SOCR Activity ANOVA FlignerKilleen MeatConsumption - Revision history

Tdlee: Text replacement - "{{translate|pageName=http://wiki.stat.ucla.edu/socr/" to ""{{translate|pageName=http://wiki.socr.umich.edu/"

2020-03-03T18:10:42Z

Text replacement - "{{translate|pageName=http://wiki.stat.ucla.edu/socr/" to ""{{translate|pageName=http://wiki.socr.umich.edu/"

IvoDinov: /* ANOVA */

2013-02-21T23:27:14Z

‎ANOVA

IvoDinov: /* Conclusions */

2013-02-21T23:25:37Z

‎Conclusions

IvoDinov: /* Fligner-Killeen Analysis */

2013-02-21T23:25:17Z

‎Fligner-Killeen Analysis

IvoDinov at 23:24, 21 February 2013

2013-02-21T23:24:38Z

IvoDinov: /* Quantitative data analysis (QDA) */

2013-02-21T23:20:04Z

‎Quantitative data analysis (QDA)

IvoDinov: /* Quantitative data analysis (QDA) */

2013-02-21T23:01:41Z

‎Quantitative data analysis (QDA)

IvoDinov at 23:00, 21 February 2013

2013-02-21T23:00:48Z

IvoDinov at 22:56, 21 February 2013

2013-02-21T22:56:11Z

IvoDinov at 22:47, 21 February 2013

2013-02-21T22:47:47Z

← Older revision		Revision as of 18:10, 3 March 2020
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	* Meat Consumption by Type and Country (2006). U.S. Department of Agriculture, Foreign Agricultural Service, Livestock, and Poultry.		* Meat Consumption by Type and Country (2006). U.S. Department of Agriculture, Foreign Agricultural Service, Livestock, and Poultry.

−	{{translate\|pageName=http://wiki.~~stat~~.~~ucla~~.edu~~/socr~~/index.php?title=SOCR_Activity_ANOVA_FlignerKilleen_MeatConsumption}}	+	"{{translate\|pageName=http://wiki.socr.umich.edu/index.php?title=SOCR_Activity_ANOVA_FlignerKilleen_MeatConsumption}}

@@ Line 219: / Line 219: @@
 : Model:
 : Degrees of Freedom = 6
-: Residual Sum of Squares = 668292765.4285718000
+: Residual Sum of Squares = 668292765.43
-: Mean Square Error = 111382127.5714286400
+: Mean Square Error = 111382127.57
 : Error:
 : Degrees of Freedom = 42
-: Residual Sum of Squares = 5204240.5714285690
+: Residual Sum of Squares = 5204240.57
-: Mean Square Error = 123910.4897959183
+: Mean Square Error = 123910.49
 : Corrected Total:
 : Degrees of Freedom = 48
-: Residual Sum of Squares = 673497006.0000004000
+: Residual Sum of Squares = 673497006.00
-: F-Value = 898.8918351858
+: F-Value = 898.89
 : P-Value =  < 1E-15
-: R-Square = 0.9922728082
+: R-Square = 0.99
 ===Fligner-Killeen Analysis===

← Older revision		Revision as of 23:25, 21 February 2013
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	Just because the assumptions of [[AP_Statistics_Curriculum_2007_ANOVA_1Way\|ANOVA]] are not satisfied, we should not give up on this data set. Without the results of the [[SOCR_EduMaterials_AnalysisActivities_FlignerKilleen\|Fligner-Killeen]], we may have missed the effects of time on meat consumption, an effect that warrants is own investigation. In such situations, the use of non-parametric alternatives to ANOVA may be appropriate (e.g., [[SOCR_EduMaterials_AnalysisActivities_KruskalWallis\|Kruskal-Wallis test]]).		Just because the assumptions of [[AP_Statistics_Curriculum_2007_ANOVA_1Way\|ANOVA]] are not satisfied, we should not give up on this data set. Without the results of the [[SOCR_EduMaterials_AnalysisActivities_FlignerKilleen\|Fligner-Killeen]], we may have missed the effects of time on meat consumption, an effect that warrants is own investigation. In such situations, the use of non-parametric alternatives to ANOVA may be appropriate (e.g., [[SOCR_EduMaterials_AnalysisActivities_KruskalWallis\|Kruskal-Wallis test]]).
−

	==Practice problems==		==Practice problems==

@@ Line 238: / Line 238: @@
 Note our extremely low p-value. The results of our one-way ANOVA reject the null hypothesis that these countries do not differ in terms of beef consumption. This shouldn’t surprise anyone. Even a third grader could have made that decision after looking at the summary table, or the earlier EDA graphs. Besides, the data represents total volume of meat consumption, whereas the populations of these countries are vastly different, and a per-capita meat consumption analysis may be more appropriate in this case.
-However, let’s say that you find a book that claims, using the results of your ANOVA as proof, that “China consumes more beef than any country other than the United States”. That book is saying that these populations are significantly different in terms of their beef consumption. Is this claim justified by the ANOVA analysis above? Going through the assumptions of the ANOVA test, remember that the different levels must follow homoscedasticity (equivalence of variance). If two populations are significantly far from this assumption, then they should be compared using [[ANOVA]]. An alternative statistical test needs to be applied (e.g., [[SOCR_EduMaterials_AnalysisActivities_KruskalWallis|Kruskal-Wallis test]]).
+However, let’s say that you find a book that claims, using the results of your ANOVA as proof, that “China consumes more beef than any country other than the United States”. That book is saying that these populations are significantly different in terms of their beef consumption. Is this claim justified by the ANOVA analysis above? Going through the assumptions of the ANOVA test, remember that the different levels must follow homoscedasticity (equivalence of variance). If two populations are significantly far from this assumption, then they should be compared using [[AP_Statistics_Curriculum_2007_ANOVA_1Way|ANOVA]]. An alternative statistical test needs to be applied (e.g., [[SOCR_EduMaterials_AnalysisActivities_KruskalWallis|Kruskal-Wallis test]]).
 To test for homoscedacity, we will use the Fligner-Killeen test, which is a non-parametric test that doesn’t assume normality. This is important, considering that we have a rather limited data set (only seven points, one for each year) and the data may not be normally distributed. Use the tab to find the [[SOCR_EduMaterials_AnalysisActivities_FlignerKilleen|Fligner-Killeen]] analysis in the [http://www.socr.ucla.edu/htmls/ana/FlignerKilleen_Analysis.html SOCR Analyses Applet] in a java-enabled browser:
@@ Line 289: / Line 289: @@
 : P-Value = .004
 The result from the [[SOCR_EduMaterials_AnalysisActivities_FlignerKilleen|Fligner-Killeen test (for variance homogeneity)]] yields a rather small p-value (0.004). Assuming α = 0.05, we would rejects the null hypothesis of equal variances between countries. Therefore, we should be wary of continuing with a [[AP_Statistics_Curriculum_2007_ANOVA_1Way|standard (parametric) Analysis of Variance (ANOVA)]]. Looking back at the data, it is easy to see why.
 ==Conclusions==

@@ Line 291: / Line 291: @@
 The result from the [[SOCR_EduMaterials_AnalysisActivities_FlignerKilleen|Fligner-Killeen test (for variance homogeneity)]] yields a rather small p-value (0.004). Assuming α = 0.05, we would rejects the null hypothesis of equal variances between countries. Therefore, we should be wary of continuing with a [[AP_Statistics_Curriculum_2007_ANOVA_1Way|standard (parametric) Analysis of Variance (ANOVA)]]. Looking back at the data, it is easy to see why.
 Note, for example, that in the data for the Chinese consumption of beef, the values are steadily rising between the years. In our ANOVA, we had made an assumption, that the overall consumption would not follow a set pattern between the years, allowing us to treat them as sample points. This results in a much different variance between the groups. Therefore, it would be incorrect to use our previous conclusion from the ANOVA that “these countries have different population values for meat consumption” without a qualifier of the date range that we were sampling within. Note that without this analysis, you might have missed the trend in Chinese beef consumption—which might be worth studying in its own right.
@@ Line 297: / Line 298: @@
 Just because the assumptions of [[AP_Statistics_Curriculum_2007_ANOVA_1Way|ANOVA]] are not satisfied, we should not give up on this data set. Without the results of the [[SOCR_EduMaterials_AnalysisActivities_FlignerKilleen|Fligner-Killeen]], we may have missed the effects of time on meat consumption, an effect that warrants is own investigation.  In such situations, the use of non-parametric alternatives to ANOVA may be appropriate (e.g., [[SOCR_EduMaterials_AnalysisActivities_KruskalWallis|Kruskal-Wallis test]]).
 ==Practice problems==
-* Finish the post-hoc t-tests for the effect of locality on shell width.
+* Run this same analysis for the pork and poultry datasets. Interpret any conclusions as shown above.
-* 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.
+* Practice running a one-way ANOVA, excluding the data from China and Japan.
-* Complete a new analysis of this [[SOCR_Data_April2011_NI_IBS_Pain| pain/neuroimaging data set]]. Use sex and disease group as independent variables. Choose for your dependent variable one of the brain volumes.
+* “Turn” the beef data set around, and run this Fligner-Killeen test between the year groups. Interpret the conclusion you find. Why is this same/different to the result from the above example?
 ==See also==
-* [[SOCR_EduMaterials_AnalysisActivities_ANOVA_2|SOCR 2-Way ANOVA Wiki Page]]
+* [[SOCR_EduMaterials_AnalysisActivities_FlignerKilleen|Fligner-Killeen activity]]
-* [[SOCR_EduMaterials_Activities_BaseballSalaryWins| Baseball Salary/Wins Activity]]
+* [[SOCR_EduMaterials_AnalysisActivities_KruskalWallis|Kruskal-Wallis activity]]
 ==References==
-* Che, Annie, Cui, Jenny, and Dinov, Ivo (2009). [http://www.jstatsoft.org/v30/i03 SOCR Analyses: Implementation and Demonstration of a New Graphical Statistics Educational Toolkit]. JSS, Vol. 30, Issue 3, Apr 2009.
+* Meat Consumption by Type and Country (2006). U.S. Department of Agriculture, Foreign Agricultural Service, Livestock, and Poultry.
 {{translate|pageName=http://wiki.stat.ucla.edu/socr/index.php?title=SOCR_Activity_ANOVA_FlignerKilleen_MeatConsumption}}

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 ==Quantitative data analysis (QDA)==
 Open the [http://www.socr.ucla.edu/htmls/ana/ANOVA2Way_Analysis.html 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 [[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:
@@ Line 232: / Line 234: @@
 : P-Value =  < 1E-15
 : R-Square = 0.9922728082
 ==Conclusions==

@@ Line 204: / Line 204: @@
 : Results of One-Way Analysis of Variance:
 : [[AP_Statistics_Curriculum_2007_ANOVA_1Way|Standard 1-Way ANOVA Table]]
-	==============================================================================================
+	<center>
-	VarianceSource 		DF 	 RSS 		 MSS 	                               F-Statistics                      	 P-value
+{| class="wikitable" style="text-align:center; width:30%" border="1"
-	TreatmentEffect (B/w Groups)	6	668292765.4285718000	111382127.5714286400	 898.8918351858	  	< 1E-15
+|-
-	Error		42	5204240.5714285690	123910.4897959183
+!VarianceSource||DF||RSS||MSS||F-Statistics||P-value
-	Total:		48	673497006.0000004000
+|-
-	==============================================================================================
+|TreatmentEffect(B/w_Groups)||6||668292765.43||111382127.57||898.89||< 1E-15
 : Model:

@@ Line 174: / Line 174: @@
 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.
-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>
-<center>
+Click on the mapping tab, and assign your independent and dependent variables appropriately:
-:Variable: Locality
+<center>[[Image:SOCR_Activity_ANOVA_FlignerKilleen_MeatConsumption_Fig9.png|500px]]</center>
-:Variable: Sex
+Set your precision to all, then click calculate:
-:Variable: Interaction Locality: Sex
+<center>[[Image:SOCR_Activity_ANOVA_FlignerKilleen_MeatConsumption_Fig10.png|500px]]</center>
-:Residual:	Degrees of Freedom = 106
+The following results should appear in the '''Results''' tab:
-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
 ==Conclusions==

@@ Line 162: / Line 162: @@
 ==[[AP_Statistics_Curriculum_2007_EDA_Pics|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?
+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.
-<center>[[Image:SOCR_Activity_ANOVA_SnailsSexualDimorphism_Fig1.jpg|500px]]</center>
+<center>[[Image:SOCR_Activity_ANOVA_FlignerKilleen_MeatConsumption_Fig2.png|500px]]</center>
 ==Quantitative data analysis (QDA)==