study was to compare the abundance number of fish of this fish species among lakes Using the following set of SPSS output test the hypothesis or hypotheses that are relevant in addressing the objective of this study Tests of Normality KomogorovSmirnov ShapiroWilk Lake Statistic df Sig Statistic df Sig Abundance Ella 128 20 200 939 20 229 Alla 206 20 026 960 20 553 Alli 193 20 049 936 20 205 Elli 105 20 200 976 20 881 Aloe 115 20 200 942 20 261 Alex 1 18 20 200 958 20 507 This is a lower bound ofthe true significance Test of Homogeneity of Variances Dependent ariableAbundance Levene Statistic df1 df2 Sig 606 5 114 696 ANOVA Dependent Variable Abundance Sum of Mean Squares df Square F Sig Between 1585467 5 317093 16384 000 Groups Within Groups 2206400 114 19354 Total 3791867 119 Test Statisticsab Abundance ChiSquare 50914 df 5 Asymp Sig 000 a Kruskal Wallis quotest b Grouping Variable Lake BIO 2801 FINAL EXAM page 5 Case Study Test of hypothesis 1 Hypotheses H0 H1 Research Question 2 Test Statistic 3 Ho rejection region 4 Conclusions Statistical Conclusion Biological Conclusion Case Study Test of hypothesis 1 Hypotheses H0 H1 Research Question 2 Test Statistic 3 Ho rejection region 4 Conclusions Statistical Conclusion Biological Conclusion BIO 2801 FINAL EXAM page 6 Case Study Test of hypothesis 1 Hypotheses H0 H1 Research Question 2 Test Statistic 3 Ho rejection region 4 Conclusions Statistical Conclusion Biological Conclusion Case Study Test of hypothesis 1 Hypotheses H0 H1 Research Question 2 Test Statistic 3 Ho rejection region 4 Conclusions Statistical Conclusion Biological Conclusion BIO 2801 FINAL EXAM page 7 Case Study Test of hypothesis 1 Hypotheses H0 H1 Research Question 2 Test Statistic 3 Ho rejection region 4 Conclusions Statistical Conclusion Biological Conclusion Case Study Test of hypothesis 1 Hypotheses H0 H1 Research Question 2 Test Statistic 3 Ho rejection region 4 Conclusions Statistical Conclusion Biological Conclusion BIO 2801 FINAL EXAM page 8 Case Study Test of hypothesis 1 Hypotheses H0 H1 Research Question 2 Test Statistic 3 Ho rejection region 4 Conclusions Statistical Conclusion Biological Conclusion Case Study Test of hypothesis 1 Hypotheses H0 H1 Research Question 2 Test Statistic 3 Ho rejection region 4 Conclusions Statistical Conclusion Biological Conclusion

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