Phototaxis in Pillbugs and Linear Regression Concepts
Explore the concept of phototaxis in pillbugs and learn about linear regression, circular data analysis, and experimental design techniques. This insightful content covers key topics such as slope, hypothesis testing, and the difference between linear and circular data treatment.
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Presentation Transcript
Phototaxis in Pillbugs: Working with Circular Data Jason Dinh and Jesse Granger
Goals for today By the end of today you will: 1. Be able to describe what slope and ?2values mean in a linear regression 2. Implement your own experiment and test a hypothesis 3. Be able to identify circular data and articulate why it must be treated differently than linear data 4. Analyze and plot your own circular data
Photokinesis and Phototaxis Photokinesis: changing your behavior in response to a change in light levels Examples? Phototaxis: orientation or movement towards or away from a light source Examples?
Linear Regression Slope Spread (?2)
Linear RegressionSlope Ho: The slope = 0 Ha: The slope =/= 0
Linear RegressionSlope P < 0.05 P < 0.05 Ho: The slope = 0 Ha: The slope =/= 0 P > 0.05 P > 0.05
RecapLinear Regression Slope: Tells you if one variable covaries with another Ex: If x gets bigger y also gets bigger ?2: Tells you how much of the variation in Y can be predicted by X How much spread is there? If you were given x, how well could you predict y?
Photokinesis & Phototaxis How would you design an experiment to test for phototaxis?
Experimental Subjects Pillbugs are terrestrial crustaceans They live in dark, cool places like under stones and leaf litter. They are best-known for their defensive behavior of rolling into a ball (aka roly poly) Why would a pillbug be sensitive to light? Would you hypothesize positive or negative phototaxis?
Experiment Details Follow the instructions on the handout to complete your experiment!
Circular Data Linear Circular Test if slope is = 0 Test if points are oriented uniformly ?2 Mean resultant vector
Circular DataTest of Uniformity Ho: The points are oriented uniformly around the circle Ha: The points are not oriented uniformly around the circle
Circular DataTest of Uniformity Rayleigh Test of Uniformity: P=0.73 Rayleigh Test of Uniformity: P<0.05 Ho: The points are oriented uniformly around the circle Ha: The points are not oriented uniformly around the circle
Circular DataMean Resultant Vector Rayleigh Test of Uniformity: P<0.05 Rayleigh Test of Uniformity: P<0.05 Rayleigh Test of Uniformity: P<0.05
Circular DataMean Resultant Vector Rayleigh Test of Uniformity: P<0.05 Rayleigh Test of Uniformity: P<0.05 Rayleigh Test of Uniformity: P<0.05 Mean Angle: ~0 Resultant Vector Length: 0.89 Mean Angle: ~0 Resultant Vector Length: 0.72 Mean Angle: ~0 Resultant Vector Length: 0.44
Coding in R Open R
Comparing two distributions Test of Uniformity: p<0.05 Mean Angle: ~0 Resultant Vector Length: 0.89 Test of Uniformity: p<0.05 Mean Angle: ~300? or 5.2 rad Resultant Vector Length: 0.89
Comparing two distributions: Watson two- sample test Watson Two-Sample Test Ho: The mean of the two distributions are the same Ha: the means of the two distributions are different P <0.001
R-Shiny https://rfitak.shinyapps.io/circbio/
Exit Ticket Email jesse.granger@duke.edu, jason.dinh@duke.edu, and snowicki@duke.edu the following: Of your group s data: A picture of the circular plot, with the mean angle, of both the light on and light off group. The mean angle, Rayleigh test p-value, and mean resultant vector for both the light on and light off group Your interpretation of the results from the Rshiny App with the whole groups data. Was your hypothesis about phototaxis supported? In total: 2 plots, 2 Rayleigh tests, 2 mean angles, 2 mean resultant vectors, and your interpretation of the whole class s data
Linear Regression Residual= Y ? Y (? ? ) Y* ? ? 2
