Difference between revisions of "SOCR Activity ANOVA FlignerKilleen MeatConsumption"

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Revision as of 18:41, 21 February 2013

SOCR Educational Materials - Activities - SOCR Meat Consumption Activity – ANOVA assumptions about the variance homogeneity Activity

Motivation and Goals

In many developed countries, when people imagine their next meal, they focus on one specific part: the meat. That choice of meat, however, varies from country to country due to the popularity and availability of various domesticated animals. Furthermore, the amount of meat eaten has a surprising degree of variability across time, cultures and geographic regions.

The following activity will study the effects of that variance on the statistical analyses. Specifically, we will consider how deviations from homoscedasticity (also known as equivalence of variance or variance homogeneity) can lead to making some incomplete or even incorrect conclusions. To do so, we will employ the Fligner-Killeen method to analyze some real meet consumption data.

Summary

This activity uses a reduced version of the open-source meat-consumption dataset. All data comes from the US Census Bureau.

This dataset summarizes the meat consumption, by animal type, of various countries (the European Union (EU) is being treated as a single country in this case). For simplicity, records from countries that did provide consumption measures for all meat types and all years were removed from the data set.

Data

Data Description

  • Number of cases: 147
  • Variables
    • Country: The country or world region in question
      • Brazil
      • China
      • European Union
      • Japan
      • Mexico
      • Russia
      • United States
    • Meat: The type of meat
      • Beef
      • Pork
      • Poultry
    • Years Represented (2000 – 2006)
  • Values are in thousands of metric tons


Data Summaries

Chicken/Poultry

Year Brazil China Europe Japan Mexico Russia UnitedStates YearAverage YearSD
2000 5110 9393 6934 1772 2163 1320 11474 5452.286 3990.459
2001 5341 9237 7359 1797 2311 1588 11558 5598.714 3942.57
2002 5873 9556 7417 1830 2424 1697 12270 5866.714 4134.211
2003 5742 9963 7312 1841 2627 1680 12540 5957.857 4234.565
2004 5992 9931 7280 1713 2713 1675 13080 6054.857 4379.591
2005 6612 10088 7596 1880 2871 2139 13430 6373.714 4388.111
2006 6853 10371 7380 1908 3005 2382 13754 6521.857 4448.974
Country_Average 5931.857 9791.286 7325.429 1820.143 2587.714 1783 12586.57
Country_SD 629.6543 407.0908 200.4826 66.03895 304.2404 357.6777 886.5564

Pork

Year Brazil China Europe Japan Mexico Russia UnitedStates YearAverage YearSD
2000 1827 40378 19242 2228 1252 2019 8455 10771.57 14570.99
2001 1919 41829 19317 2268 1298 2076 8389 11013.71 15049.33
2002 1975 43238 19746 2377 1349 2453 8685 11403.29 15502.7
2003 1957 45054 20043 2373 1423 2420 8816 11726.57 16145.49
2004 1979 46648 19773 2562 1556 2337 8817 11953.14 16648.16
2005 1949 49703 19768 2507 1556 2476 8669 12375.43 17714.83
2006 2191 51809 20015 2450 1580 2637 8640 12760.29 18438.64
Country_Average 1971 45522.71 19700.57 2395 1430.571 2345.429 8638.714
Country_SD 110 4159.521 312.355 121.3013 135.3808 223.0148 164.5121

Beef

Year Brazil China Europe Japan Mexico Russia UnitedStates YearAverage YearSD
2000 6102 5284 8106 1585 2309 2246 12502 5447.714 3922.316
2001 6191 5434 7658 1419 2341 2400 12351 5399.143 3835.093
2002 6437 5818 8187 1319 2409 2450 12737 5622.429 4016.753
2003 6273 6274 8315 1366 2308 2378 12340 5607.714 3933.847
2004 6400 6703 8292 1182 2368 2308 12667 5702.857 4077.861
2005 6774 7026 8194 1200 2419 2503 12663 5825.571 4056.693
2006 6939 7395 8270 1173 2509 2370 12830 5926.571 4148.408
Country_Average 6445.143 6276.286 8146 1320.571 2380.429 2379.286 12584.29
Country_SD 307.1685 806.2036 226.9295 151.2138 71.75388 85.31259 190.4396

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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