Difference between revisions of "SOCR Activity ANOVA FlignerKilleen MeatConsumption"

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Open the [http://www.socr.ucla.edu/htmls/ana/ANOVA2Way_Analysis.html SOCR ANOVA-Two Way applet] (requires Java-enabled browser).
 
Open the [http://www.socr.ucla.edu/htmls/ana/ANOVA2Way_Analysis.html SOCR ANOVA-Two Way applet] (requires Java-enabled browser).
  
<center>[[Image:SOCR_Activity_ANOVA_SnailsSexualDimorphism_Fig7.png|500px]]</center>
+
For the following analyses, we will focus on the data for Beef consumption. Let us test to see if different countries eat different amounts of beef.
 +
Usually when we compare a set of groups as this one, we would use a one-way ANOVA (comparing the seven countries). To run this test, open up the [[AP_Statistics_Curriculum_2007_ANOVA_1Way|one-way ANOVA analysis]] in the [http://www.socr.ucla.edu/htmls/ana/ANOVA1Way_Analysis.html SOCR Analyses Applet] in a java-enabled browser. It should be the default setting when you open up the page:
  
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.  
+
<center>[[Image:SOCR_Activity_ANOVA_FlignerKilleen_MeatConsumption_Fig6.png|500px]]</center>
  
<center>[[Image:SOCR_Activity_ANOVA_SnailsSexualDimorphism_Fig8.png|500px]]</center>
+
Now, prepare your dataset (it will be the Beef table from the above summary tables). We will be treating the yearly results as being our sample’s data points, attempting to capture the overall population consumption. This seems reasonable; the average meet consumption of a country should not change that much in a seven-year timespan.  
  
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,
+
Once you have rearranged your dataset for use in the ANOVA applet (if you do not know what it should look like, try considering one of the SOCR ANOVA tutorials). It should look like this in the applet data screen:
  
<center>[[Image:SOCR_Activity_ANOVA_SnailsSexualDimorphism_Fig9.png|500px]]</center>
+
<center>[[Image:SOCR_Activity_ANOVA_FlignerKilleen_MeatConsumption_Fig7.png|500px]]</center>
  
Press the '''Calculate''' button. This should bring up the results page with the following text:
+
Rename your column headers to define the independent and dependent variables.
  
:ANOVA results
+
<center>[[Image:SOCR_Activity_ANOVA_FlignerKilleen_MeatConsumption_Fig8.png|500px]]</center>
:Sample Size = 112
 
:Dependent Variable = Shell.h
 
:Independent Variable(s) = Locality Sex Interaction Locality: Sex
 
: *** Two-Way Analysis of Variance Results ***
 
: [[AP_Statistics_Curriculum_2007_ANOVA_2Way| See EBook's Standard 2-Way ANOVA Table]]
 
  
<center>
+
Click on the mapping tab, and assign your independent and dependent variables appropriately:
{| class="wikitable" style="text-align:center; width:30%" border="1"
 
|-
 
!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|| || ||
 
|}
 
</center>
 
  
:Variable: Locality
+
<center>[[Image:SOCR_Activity_ANOVA_FlignerKilleen_MeatConsumption_Fig9.png|500px]]</center>
:Degrees of Freedom = 2
 
:Residual Sum of Squares = 1912452.01667
 
:Mean Square Error = 956226.00833
 
:F-Value = 18.39651
 
:P-Value = .00000
 
  
:Variable: Sex
+
Set your precision to all, then click calculate:
: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
+
<center>[[Image:SOCR_Activity_ANOVA_FlignerKilleen_MeatConsumption_Fig10.png|500px]]</center>
: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
+
The following results should appear in the '''Results''' tab:  
: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.
+
: Sample Size = 49
 +
: Independent Variable = Country
 +
: Dependent Variable  = Consumption
 +
: Results of One-Way Analysis of Variance:
 +
: [[AP_Statistics_Curriculum_2007_ANOVA_1Way|Standard 1-Way ANOVA Table]]
 +
==============================================================================================
 +
VarianceSource DF RSS MSS                               F-Statistics                      P-value
 +
TreatmentEffect (B/w Groups) 6 668292765.4285718000 111382127.5714286400 898.8918351858   < 1E-15
 +
Error 42 5204240.5714285690 123910.4897959183
 +
Total: 48 673497006.0000004000
 +
==============================================================================================
 +
 
 +
: Model:
 +
: Degrees of Freedom = 6
 +
: Residual Sum of Squares = 668292765.4285718000
 +
: Mean Square Error = 111382127.5714286400
 +
 
 +
: Error:
 +
: Degrees of Freedom = 42
 +
: Residual Sum of Squares = 5204240.5714285690
 +
: Mean Square Error = 123910.4897959183
 +
 
 +
: Corrected Total:
 +
: Degrees of Freedom = 48
 +
: Residual Sum of Squares = 673497006.0000004000
 +
 
 +
: F-Value = 898.8918351858
 +
: P-Value =  < 1E-15
 +
: R-Square = 0.9922728082
  
 
==Conclusions==
 
==Conclusions==

Revision as of 18:56, 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

Country Meat 2000 2001 2002 2003 2004 2005 2006
Brazil Beef 6102 6191 6437 6273 6400 6774 6939
Brazil Pork 1827 1919 1975 1957 1979 1949 2191
Brazil Poultry 5110 5341 5873 5742 5992 6612 6853
China Beef 5284 5434 5818 6274 6703 7026 7395
China Pork 40378 41829 43238 45054 46648 49703 51809
China Poultry 9393 9237 9556 9963 9931 10088 10371
EuropeanUnion Beef 8106 7658 8187 8315 8292 8194 8270
EuropeanUnion Pork 19242 19317 19746 20043 19773 19768 20015
EuropeanUnion Poultry 6934 7359 7417 7312 7280 7596 7380
Japan Beef 1585 1419 1319 1366 1182 1200 1173
Japan Pork 2228 2268 2377 2373 2562 2507 2450
Japan Poultry 1772 1797 1830 1841 1713 1880 1908
Mexico Beef 2309 2341 2409 2308 2368 2419 2509
Mexico Pork 1252 1298 1349 1423 1556 1556 1580
Mexico Poultry 2163 2311 2424 2627 2713 2871 3005
Russia Beef 2246 2400 2450 2378 2308 2503 2370
Russia Pork 2019 2076 2453 2420 2337 2476 2637
Russia Poultry 1320 1588 1697 1680 1675 2139 2382
UnitedStates Beef 12502 12351 12737 12340 12667 12663 12830
UnitedStates Pork 8455 8389 8685 8816 8817 8669 8640
UnitedStates Poultry 11474 11558 12270 12540 13080 13430 13754

Exploratory data analyses (EDA)

In the following analysis, we will aim to perform an analysis of variance (ANOVA) to compare the meat consumption amounts between different countries and/or across time. Note that the data points for each country-meat type combination are from the various years. Typically, we would expect the amount not to change between the years (especially in this 7-year timespan). Even if it did, in assuming homoscedasticity, we are making the assumption that any increase or decrease is constant between countries. Applying the Fligner-Killeen test will help us decide if this assumption is valid. Look at the bar graphs listed below and note which of them seem to vary more than the others between the years.

SOCR Activity ANOVA FlignerKilleen MeatConsumption Fig2.png
SOCR Activity ANOVA FlignerKilleen MeatConsumption Fig3.png
SOCR Activity ANOVA FlignerKilleen MeatConsumption Fig4.png
SOCR Activity ANOVA FlignerKilleen MeatConsumption Fig5.png


Quantitative data analysis (QDA)

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

For the following analyses, we will focus on the data for Beef consumption. Let us test to see if different countries eat different amounts of beef. Usually when we compare a set of groups as this one, we would use a one-way ANOVA (comparing the seven countries). To run this test, open up the one-way ANOVA analysis in the SOCR Analyses Applet in a java-enabled browser. It should be the default setting when you open up the page:

SOCR Activity ANOVA FlignerKilleen MeatConsumption Fig6.png

Now, prepare your dataset (it will be the Beef table from the above summary tables). We will be treating the yearly results as being our sample’s data points, attempting to capture the overall population consumption. This seems reasonable; the average meet consumption of a country should not change that much in a seven-year timespan.

Once you have rearranged your dataset for use in the ANOVA applet (if you do not know what it should look like, try considering one of the SOCR ANOVA tutorials). It should look like this in the applet data screen:

SOCR Activity ANOVA FlignerKilleen MeatConsumption Fig7.png

Rename your column headers to define the independent and dependent variables.

SOCR Activity ANOVA FlignerKilleen MeatConsumption Fig8.png

Click on the mapping tab, and assign your independent and dependent variables appropriately:

SOCR Activity ANOVA FlignerKilleen MeatConsumption Fig9.png

Set your precision to all, then click calculate:

SOCR Activity ANOVA FlignerKilleen MeatConsumption Fig10.png

The following results should appear in the Results tab:

Sample Size = 49
Independent Variable = Country
Dependent Variable = Consumption
Results of One-Way Analysis of Variance:
Standard 1-Way ANOVA Table

============================================================================================== VarianceSource DF RSS MSS F-Statistics P-value TreatmentEffect (B/w Groups) 6 668292765.4285718000 111382127.5714286400 898.8918351858 < 1E-15 Error 42 5204240.5714285690 123910.4897959183 Total: 48 673497006.0000004000 ==============================================================================================

Model:
Degrees of Freedom = 6
Residual Sum of Squares = 668292765.4285718000
Mean Square Error = 111382127.5714286400
Error:
Degrees of Freedom = 42
Residual Sum of Squares = 5204240.5714285690
Mean Square Error = 123910.4897959183
Corrected Total:
Degrees of Freedom = 48
Residual Sum of Squares = 673497006.0000004000
F-Value = 898.8918351858
P-Value = < 1E-15
R-Square = 0.9922728082

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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