# SOCR Activity ANOVA SnailsSexualDimorphism

(Difference between revisions)
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:Variable: Locality :Variable: Locality

## SOCR Educational Materials - Activities - SOCR ANOVA: Snails Sexual Dimorphism Activity

Many natural processes are observed directly or indirectly via recording quantitative measurements (e.g., height, length, time, size, etc.) These observations (or data) may have additional meta-data that describe the units, objects or subjects that we measure (e.g., gender, race, type, taxa, species, etc.)

## Motivation and Goals

When there are diverse types of qualitative and quantitative measurements that can be observed about the process, how can we make scientifically valid and robust inference of the data? This activity deals with the situation of a two-way analysis of variance (ANOVA). You will learn how to use the SOCR tools to deal with data that involves multiple variables.

## Summary

This activity will recreate part of the design of a classification method for the Cocholotoma septemspirale snail. By observing multiple traits of the shells, the original researchers were able to decide on a series of dimorphisms (difference in forms) between male and female snails.

The data set below is a reduced version of the Sexual Dimorphism in Snails dataset.

## Data Description

• Number of cases: 112
• Variable Names:
• Sex: Sex of the snail; 1 = female, 2 = male
• Location: Where the snail was found in Switzerland; 1 = Chasseral, 2 = Orvine, 3 = Combes de Nods
• shell.h: Height of the shell, in micrometers
• shell.w: Width of the shell, in micrometers
• aperture.h: Height of the shell aperture (where the snail comes out of), in micrometers
• aperture.w: Height of the shell aperture, in micrometers
• whorl.w: Width of the last whorl (spiral section) on the shell, in micrometers.
• rib.n: Number of ribs on the last whorl on the shell, in micrometers.

## Dataset

Sexlocalityshell.hshell.waperture.haperture.wwhorl.wrib.n
117063386025642522311929
117535384625222629333237
117484395226802541325834
117516376326712703321731
117211369825552541313330
117526382825732555314328
117576385124392504320732
117558378124712481314335
117674382826522513323031
117526378624392555316629
117641394325872481330030
117470408727122606328633
117262369325732504312438
117410378125322499315228
117799404527822666334231
117567385525832647322633
117428395224812546322632
117368373024482407311933
116915361524072259306929
117327392025872522321736
117502383726572536308732
217188400326292546327731
217178411927542670325825
217192386525872374310127
217035397126522647320731
216674382325322573300430
217470402728372694318427
217252395226292407316627
216739385526062439308729
217345399427212555316631
217419386926892564319829
217040383725132481312433
216623392025642564312426
217169398028282434316130
216956377726152495305029
216549374924712425299425
216831376325362407303630
217053398528052573318432
216919383724812448315232
216808391126662499310133
217137357324712522305027
216928385125872495316628
127294367924582356310133
127576378627212777314331
127840389227122471308232
127586386025732647320731
127715386025362546318433
127715401727772638330535
127456392926292680320332
127526387825832606329135
127526377226062564315233
127780377227352629321731
127077370323052337309234
127336378125552439314336
127544385525832638311936
227086407727722629314331
226716384626942689306929
227276392925872481317032
226928386027122564308234
226716381826892439308234
226915386927212388306935
227095392927122490311032
226928395227542638309230
227387380425922564311031
227095386926152541327233
227095384626382587311928
226938384626382638306932
227169372127452629309229
227035368925132397301829
227086378625962356310131
227123405927312819321734
227137387826842546313335
226956361924072296308231
227123392925502541312434
227220386926572448320733
227493397126802638323530
227271399426382620319333
137831394826472708336033
137863420727122694341630
137775395227212573329132
137715406826892430330029
137493389227312578317533
137243400826892786311032
138187420729532902349033
137850411927212680349935
138086412828192680329134
138211390626472541327731
137799392925642499335130
137683396227212666327231
137428395225412527325834
137715399427542657329136
137780399426472680338333
137567386925832365324934
137891394325732564320726
137526380426382522321732
137664388825552541324933
237003396225642439326834
237368407728602712315636
237276383725042300314330
237276381425462374316132
236989363321892161327735
237104381427632680308736
237123397127212564321732
237229385524392388328131
237396411925962661326830
237660372126802458319836
237044389227352546303634
237220377226472416308729
237317411929112869323532
236841396227632703315235
237294405427542416316632
237873419329202893334230

## Exploratory data analyses (EDA)

Various data patterns may be observed and explored using different types of graphical tools for plotting variables. Which of the following graphs are more or less likely to demonstrate visually significant grouping differences?

## Quantitative data analysis (QDA)

Open the SOCR ANOVA-Two Way applet (requires Java-enabled browser).

Copy and paste the Sex and Locality data into the first two columns. Pick one of the other six variables (in this case, Shell.h) and copy that data into the third. Use the ctrl + c command and the "paste" button in the applet. Name the three columns appropriately.

Next, click on the “mapping tab”. Select "sex" and "locality" as the independent variables. Next, name the third column as your dependent variable. We will use "shell.h" in the following example, but it is recommended that you use another in its place to explore these measures. Make sure you click “turn the interaction” on,

Press the Calculate button. This should bring up the results page with the following text:

ANOVA results
Sample Size = 112
Dependent Variable = Shell.h
Independent Variable(s) = Locality Sex Interaction Locality: Sex
*** Two-Way Analysis of Variance Results ***
See EBook's Standard 2-Way ANOVA Table
Main Effect: Locality21912452.01667956226.0083318.396510.00000
Main Effect: Sex16197835.013126197835.01312119.238090.00000
Interaction Locality: Sex2161192.2539280596.126961.550560.21690
Error1065509737.0135951978.65107
Total:11113170123.10714
Variable: Locality
Degrees of Freedom = 2
Residual Sum of Squares = 1912452.01667
Mean Square Error = 956226.00833
F-Value = 18.39651
P-Value = .00000
Variable: Sex
Degrees of Freedom = 1
Residual Sum of Squares = 6197835.01312
Mean Square Error = 6197835.01312
F-Value = 119.23809
P-Value = .00000
Variable: Interaction Locality: Sex
Degrees of Freedom = 2
Residual Sum of Squares = 161192.25392
Mean Square Error = 80596.12696
F-Value = 1.55056
P-Value = .21690
Residual: Degrees of Freedom = 106
Residual Sum of Squares = 5509737.01359
Mean Square Error = 51978.65107
F-Value = 29.47512
P-Value = 0.0
R-Square = .60598

For the effect of locality and the interaction effects, you can need to conduct post-hoc t-tests, in this case, a pooled independent samples t-test. You can do this in a similar manner to the two-way ANOVA; however will have to enter the values in a slightly different way (see below). Note that your critical t-values must have Bonferoni correction.

## Conclusions

According to the results of the analysis, you will find that there is are significant main effects of locality (F(2, 106) = 18.39651, p < 0.001) and sex (F(1, 106) = 119.23809, p < 0.001) on shell width. The interaction between sex and locality is not significant on shell width (F (2,106) = 1.55056, p > 0.20). Post-hoc tests reveal that t-tests will reveal that there is a significant difference in width between male (M 7106.88136, SD = 247.06778) and female (M = 7578.03773, SD = 256.89806) snails shells (t (110) = 9.88846, p < 0.001). The 99.7% confidence interval for the difference is 471.15638 ± 157.08993. Note that this interval does not include 0 (a lack of difference between the means). There is also a significant difference in width between the snails collected at localities one and two, two and three, & one and three. We leave these analyses to you in the first practice problems

Based on these results, it would be possible to classify whether a Cocholotoma septemspirale is male or female, regardless of the locality it comes from (there is no interaction of the two effects); females have significantly taller shells. Limitations of the study include its correlational nature. One issue with the study, for example, is that age might be a confounding variable, if these snails are the type that grows throughout their lifecycle.

## Practice problems

• Finish the post-hoc t-tests for the effect of locality on shell width.
• Complete an analysis similar to the one above, using one of the variables other than shell.h as -your dependent variable. See if that variable would be of use in classifying the snails.
• Complete a new analysis of this pain/neuroimaging data set. Use sex and disease group as independent variables. Choose for your dependent variable one of the brain volumes.