SOCR EduMaterials Activities BMI Modeling Activity - Revision history

Dinov: /* Data Description */

2014-07-01T19:52:45Z

‎Data Description

IvoDinov: /* See also */

2013-01-30T23:08:29Z

‎See also

IvoDinov: /* See also */

2013-01-30T23:08:20Z

‎See also

IvoDinov: /* Chi-Square Goodness-of-Fit Test */

2013-01-30T23:05:21Z

‎Chi-Square Goodness-of-Fit Test

IvoDinov: /* References */

2013-01-30T23:04:31Z

‎References

IvoDinov at 22:58, 30 January 2013

2013-01-30T22:58:43Z

IvoDinov at 22:48, 30 January 2013

2013-01-30T22:48:33Z

IvoDinov at 22:32, 30 January 2013

2013-01-30T22:32:09Z

IvoDinov: /* Exploratory data analyses (EDA) */

2013-01-30T22:18:56Z

‎Exploratory data analyses (EDA)

IvoDinov: /* Summary */

2013-01-30T22:16:14Z

‎Summary

@@ Line 18: / Line 18: @@
 ** Weight
 ** BMI—Body Mass Index, calculated as  \( \frac{weight}{height^2} \).
 ===Data Summary===

@@ Line 681: / Line 681: @@
 ==See also==
 * [[SOCR_EduMaterials_AnalysisActivities_Chi_Goodness| SOCR Chi-Square Goodness-of-Fit Test]]
-* [[AP_Statistics_Curriculum_2007_Contingency_Fit| SOCR EBook, Chi-Square Modeling]]]
+* [[AP_Statistics_Curriculum_2007_Contingency_Fit| SOCR EBook, Chi-Square Modeling]]
 ==References==

@@ Line 681: / Line 681: @@
 ==See also==
 * [[SOCR_EduMaterials_AnalysisActivities_Chi_Goodness| SOCR Chi-Square Goodness-of-Fit Test]]
 ==References==

@@ Line 633: / Line 633: @@
 : ********** Chi-Square p-value is: '''.072''' *********
-Based on ''α =  0.05'', there is not enough evidence to conclude that the BMI data distribution does not fit a normal distribution. However, it is worth noting that it does come very close. This understanding of a distribution is very important to health officials; for example, it helps creates the charts that doctors national-wide use to understand. In addition, a deviation from that distribution can be used to chart changes in the overall health of the nation (Penman, 2006).
+Based on ''α =  0.05'', there is not enough evidence to conclude that the BMI data distribution does not fit a normal distribution. However, it is worth noting that it does come very close. This understanding of a distribution is very important to health officials; for example, it helps creates the charts that doctors national-wide use to understand. In addition, a deviation from that distribution can be used to chart changes in the overall health of the nation ([[SOCR_EduMaterials_Activities_BMI_Modeling_Activity#References|Penman, 2006]]).
 ===Linear Regression===

@@ Line 684: / Line 684: @@
 ==References==
 * K.W. Penrose, A.G. Nelson, A.G. Fisher, FACSM, Human Performance Research Center, Brigham Young University, Provo, Utah 84602 as listed in Medicine and Science in Sports and Exercise, vol. 17, no. 2, April 1985, p. 189.
-* A.D. Penman and W.D. Johnson. University of Missisippi . Changing shape of the body mass index distribution curve in the population: implications for public health policy to reduce the prevalence of adult obesity." as listed in Preventing chronic disease, vol. 3, no. 2, 2006
+* A.D. Penman and W.D. Johnson. [http://www.ncbi.nlm.nih.gov/pmc/articles/pmc1636707/ Changing shape of the body mass index distribution curve in the population: implications for public health policy to reduce the prevalence of adult obesity],  Preventing chronic disease, vol. 3, no. 2, 2006.
 {{translate|pageName=http://wiki.stat.ucla.edu/socr/index.php?title=SOCR_EduMaterials_Activities_BMI_Modeling_Activity}}

@@ Line 547: / Line 547: @@
 <center>[[Image:SOCR_Activity_BMI_ChiSquare_Fig3.png|500px]]</center>
 Enter in the values for the mean and standard deviation, then drag the graph down to see your full distribution.
@@ Line 600: / Line 601: @@
 <center>[[Image:SOCR_Activity_BMI_ChiSquare_Fig6.png|500px]]</center>
 With these values now settled, we can begin the [[AP_Statistics_Curriculum_2007_Contingency_Fit|Chi-square analysis]]. Open up the [http://socr.ucla.edu/htmls/SOCR_Analyses.html SOCR Analyses Applet] in a Java-enabled browser, and then select the '''Chi-square Goodness of Fit''' in the pull-down menu on the left:
@@ Line 633: / Line 635: @@
 Based on ''α =  0.05'', there is not enough evidence to conclude that the BMI data distribution does not fit a normal distribution. However, it is worth noting that it does come very close. This understanding of a distribution is very important to health officials; for example, it helps creates the charts that doctors national-wide use to understand. In addition, a deviation from that distribution can be used to chart changes in the overall health of the nation (Penman, 2006).
 Finally, we can explore the correlation between the observed frequencies and the prediction-model values (predicted frequencies) of the BMI data within each of the 16 bins. If there is a good agreement (e.g., high correlation) this would indicate that the normal distribution model fits well the observed data (BMI frequencies).
-Copy and paste the 2 column data (observed and predicted frequencies) into the [http://www.socr.ucla.edu/htmls/ana/SimpleRegression_Analysis.html Simple Linear Regression applet of [http://socr.ucla.edu/htmls/SOCR_Analyses.html SOCR Analysis].
+Copy and paste the 2 column data (observed and predicted frequencies) into the [http://www.socr.ucla.edu/htmls/ana/SimpleRegression_Analysis.html Simple Linear Regression applet] of [http://socr.ucla.edu/htmls/SOCR_Analyses.html SOCR Analysis].
 <center>[[Image:SOCR_Activity_BMI_ChiSquare_Fig12.png|500px]]</center>
@@ Line 659: / Line 662: @@
 :: P-Value:            .00000
 The '''Graphs''' tab includes a regression model plot, scatter plot with confidence/prediction limits, and various plots of the residuals.

← Older revision		Revision as of 22:32, 30 January 2013
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	<center>[[Image:SOCR_Activity_BMI_ChiSquare_Fig2.png\|700px]]</center>		<center>[[Image:SOCR_Activity_BMI_ChiSquare_Fig2.png\|700px]]</center>

−	==~~Conclusions~~==	+	==Quantitative Data Analyses (QDA)==
		+	In this section, we will be testing the BMI variable for normality, although the same analysis can be carried for the other variables. As the name '''goodness-of-fit''' implies, we first need to create a normal model to compare to. We will use the sample mean (25.18643319) and standard deviation (3.146481308) as the parameters of the normal distribution.
		+
		+	The next few steps will use the [http://socr.ucla.edu/htmls/SOCR_Distributions.html SOCR Distributions Applet] (see [[SOCR_EduMaterials_DistributionsActivities\|Distribution Activities]]). Open the [http://socr.ucla.edu/htmls/SOCR_Distributions.html applet] in a java-enabled browser.
		+
		+	<center>[[Image:SOCR_Activity_BMI_ChiSquare_Fig3.png\|500px]]</center>
		+
		+	Enter in the values for the mean and standard deviation, then drag the graph down to see your full distribution.
		+
		+	<center>[[Image:SOCR_Activity_BMI_ChiSquare_Fig4.png\|500px]]</center>
		+
		+	To run a goodness of fit test, we will need to create a set of bins to compare between the real distribution and the '''expected''' normal one. For simplicity’s sake, we will use a 16 bins of bin-size 1 beginning with BMI=18 and ending with BMI=34. To find the frequency of results in each bin from the normal distribution, click on the edges of the bin size (try to be as accurate as possible) on the normal distribution applet. The example shown alternatively, use the [[AP_Statistics_Curriculum_2007_Normal_Std\|normal CDF function]].
		+
		+	<center>[[Image:SOCR_Activity_BMI_ChiSquare_Fig5.png\|500px]]</center>
		+
		+	After calculating the probability of each bin, multiply each of these probabilities by the total number of cases (in this case, 248). Now we can place these calculated frequencies next to the frequencies from the observed distribution (the observed frequencies were found by plain counting):
		+
		+	<center>
		+	{\| class="wikitable" style="text-align:center; width:30%" border="1"
		+	\|-
		+	!Bin(Simplified)\|\|Bin(Actual)\|\|Normal_Probability\|\|EstimatedNormalFrequency\|\|ObservedFrequency
		+	\|-
		+	\|18-19\|\|18.000-18.999\|\|0.013454035\|\|3.39041682\|\|1
		+	\|-
		+	\|19-20\|\|19.000-19.999\|\|0.025001757\|\|6.300442764\|\|6
		+	\|-
		+	\|20-21\|\|20.000-20.999\|\|0.042032155\|\|10.59210306\|\|11
		+	\|-
		+	\|21-22\|\|21.000-21.999\|\|0.06392769\|\|16.10977788\|\|23
		+	\|-
		+	\|22-23\|\|22.000-22.999\|\|0.087962245\|\|22.16648574\|\|20
		+	\|-
		+	\|23-24\|\|23.000-23.999\|\|0.109497598\|\|27.5933947\|\|38
		+	\|-
		+	\|24-25\|\|24.000-24.999\|\|0.123313845\|\|31.07508894\|\|26
		+	\|-
		+	\|25-26\|\|25.000-25.999\|\|0.125638222\|\|31.66083194\|\|31
		+	\|-
		+	\|26-27\|\|26.000-26.999\|\|0.115806485\|\|29.18323422\|\|26
		+	\|-
		+	\|27-28\|\|27.000-27.999\|\|0.096570457\|\|24.33575516\|\|21
		+	\|-
		+	\|28-29\|\|28.000-28.999\|\|0.072854419\|\|18.35931359\|\|9
		+	\|-
		+	\|29-30\|\|29.000-29.999\|\|0.049724263\|\|12.53051428\|\|15
		+	\|-
		+	\|30-31\|\|30.000-30.999\|\|0.030702836\|\|7.737114672\|\|10
		+	\|-
		+	\|31-32\|\|31.000-31.999\|\|0.017150734\|\|4.321984968\|\|6
		+	\|-
		+	\|32-33\|\|32.000-32.999\|\|0.008667207\|\|2.184136164\|\|2
		+	\|-
		+	\|33-34\|\|33.000-33.999\|\|0.00396249\|\|0.99854748\|\|3
		+	\|}
		+	</center>

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 ==[[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?
+Before we run any quantitative tests, let’s examine what these variables look like in graphical form. Keep an eye out for which variables appear to follow a normal distribution.
 ==Conclusions==

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 ==Summary==
 This activity uses a simplified version of the [[SOCR_Data_BMI_Regression| BMI data sets found here]]. Four cases of data were excluded due to extremely high BMIs that hinted at a mistake in the entry process.  10 variables from the original dataset were left out in the dataset presented here, though the same process presented here may be used on them for additional practice.
 ==Data==