SOCR Activity ANOVA SnailsSexualDimorphism

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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

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.

Data Summary

CategoryLabel shell.h shell.w aperture.h aperture.w whorl.w rib.n category
Sex Locality Shell.H_Mean Shell.H_SD Shell.W_Mean Shell.W_SD Aperture.H_Mean Aperture.H_SD Aperture.W_Mean Aperture.W_SD Whorl.W_Mean Whorl.W_SD rib.n_Mean rib.n_SD
1 1 7446 204 3841 115 2567 100 2534 94 3195 79 32 3 11
2 1 7024 257 3889 120 2627 113 2515 89 3133 77 29 2 21
1 2 7536 211 3830 93 2598 127 2564 130 3172 71 33 2 12
2 2 7081 189 3871 110 2651 87 2543 123 3127 64 32 2 22
1 3 7753 247 3988 112 2679 101 2610 126 3299 99 32 2 13
2 3 7251 255 3925 159 2662 188 2536 204 3192 84 33 2 23

Raw Dataset

Sex locality shell.h shell.w aperture.h aperture.w whorl.w rib.n
1 1 7063 3860 2564 2522 3119 29
1 1 7535 3846 2522 2629 3332 37
1 1 7484 3952 2680 2541 3258 34
1 1 7516 3763 2671 2703 3217 31
1 1 7211 3698 2555 2541 3133 30
1 1 7526 3828 2573 2555 3143 28
1 1 7576 3851 2439 2504 3207 32
1 1 7558 3781 2471 2481 3143 35
1 1 7674 3828 2652 2513 3230 31
1 1 7526 3786 2439 2555 3166 29
1 1 7641 3943 2587 2481 3300 30
1 1 7470 4087 2712 2606 3286 33
1 1 7262 3693 2573 2504 3124 38
1 1 7410 3781 2532 2499 3152 28
1 1 7799 4045 2782 2666 3342 31
1 1 7567 3855 2583 2647 3226 33
1 1 7428 3952 2481 2546 3226 32
1 1 7368 3730 2448 2407 3119 33
1 1 6915 3615 2407 2259 3069 29
1 1 7327 3920 2587 2522 3217 36
1 1 7502 3837 2657 2536 3087 32
2 1 7188 4003 2629 2546 3277 31
2 1 7178 4119 2754 2670 3258 25
2 1 7192 3865 2587 2374 3101 27
2 1 7035 3971 2652 2647 3207 31
2 1 6674 3823 2532 2573 3004 30
2 1 7470 4027 2837 2694 3184 27
2 1 7252 3952 2629 2407 3166 27
2 1 6739 3855 2606 2439 3087 29
2 1 7345 3994 2721 2555 3166 31
2 1 7419 3869 2689 2564 3198 29
2 1 7040 3837 2513 2481 3124 33
2 1 6623 3920 2564 2564 3124 26
2 1 7169 3980 2828 2434 3161 30
2 1 6956 3777 2615 2495 3050 29
2 1 6549 3749 2471 2425 2994 25
2 1 6831 3763 2536 2407 3036 30
2 1 7053 3985 2805 2573 3184 32
2 1 6919 3837 2481 2448 3152 32
2 1 6808 3911 2666 2499 3101 33
2 1 7137 3573 2471 2522 3050 27
2 1 6928 3851 2587 2495 3166 28
1 2 7294 3679 2458 2356 3101 33
1 2 7576 3786 2721 2777 3143 31
1 2 7840 3892 2712 2471 3082 32
1 2 7586 3860 2573 2647 3207 31
1 2 7715 3860 2536 2546 3184 33
1 2 7715 4017 2777 2638 3305 35
1 2 7456 3929 2629 2680 3203 32
1 2 7526 3878 2583 2606 3291 35
1 2 7526 3772 2606 2564 3152 33
1 2 7780 3772 2735 2629 3217 31
1 2 7077 3703 2305 2337 3092 34
1 2 7336 3781 2555 2439 3143 36
1 2 7544 3855 2583 2638 3119 36
2 2 7086 4077 2772 2629 3143 31
2 2 6716 3846 2694 2689 3069 29
2 2 7276 3929 2587 2481 3170 32
2 2 6928 3860 2712 2564 3082 34
2 2 6716 3818 2689 2439 3082 34
2 2 6915 3869 2721 2388 3069 35
2 2 7095 3929 2712 2490 3110 32
2 2 6928 3952 2754 2638 3092 30
2 2 7387 3804 2592 2564 3110 31
2 2 7095 3869 2615 2541 3272 33
2 2 7095 3846 2638 2587 3119 28
2 2 6938 3846 2638 2638 3069 32
2 2 7169 3721 2745 2629 3092 29
2 2 7035 3689 2513 2397 3018 29
2 2 7086 3786 2596 2356 3101 31
2 2 7123 4059 2731 2819 3217 34
2 2 7137 3878 2684 2546 3133 35
2 2 6956 3619 2407 2296 3082 31
2 2 7123 3929 2550 2541 3124 34
2 2 7220 3869 2657 2448 3207 33
2 2 7493 3971 2680 2638 3235 30
2 2 7271 3994 2638 2620 3193 33
1 3 7831 3948 2647 2708 3360 33
1 3 7863 4207 2712 2694 3416 30
1 3 7775 3952 2721 2573 3291 32
1 3 7715 4068 2689 2430 3300 29
1 3 7493 3892 2731 2578 3175 33
1 3 7243 4008 2689 2786 3110 32
1 3 8187 4207 2953 2902 3490 33
1 3 7850 4119 2721 2680 3499 35
1 3 8086 4128 2819 2680 3291 34
1 3 8211 3906 2647 2541 3277 31
1 3 7799 3929 2564 2499 3351 30
1 3 7683 3962 2721 2666 3272 31
1 3 7428 3952 2541 2527 3258 34
1 3 7715 3994 2754 2657 3291 36
1 3 7780 3994 2647 2680 3383 33
1 3 7567 3869 2583 2365 3249 34
1 3 7891 3943 2573 2564 3207 26
1 3 7526 3804 2638 2522 3217 32
1 3 7664 3888 2555 2541 3249 33
2 3 7003 3962 2564 2439 3268 34
2 3 7368 4077 2860 2712 3156 36
2 3 7276 3837 2504 2300 3143 30
2 3 7276 3814 2546 2374 3161 32
2 3 6989 3633 2189 2161 3277 35
2 3 7104 3814 2763 2680 3087 36
2 3 7123 3971 2721 2564 3217 32
2 3 7229 3855 2439 2388 3281 31
2 3 7396 4119 2596 2661 3268 30
2 3 7660 3721 2680 2458 3198 36
2 3 7044 3892 2735 2546 3036 34
2 3 7220 3772 2647 2416 3087 29
2 3 7317 4119 2911 2869 3235 32
2 3 6841 3962 2763 2703 3152 35
2 3 7294 4054 2754 2416 3166 32
2 3 7873 4193 2920 2893 3342 30

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?

SOCR Activity ANOVA SnailsSexualDimorphism Fig1.jpg
SOCR Activity ANOVA SnailsSexualDimorphism Fig2.jpg
SOCR Activity ANOVA SnailsSexualDimorphism Fig3.jpg
SOCR Activity ANOVA SnailsSexualDimorphism Fig4.jpg
SOCR Activity ANOVA SnailsSexualDimorphism Fig5.jpg
SOCR Activity ANOVA SnailsSexualDimorphism Fig6.jpg
SOCR Activity ANOVA SnailsSexualDimorphism Fig10.png
SOCR Activity ANOVA SnailsSexualDimorphism Fig11.png
SOCR Activity ANOVA SnailsSexualDimorphism Fig12.png

Quantitative data analysis (QDA)

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

SOCR Activity ANOVA SnailsSexualDimorphism Fig7.png

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.

SOCR Activity ANOVA SnailsSexualDimorphism Fig8.png

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,

SOCR Activity ANOVA SnailsSexualDimorphism Fig9.png

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
Variance Source DF RSS MSS F-Statistics P-value
Main Effect: Locality 2 1912452.01667 956226.00833 18.39651 0.00000
Main Effect: Sex 1 6197835.01312 6197835.01312 119.23809 0.00000
Interaction Locality: Sex 2 161192.25392 80596.12696 1.55056 0.21690
Error 106 5509737.01359 51978.65107
Total: 111 13170123.10714
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.

See also

References



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