Ecostat Paper (Acne Statistics)

August 23, 2011

Dr. Cesar Rufino - ECOSTAT Page

“Acne: A Comparative Study in Relation with Gender and Race”

Presented to

The Faculty of the School of Economics

De La Salle University

In Partial Fulfillment of the Requirements for the Course

ECOSTAT

Submitted by:

Co, Mark Anthony F.

Submitted to:

Dr. Cesar Rufino

August 23, 2011

Introduction:

August 23, 2011


Thousands and even millions of people both teenagers and adults what they do

when they woke up in the morning is to view or watch themselves in the mirror, looking

for some flaws. We would find ourselves painfully staring at our reflection in the mirror.

Why the bloody scabbing, unsightly bumps, and burning inflammation of our skin? Acne

also called as pimples, zit or “tigyawat” in Tagalog, is a common skin disease that

typically affects adolescents and young adults. Hundreds of treatment products exist for

clear skin, yet there is still no cure for this dreadful and hideous disease.

Acne has infected almost everyone in their life but only some were affected

severely that would really affect their self esteem and confidence, personally this have

been my problem for my whole college life. This has affected the way I think, the way I

do things and the way I prioritize my responsibilities. It has affected everything that I

want my life to go upon to; to be able to make new friends and go out with them in

events and parties, to be able to court the girl I like, to be able to go out from my room

and have that confidence and pride to myself without having a single doubt at myself of

having this terrible flaw.

Going to school has always been so hard and stressing for me, every time I take a

bath and see my reflection in the mirror, every time I wash my face then suddenly feel

the bumps in my skin. Commuting really takes the challenge in my day to day activity,

people usually looks at my face and then suddenly looks away; deep in my mind they

were curious on how I got this acne that looks so monstrous.

Acne affects approximately 85% of teenagers and young adults, ages 12 to 24.

The disease usually starts in adolescence, with the onset of puberty (“Acne statistics,”

n.d.). Acne occurs more commonly on the face, because it is the area with the highest

concentration of oil producing glands. However, it is important to know that acne can

occur on the neck, chest, back, arms, legs, and of the body (Mitchell & Dudley, 2002).

Though clogged pores cause acne, there are several reasons why these pores are

blocked initially. One explanation for acne is genetics. If a person has acne, it is likely his

or her children will also have acne. Stress and physical irritation are widely believed to

August 23, 2011


worsen acne. It is debatable among dermatologists whether diet and exercise affects

the condition (“Acne statistics,” n.d.).

Acne is one of the most common diseases, as almost everyone worldwide has

acne to some extent during puberty. The effects of acne, including physical and

emotional problems, can be very serious. Researchers continue to look for a cure for

this ubiquitous disease, such that millions of people can look in the mirror and have a

clear face looking back at them.

This is the reason why I want to make a study about acne, on how it is affected

by race and gender differences affects the severity and outcome of acne to an individual

or to a group.

This paper has the following objectives:

A. To determine if gender affects how severe or frequent acne would occur.

B. To determine if race is one of the factors that affects the severity of acne.

Scope, Limitations and Nature of the Study:

The focus of the study is to find out if gender and race are the key factors that

affect the production or outbreak of acne. Some people believe that the female

population is greatly affected by acne more than those of the male population. They say

that genetics has a primal role on the glands that produces this oil called sebum that

greatly affects the outbreaks of acne. Race as they say also is one factor to be

considered, they say that Caucasians tend to be more acne-prone than any of the other

races and is given the acne equation of, [Caucasian>Asians>Hispanic>Blacks], having the

Black population as having less acne than of the other three races. There are two

important key variables that must be used in this study, the gender difference and the

racial agenda.

August 23, 2011


Key Variables:

Gender: A set of classes that together include all nouns, membership in a

particular class being shown by the form of the noun itself or by the form or

choice of words that modify, replace sex. Can be grouped by male and female.

Race: An arbitrary classification of modern humans, sometimes, especially

formerly, based on any or a combination of various physical characteristics, as

skin color, facial form, or eye shape, and now frequently based on such genetic

markers as blood groups. Can be grouped by Caucasian, Asian, Hispanic and

Negro.

[Encarta Encyclopedia (2010)]

The study includes 77 major countries that are grouped by sub-heritage or

continental difference. The observations on the number of acne infected male and

female based on the total population would be the basis for the computation of the

sample mean, sample standard deviation, and sample variance. Other basis also would

be the infected race of Caucasian, Asians, Hispanic, and Negro. To be able to fully

understand the situations of each category their corresponding sample mean, sample

standard deviation, and sample variance will be computed to show the distribution of

infected individuals across each category.

Aside from the basics of mean, variances, and standard deviation, other

descriptive statistics would also be presented to the reader to better understand the

data. Other statistical measure would also be used to better clarify each category of

study such as the frequency table, hypothesis testing, confidence intervals, the ANOVA

test, the chi-square analysis and much more.

Descriptive Statistics

August 23, 2011


A. Acne for Males and Females (Totality)

To be able to understand if gender affects the production of acne, we

must look at the data presented at Table 1, it shows there the total

population of acne infected individuals in selected countries. Based on

percentage points the lowest percentage points of males infected in a

country is .4 and the highest being .52. In the female acne infected

population of a country the lowest percentage is .48 and the highest

being .6 of the total acne population of the country. Based on the data

presented in Table 1, we can say that the female population is

predominantly more affected than of the males in regards of having acne

troubles but we cannot conclude that because other factors and test

must be made to be able to comply and conclude that such event is true.

Countries that have the lowest percentage of .4 of acne infected boys are

Sudan and Zimbabwe. Country that has the lowest percentage of .48 of

acne infected boys is Denmark.

In the Descriptive Statistic we can see in Table 2-1 that the total

population of countries used was 77 (n=77). The mean of acne infected

boys are 1,894,901.74 and for the girls are 2,272,059.82. The study also

reveals that the sample variance, which shows the dispersion or variation

of observations in the population has a difference of 11,457,244,388,985

in favor of the girls population and the standard deviation, which is the

square root of the sample variance have a difference of 930,795.64. The

standard deviation observed in the female population clustered nearer

the mean shown in the same year than the previous study therefore

implying that the difference computed from the statistical average is

smaller. We can see here now that the sample standard deviation for the

boys is closer to its mean than those of the girls’ population hinting that

the computed average of it smaller than the other one.

August 23, 2011


To better understand this situation I grouped now that total population to 4

depending on its geography and race factor to better understands the breakdown of the

data. Let us see now if the mean, standard deviation and sample variance would change

from the observations of the breakdown.

B. Acne for Males and Females (North and South America)





of observations in the population has a difference of 4,764,311,634,744.8








the computed average of it smaller than the other one. The result is

almost the same of the descriptive statistics of the totality as a whole.

C. Acne for Males and Females (Europe)



boys are 588,478.25 and for the girls are 719,613.79. The study also


of observations in the population has a difference of 260,745,779,834 in

favor of the girls population and the standard deviation, which is the


August 23, 2011









D. Acne for Males and Females (Asia and the Pacific)





of observations in the population has a difference of 32,013,084,235,275


square root of the sample variance have a difference of 1,525,443.58.

The standard deviation observed in the female population clustered

nearer the mean shown in the same year than the previous study

therefore implying that the difference computed from the statistical

average is smaller. We can see here now that the sample standard

deviation for the boys is closer to its mean than those of the girls’

population hinting that the computed average of it smaller than the other

one. The result is almost the same of the descriptive statistics of the

totality as a whole.

E. Acne for Males and Females (Africa)



boys are 599,071.52 and for the girls are 773,173.56. The study also

August 23, 2011



of observations in the population has a difference of 331,426,072,957.48










Frequency Distribution Table

A. The Male Population

Across the 77 samples from different counties, I used the percentage points

of male and female acne infected population as in comparison of the total

population because the population of each county’s difference is relatively

high in comparison and it is easier and more convenient to analyze the

percentage points of this data that analyzing the exact numerical values for

each. Looking at Table 3-1, in the frequency table we can see that the

distance of the lower and the upper interval is at 2% starting from 40 up to

54 consisting of 7 sets of placement. We can see that the frequency of the

male population having acne is greatest at the 40 < 42 bracket meaning that

many countries have more acne infected females in comparison of the

males. We can also see in the data that only 9 countries out of 77 has greater

acne infected male than that of the females. The frequency distribution table

is great in assessing and analyzing the data of which each category falls upon

into.

August 23, 2011


B. The Female Population

Looking at Table 3-2, in the frequency table we can see that the distance of

the lower and the upper interval is at 2% starting from 48 up to 62 consisting

of 7 sets of placement. We can see that the frequency of the female

population having acne is greatest at the 58 < 60 bracket meaning that many

countries have more acne infected females in comparison of the males. We

can also see in the data that only 6 countries or less out of 77 has greater

acne infected male than that of the females.

Looking up at the table of the histogram of the frequency table we could greatly analyze

which part of the categories have the highest number of population, this could really

help us understand more and easier the information that is presented by the study.

Inferential Statistics

August 23, 2011


After getting the descriptive statistics of the data, lets now move on to the inferential

statistics to be able to answer our main problem and to further analyze and conclude

what the data shows us. This kind of statistics would give us concrete proof and proper

analysis.

Confidence Interval

For us to determine the estimated intervals we would the confident interval

statistics; a confidence interval gives an estimated range of values which is

likely to include an unknown population parameter, the estimated range

being calculated from a given set of sample data. (John H. McColl's Statistics

Glossary). For this study I used a 95% confidence level because the current

dates were not exact and only sample sets were presented by the data.

There might be some other people who have been counted of the

population. Based on the population used which is n=77 (countries) out of

the whole countries, we can say that this is a good sample size because of its

concrete and near numbers to the actual size. Looking at Table 4-1, we can

see the Confidence Intervals of the Mean for the boys. At 95% confidence

level we can see that the lowest point is 624,182.0018 while the highest

point is 3,165,621.4837. Looking at the other table 4-2, we can see here the

Confidence Intervals of the Mean for the girls. At 95% confidence level we

can see that the lowest point is 793,438.8441 while the highest point is

3,750,680.7966.

Hypothesis Testing

August 23, 2011


For this experiment we will now find out if we are going to accept or reject

the mean and variances that acne has equal outbreaks in both males and

females. The null hypothesis is that acne has equal outbreaks in both males

and females and the alternative hypothesis is that gender affects acne

outbreaks. Looking at Table 5-1, having a population size of n=77, we can see

here that the p-value is equal to .7046 which is not significant the p-value did

not fall in the rejection of null hypothesis so there is basically no hard

evidence against the hypothesized mean. We accept now the null

hypothesis.

Let: X = Means of Male, Y = Means of Female

Ho = X = Y

H1 = X ≠Y

At Significance Level of 95%

One-Factor ANOVA

Another way of testing or experimenting if we are going to accept or reject

the null hypothesis is the one-factor ANOVA, we now look at Table 6-1, based

on the population size of n=77, we then use the one-factor ANOVA as an

experiment to answer the problem, after imputing and analyzing the data we

can see that the p-value resulted to a .7051 and we got an F of 0.14 since CR:

F<p-value or 0.14<0.7051 we can conclude that it is not significant so we

must accept the null hypothesis. Both the hypothesis testing and the one-

factor ANOVA proved that gender has no relation to acne breakouts but is

caused by some other factors.

Chi-square Analysis for Independence

August 23, 2011


We are not testing for the chi-square analysis for independence we would

now look at Table 7-1, we then test the sample data for their independence

level, almost all of the sample population observed and expected percent are

almost equal resulting to a near 0% chi-squared only certain countries

showed significant result which is the USA and India with 30.8% and 27.5%

respectively. This means that larger geography and countries that are more

populated differ from their expected outcome than the rest of the data.

Conclusion and Recommendation

In my paper we could see the difference in the descriptive statistics and the

inferential statistics, in the descriptive statistics we could see the simple

result of mean, median, simple variance and standard deviation, and we

could compare and contrast the difference of each result to the totality as a

whole. In the descriptive statistic we could easily infer that the female

population is more prone to the male population if we are going to based it

in numerical values. In the inferential statistics we are given a more detailed

answer and experiment that is able to explain the direct and close

relationship of each data. In here we have found out that acne and genders

and race have no direct contact or is independent to one another.

Reference

Acne Statistics (2005). Statistics by Country for Acne. Retrieve on August 15,

2011 at http://www.cureresearch.com/a/acne/stats-country_printer.htm

Guide Paper: Nadine Estrella from Dr. Rufino’s sample project.

August 23, 2011


Table 1: Recorded Acne Patients for 2004

Countries Total Male FemaleNorth and South America 47,245,184 20,673,649 26,571,535

USA 18,353,462 7,341,385 11,012,077Canada 2,031,742 853,332 1,178,410Belize 17,059 7,677 9,382Brazil 11,506,319 5,523,033 5,983,286Chile 988,997 405,489 583,508

Colombia 2,644,423 1,348,656 1,295,767Guatemala 892,537 428,418 464,119

Mexico 6,559,974 2,951,988 3,607,986Nicaragua 334,984 150,743 184,241Paraguay 386,960 170,262 216,698

Peru 1,721,519 705,823 1,015,696Puerto Rico 243,622 114,502 129,120Venezuela 1,563,586 672,342 891,244

Europe 31,401,329 14,123,478 17,270,731Austria 510,922 204,369 281,007Belgium 646,767 271,642 355,722Britain 3,766,919 1,695,114 2,071,805

Czech Republic 77,886 37,385 42,837Denmark 338,337 138,718 186,085Finland 325,907 166,213 179,249France 3,776,513 1,812,726 2,077,082Greece 665,470 299,462 366,009

Germany 5,151,538 2,060,615 2,833,346Iceland 18,372 7,716 10,105

Hungary 627,023 282,160 344,863Liechtenstein 2,089 836 1,149

Ireland 248,097 104,201 136,453Italy 3,628,592 1,632,866 1,995,726

Luxembourg 28,918 13,881 15,905Monaco 2,016 827 1,109

Netherlands 1,019,887 520,142 560,938Poland 2,414,146 1,158,790 1,327,780

Portugal 657,759 295,992 361,767Spain 2,517,548 1,132,897 1,384,651

Sweden 561,650 247,126 308,908Switzerland 465,679 190,928 256,123

United Kingdom 3,766,919 1,770,452 2,071,805Wales 182,375 78,421 100,306

Asia and The Pacific 215,882,842 101,525,163 118,735,563Bangladesh 8,833,779 3,533,512 4,858,578

August 23, 2011


Bhutan 136,598 57,371 75,129China 81,177,976 36,530,089 44,647,887

East Timor 63,703 30,577 35,037Hong Kong 428,445 175,662 235,645

India 66,566,912 33,949,125 36,611,802Indonesia 14,903,309 7,153,588 8,196,820

Japan 7,958,312 3,581,240 4,377,072Laos 379,257 170,666 208,591

Macau 27,830 12,245 15,307Malaysia 1,470,155 602,764 808,585Mongolia 171,957 68,783 94,576

Philippines 5,390,106 2,263,845 2,964,558Papua New Guinea 338,767 152,445 186,322

Vietnam 5,166,425 2,479,884 2,841,534Singapore 272,118 111,568 149,665Pakistan 9,949,771 5,074,383 5,472,374

North Korea 1,418,597 680,927 780,228South Korea 3,014,610 1,356,575 1,658,036

Sri Lanka 1,244,072 559,832 684,240Taiwan 1,421,864 625,620 782,025

Thailand 4,054,095 1,662,179 2,229,752Australia 1,244,571 584,948 684,514

New Zealand 249,613 107,334 137,287Africa 22,492,322 9,585,144 12,370777Angola 1,782,104 712,842 980,157

Botswana 4,757,338 1,998,082 2,616,536Central Republic 82,811 33,124 45,546

Chad 4,218,950 1,687,580 2,320,423Congo Brazzaville 1,585,918 666,086 872,255Congo Kinshasa 387,438 174,347 213,091

Ethiopia 350,700 168,336 192,885Ghana 141,096 57,849 77,603Kenya 236,076 120,399 129,842Sudan 351,974 168,948 193,586

South Africa 1,612,246 725,511 886,735Swaziland 1,126,054 506,724 619,330Tanzania 4,305,869 1,894,582 2,368,228Uganda 157,744 64,675 86,759Zambia 144,450 67,892 79,448

Zimbabwe 1,251,554 538,168 688,355Table 2-1: Descriptive Statistics (Recorded Acne Patients for 2004 – World)

August 23, 2011



Totality (World) Boys GirlsCount 77 77 Mean 1,894,901.742727 2,272,059.820390 Sample Variance 32,366,377,624,893.300000 43,823,622,013,878.700000 Sample Standard Deviation 5,689,145.597090 6,619,941.239458 Minimum 826.56 1108.8 Maximum 36530089.2 44647886.8 Range 36529262.64 44646778 Population Variance 31,946,035,058,336.300000 43,254,484,065,646.500000 Population Standard Deviation 5,652,082.364787 6,576,814.127345 Standard Error of the Mean 648,338.311807 754,412.319778 Confidence Interval 95.% lower Confidence Interval 95.% Upper -3,794,243.854363 -4,347,881.419069 Half-width 7,584,047.339818 8,892,001.059848 97.4% 96.1%

Empirical Rule -9,483,389.451454 -10,967,822.658527 Mean - 1s 13,273,192.936908 15,511,942.299306 Mean + 1s 97.4% 97.4%

Percent in Interval (68.26%) -15,172,535.048544 -17,587,763.897985 Mean - 2s 18,962,338.533999 22,131,883.538764 Mean + 2s 97.4% 97.4% Percent in Interval (95.44%) Mean - 3s -15,172,535.048544 -17,587,763.897985 Mean + 3s 18,962,338.533999 22,131,883.538764 Percent in Interval (99.73%) 17,067,436.791271 19,859,823.718374 Skewness 5.475584 5.455699 Kurtosis 30.818791 31.156550 Coefficient of Variation (CV) 300.23% 291.36% 1st Quartile 120,398.760000 149,664.900000 Median 428,417.760000 560,937.850000 3rd Quartile 1,632,866.400000 1,995,725.600000 Inter Quartile range 1,512,467.640000 1,846,060.700000 Mode #N/A #N/A Low Extremes 0 0 Low Outliers 0 0 High Outliers 2 3 High Extremes 4 4

Table 2-2: Descriptive Statistics (Recorded Acne Patients for 2004 – North and South America)


August 23, 2011


North and South America Boys Girls

Count 13 13 Mean 1,590,280.690769 2,043,964.232308 Sample Variance 5,345,606,482,950.080000 10,109,918,117,694.900000 Sample Standard Deviation 2,312,056.764647 3,179,609.742987 Minimum 7676.55 9382.45 Maximum 7341384.8 11012077.2 Range 7333708.25 11002694.75 Population Variance 4,934,405,984,261.620000 9,332,232,108,641.450000 Population Standard Deviation 2,221,352.287293 3,054,870.227791 Standard Error of the Mean 641,249.170517 881,865.074177 Confidence Interval 95.% lower 193,118.772638 122,545.296862 Confidence Interval 95.% Upper 2,987,442.608900 3,965,383.167754 Half-width 1,397,161.918131 1,921,418.935446 Empirical Rule Mean - 1s -721,776.073878 -1,135,645.510679 Mean + 1s 3,902,337.455416 5,223,573.975294 Percent in Interval (68.26%) 84.6% 84.6%

Mean - 2s -3,033,832.838525 -4,315,255.253665 Mean + 2s 6,214,394.220063 8,403,183.718281 Percent in Interval (95.44%) 92.3% 92.3%

Mean - 3s -5,345,889.603172 -7,494,864.996652 Mean + 3s 8,526,450.984710 11,582,793.461267 Percent in Interval (99.73%) 100.0% 100.0% Skewness 1.876046 2.290172 Kurtosis 2.641628 5.223513 Coefficient of Variation (CV) 145.39% 155.56% 1st Quartile 170,262.400000 216,697.600000 Median 672,341.980000 891,244.020000 3rd Quartile 1,348,655.730000 1,295,767.270000 Inter Quartile range 1,178,393.330000 1,079,069.670000 Mode #N/A #N/A Low Extremes 0 0 Low Outliers 0 0 High Outliers 0 1 High Extremes 2 2

Table 2-3: Descriptive Statistics (Recorded Acne Patients for 2004 – Europe)


August 23, 2011


Europe Boys Girls Count 24 24 Mean 588,478.256250 719,613.789583 Sample Variance 492,487,975,782.363000 753,233,755,616.357000 Sample Standard Deviation 701,774.875428 867,890.405303 Minimum 826.56 1108.8 Maximum 2060615.2 2833345.9 Range 2059788.64 2832237.1 Population Variance 471,967,643,458.098000 721,849,015,799.009000 Population Standard Deviation 686,999.012705 849,616.981821 Standard Error of the Mean 143,249.196592 177,157.387137 Confidence Interval 95.% lower 292,144.717225 353,135.814532 Confidence Interval 95.% Upper 884,811.795275 1,086,091.764635 Half-width 296,333.539025 366,477.975052 Empirical Rule Mean - 1s -113,296.619178 -148,276.615719 Mean + 1s 1,290,253.131678 1,587,504.194886 Percent in Interval (68.26%) 79.2% 79.2%

Mean - 2s -815,071.494607 -1,016,167.021022 Mean + 2s 1,992,028.007107 2,455,394.600189 Percent in Interval (95.44%) 95.8% 95.8%

Mean - 3s -1,516,846.370035 -1,884,057.426325 Mean + 3s 2,693,802.882535 3,323,285.005491 Percent in Interval (99.73%) 100.0% 100.0% Skewness 1.081026 1.199782 Kurtosis -0.496993 0.036280 Coefficient of Variation (CV) 119.25% 120.61% 1st Quartile 97,755.867500 127,416.575000 Median 259,384.070000 326,885.075000 3rd Quartile 1,139,369.970000 1,341,998.075000 Inter Quartile range 1,041,614.102500 1,214,581.500000 Mode #N/A #N/A Low Extremes 0 0 Low Outliers 0 0 High Outliers 0 0 High Extremes 0 0

Table 2-4: Descriptive Statistics (Recorded Acne Patients for 2004 – Asia and the Pacific)


August 23, 2011


Asia and The Pacific Boys Girls

Count 24 24 Mean 4,230,215.111667 4,947,315.129167 Sample Variance 94,679,114,136,653.800000 126,692,198,371,929.000000 Sample Standard Deviation 9,730,319.323468 11,255,762.896043 Minimum 12245.2 15306.5 Maximum 36530089.2 44647886.8 Range 36517844 44632580.3 Population Variance 90,734,151,047,626.500000 121,413,356,773,099.000000 Population Standard Deviation 9,525,447.551041 11,018,772.925018 Standard Error of the Mean 1,986,193.114737 2,297,572.980088 Confidence Interval 95.% lower 121,461.632559 194,423.325545 Confidence Interval 95.% Upper 8,338,968.590775 9,700,206.932788 Half-width 4,108,753.479108 4,752,891.803621 Empirical Rule Mean - 1s -5,500,104.211801 -6,308,447.766876 Mean + 1s 13,960,534.435135 16,203,078.025209 Percent in Interval (68.26%) 91.7% 91.7%

Mean - 2s -15,230,423.535269 -17,564,210.662919 Mean + 2s 23,690,853.758603 27,458,840.921252 Percent in Interval (95.44%) 91.7% 91.7%

Mean - 3s -24,960,742.858737 -28,819,973.558961 Mean + 3s 33,421,173.082071 38,714,603.817295 Percent in Interval (99.73%) 91.7% 95.8% Skewness 3.039926 3.090067 Kurtosis 8.357948 8.864279 Coefficient of Variation (CV) 230.02% 227.51% 1st Quartile 142,225.957500 177,157.612500 Median 614,191.855000 781,126.775000 3rd Quartile 2,743,290.900000 3,317,686.625000 Inter Quartile range 2,601,064.942500 3,140,529.012500 Mode #N/A #N/A Low Extremes 0 0 Low Outliers 0 0 High Outliers 1 1 High Extremes 2 2

Table 2-5: Descriptive Statistics (Recorded Acne Patients for 2004 – Africa)

August 23, 2011



Africa Boys GirlsCount 16 16 Mean 599,071.523750 773,173.568750 Sample Variance 455,139,695,132.094000 786,565,768,089.565000 Sample Standard Deviation 674,640.419136 886,885.431208 Minimum 33124.4 45546.05 Maximum 1998081.96 2616535.9 Range 1964957.56 2570989.85 Population Variance 426,693,464,186.338000 737,405,407,583.968000 Population Standard Deviation 653,217.776998 858,723.126266 Standard Error of the Mean 168,660.104784 221,721.357802 Confidence Interval 95.% lower 239,581.021721 300,585.683613 Confidence Interval 95.% Upper 958,562.025779 1,245,761.453887 Half-width 359,490.502029 472,587.885137 Empirical Rule Mean - 1s -75,568.895386 -113,711.862458 Mean + 1s 1,273,711.942886 1,660,058.999958 Percent in Interval (68.26%) 81.3% 81.3%

Mean - 2s -750,209.314522 -1,000,597.293667 Mean + 2s 1,948,352.362022 2,546,944.431167 Percent in Interval (95.44%) 93.8% 93.8%

Mean - 3s -1,424,849.733658 -1,887,482.724875 Mean + 3s 2,622,992.781158 3,433,829.862375 Percent in Interval (99.73%) 100.0% 100.0% Skewness 1.294489 1.291175 Kurtosis 0.406018 0.352179 Coefficient of Variation (CV) 112.61% 114.71% 1st Quartile 107,271.945000 119,071.150000 Median 340,535.700000 416,210.300000 3rd Quartile 716,008.875000 910,090.775000 Inter Quartile range 608,736.930000 791,019.625000 Mode #N/A #N/A Low Extremes 0 0 Low Outliers 0 0 High Outliers 3 3 High Extremes 0 0

Table 3-1: Frequency Distribution - Quantitative (Male Acne Patients in terms of %)

August 23, 2011


Frequency Distribution - Quantitative Data Cumulative

low

er upper midpointwidt

h frequenc

y percent frequen

cy percent 40 < 42 41 2 12 15.6 12 15.6 42 < 44 43 2 19 24.7 31 40.3 44 < 46 45 2 10 13.0 41 53.2 46 < 48 47 2 15 19.5 56 72.7 48 < 50 49 2 12 15.6 68 88.3 50 < 52 51 2 8 10.4 76 98.7 52 < 54 53 2 1 1.3 77 100.0 77 100.0

40 42

44 46

48 50

52 54

0

5

10

15

20

25

30

Histogram

% of Boys with Acne

Num

ber o

f Cou

ntrie

s

Table 3-2: Frequency Distribution - Quantitative (Female Acne Patients in terms of %)

August 23, 2011


Frequency Distribution - Quantitative

Dat

a cumulative

low

erupp

ermidpoi

ntwidt

h frequen

cyperce

nt freque

ncyperce

nt 48 < 50 49 2 6 7.8 6 7.8 50 < 52 51 2 6 7.8 12 15.6 52 < 54 53 2 16 20.8 28 36.4 54 < 56 55 2 16 20.8 44 57.1 56 < 58 57 2 9 11.7 53 68.8 58 < 60 59 2 20 26.0 73 94.8 60 < 62 61 2 4 5.2 77 100.0 77 100.0

48 50

52 54

56 58

60 62

0

5

10

15

20

25

30

Histogram

Series1

% of Girls with Acne

Num

ber o

f Cou

ntrie

s

August 23, 2011


Table 4-1: Confidence Intervals of the Mean; Boys

Confidence Interval - Mean 95% Confidence Level 1894901.743 Mean 5689145.597 Std. Dev. 77 n 1.960 z 1,270,719.7409 Half-width 3,165,621.4837 Upper confidence limit 624,182.0018 Lower confidence limit

Table 4-2: Confidence Intervals of the Mean; Girls

Confidence Interval - Mean

95% Confidence Level

2272059.82 Mean

6619941.239 Std. Dev.

77 n

1.960 z

1,478,620.9763 Half-width

3,750,680.7966 Upper confidence limit

793,438.8441 Lower confidence limit

August 23, 2011


Table 5-1: Hypothesis Testing

Hypothesis Test: Independent Groups (z-test) Group 1 Group 2 1,894,901.742727 2,272,059.820390 mean 5,689,145.597090 6,619,941.239458 std. dev. 77 77 n -377,158.0776623 difference (Group 1 - Group 2) 994,726.3517115 standard error of difference 0 hypothesized difference -0.38 z .7046 p-value (2-tailed) -2,326,785.9014898 confidence interval 95.% lower 1,572,469.7461651 confidence interval 95.% upper 1,949,627.8238274 half-width

Table 6-1: One-Factor ANOVA

August 23, 2011


One factor ANOVA Mean n Std. Dev 1,894,901.74273 77 5,689,145.597090 Boys 2,272,059.82039 77 6,619,941.239458 Girls

2,083,480.78156 15

4 6,154,819.849360 Total

ANOVA table

Source SS d

f MS F p-valueTreatment 5,476,556,298,519.1 1 5,476,556,298,519.1 0.14 .7051

Error 5,790,439,972,546,680.0 15

2 38,094,999,819,386.0

Total 5,795,916,528,845,200.0 15

3

Boys Girls1,700,000.00000

1,800,000.00000

1,900,000.00000

2,000,000.00000

2,100,000.00000

2,200,000.00000

2,300,000.00000

2,400,000.00000

Comparison of Groups

August 23, 2011


Table 7-1: Chi-square Contingency Table Test for Independence

Chi-square Contingency Table Test for Independence Boys Girls Total USA Observed 7341385 11012077 18353462 Expected 8346131.05 10007330.95 18353462.00 % of chisq 16.8% 14.0% 30.8% Canada Observed 853332 1178410 2031742 Expected 923922.96 1107819.04 2031742.00 % of chisq 0.7% 0.6% 1.4% Belize Observed 7677 9382 17059 Expected 7757.48 9301.52 17059.00 % of chisq 0.0% 0.0% 0.0% Brazil Observed 5523033 5983286 11506319 Expected 5232432.24 6273886.76 11506319.00 % of chisq 2.2% 1.9% 4.1% Chile Observed 405489 583508 988997 Expected 449740.68 539256.32 988997.00 % of chisq 0.6% 0.5% 1.1% Colombia Observed 1348656 1295767 2644423 Expected 1202536.12 1441886.88 2644423.00 % of chisq 2.5% 2.1% 4.5% Guatemala Observed 428418 464119 892537 Expected 405876.06 486660.94 892537.00 % of chisq 0.2% 0.1% 0.3% Mexico Observed 2951988 3607986 6559974 Expected 2983110.36 3576863.64 6559974.00 % of chisq 0.0% 0.0% 0.1% Nicaragua Observed 150743 184241 334984 Expected 152332.04 182651.96 334984.00 % of chisq 0.0% 0.0% 0.0% Paraguay Observed 170262 216698 386960 Expected 175967.83 210992.17 386960.00 % of chisq 0.0% 0.0% 0.0% Peru Observed 705823 1015696 1721519 Expected 782850.84 938668.16 1721519.00 % of chisq 1.1% 0.9% 1.9%

August 23, 2011


Puerto Rico Observed 114502 129120 243622 Expected 110785.70 132836.30 243622.00 % of chisq 0.0% 0.0% 0.0% Venezuela Observed 672342 891244 1563586 Expected 711031.72 852554.28 1563586.00 % of chisq 0.3% 0.2% 0.5% Austria Observed 204369 281007 485376 Expected 220721.94 264654.06 485376.00 % of chisq 0.2% 0.1% 0.3% Belgium Observed 271642 355722 627364 Expected 285290.16 342073.84 627364.00 % of chisq 0.1% 0.1% 0.2% Britain Observed 1695114 2071805 3766919 Expected 1712984.70 2053934.30 3766919.00 % of chisq 0.0% 0.0% 0.0% Czech Republic Observed 37385 42837 80222 Expected 36480.49 43741.51 80222.00 % of chisq 0.0% 0.0% 0.0% Denmark Observed 138718 186085 324803 Expected 147702.29 177100.71 324803.00 % of chisq 0.1% 0.1% 0.1% Finland Observed 166213 179249 345462 Expected 157096.85 188365.15 345462.00 % of chisq 0.1% 0.1% 0.1% France Observed 1812726 2077082 3889808 Expected 1768867.77 2120940.23 3889808.00 % of chisq 0.2% 0.1% 0.3% Greece Observed 299462 366009 665471 Expected 302619.10 362851.90 665471.00 % of chisq 0.0% 0.0% 0.0% Germany Observed 2060615 2833346 4893961 Expected 2225500.55 2668460.45 4893961.00 % of chisq 1.7% 1.4% 3.1% Iceland Observed 7716 10105 17821 Expected 8104.00 9717.00 17821.00 % of chisq 0.0% 0.0% 0.0% Hungary Observed 282160 344863 627023 Expected 285135.09 341887.91 627023.00 % of chisq 0.0% 0.0% 0.0% Liechtenstein Observed 836 1149 1985 Expected 902.67 1082.33 1985.00 % of chisq 0.0% 0.0% 0.0% Ireland Observed 104201 136453 240654 Expected 109436.02 131217.98 240654.00

August 23, 2011


% of chisq 0.0% 0.0% 0.1% Italy Observed 1632866 1995726 3628592 Expected 1650081.30 1978510.70 3628592.00 % of chisq 0.0% 0.0% 0.0% Luxembourg Observed 13881 15905 29786 Expected 13545.01 16240.99 29786.00 % of chisq 0.0% 0.0% 0.0% Monaco Observed 827 1109 1936 Expected 880.38 1055.62 1936.00 % of chisq 0.0% 0.0% 0.0% Netherlands Observed 520142 560938 1081080 Expected 491614.90 589465.10 1081080.00 % of chisq 0.2% 0.2% 0.4% Poland Observed 1158790 1327780 2486570 Expected 1130753.37 1355816.63 2486570.00 % of chisq 0.1% 0.1% 0.2% Portugal Observed 295992 361767 657759 Expected 299112.11 358646.89 657759.00 % of chisq 0.0% 0.0% 0.0% Spain Observed 1132897 1384651 2517548 Expected 1144840.44 1372707.56 2517548.00 % of chisq 0.0% 0.0% 0.0% Sweden Observed 247126 308908 556034 Expected 252853.26 303180.74 556034.00 % of chisq 0.0% 0.0% 0.0% Switzerland Observed 190928 256123 447051 Expected 203293.87 243757.13 447051.00 % of chisq 0.1% 0.1% 0.2% United Kingdom Observed 1770452 2071805 3842257 Expected 1747244.22 2095012.78 3842257.00 % of chisq 0.0% 0.0% 0.1% Wales Observed 78421 100306 178727 Expected 81275.07 97451.93 178727.00 % of chisq 0.0% 0.0% 0.0% Bangladesh Observed 3533512 4858578 8392090 Expected 3816254.55 4575835.45 8392090.00 % of chisq 2.9% 2.4% 5.3% Bhutan Observed 57371 75129 132500 Expected 60253.61 72246.39 132500.00 % of chisq 0.0% 0.0% 0.0% China Observed 36530089 44647887 81177976 Expected 36915216.64 44262759.36 81177976.00 % of chisq 0.6% 0.5% 1.0% East Timor Observed 30577 35037 65614

August 23, 2011


Expected 29837.59 35776.41 65614.00 % of chisq 0.0% 0.0% 0.0% Hong Kong Observed 175662 235645 411307 Expected 187039.49 224267.51 411307.00 % of chisq 0.1% 0.1% 0.2% India Observed 33949125 36611802 70560927 Expected 32087174.81 38473752.19 70560927.00 % of chisq 15.0% 12.5% 27.5% Indonesia Observed 7153588 8196820 15350408 Expected 6980509.55 8369898.45 15350408.00 % of chisq 0.6% 0.5% 1.1% Japan Observed 3581240 4377072 7958312 Expected 3618996.51 4339315.49 7958312.00 % of chisq 0.1% 0.0% 0.1% Laos Observed 170666 208591 379257 Expected 172464.93 206792.07 379257.00 % of chisq 0.0% 0.0% 0.0% Macau Observed 12245 15307 27552 Expected 12529.11 15022.89 27552.00 % of chisq 0.0% 0.0% 0.0% Malaysia Observed 602764 808585 1411349 Expected 641802.82 769546.18 1411349.00 % of chisq 0.3% 0.3% 0.6% Mongolia Observed 68783 94576 163359 Expected 74286.56 89072.44 163359.00 % of chisq 0.1% 0.0% 0.1% Philippines Observed 2263845 2964558 5228403 Expected 2377586.13 2850816.87 5228403.00 % of chisq 0.8% 0.6% 1.4%

Papua New Guinea Observed 152445 186322 338767

Expected 154052.34 184714.66 338767.00 % of chisq 0.0% 0.0% 0.0% Vietnam Observed 2479884 2841534 5321418 Expected 2419884.16 2901533.84 5321418.00 % of chisq 0.2% 0.2% 0.4% Singapore Observed 111568 149665 261233 Expected 118794.20 142438.80 261233.00 % of chisq 0.1% 0.1% 0.1% Pakistan Observed 5074383 5472374 10546757 Expected 4796076.95 5750680.05 10546757.00 % of chisq 2.2% 1.9% 4.1% North Korea Observed 680927 780228 1461155 Expected 664451.81 796703.19 1461155.00

August 23, 2011


% of chisq 0.1% 0.0% 0.1% South Korea Observed 1356575 1658036 3014611 Expected 1370876.97 1643734.03 3014611.00 % of chisq 0.0% 0.0% 0.0% Sri Lanka Observed 559832 684240 1244072 Expected 565734.57 678337.43 1244072.00 % of chisq 0.0% 0.0% 0.0% Taiwan Observed 625620 782025 1407645 Expected 640118.45 767526.55 1407645.00 % of chisq 0.0% 0.0% 0.1% Thailand Observed 1662179 2229752 3891931 Expected 1769833.19 2122097.81 3891931.00 % of chisq 0.9% 0.8% 1.7% Australia Observed 584948 684514 1269462 Expected 577280.53 692181.47 1269462.00 % of chisq 0.0% 0.0% 0.0% New Zealand Observed 107334 137287 244621 Expected 111239.99 133381.01 244621.00 % of chisq 0.0% 0.0% 0.0% Angola Observed 712842 980157 1692999 Expected 769881.54 923117.46 1692999.00 % of chisq 0.6% 0.5% 1.1% Botswana Observed 1998082 2616536 4614618 Expected 2098470.93 2516147.07 4614618.00 % of chisq 0.7% 0.6% 1.2%

Central Republic Observed 33124 45546 78670

Expected 35774.73 42895.27 78670.00 % of chisq 0.0% 0.0% 0.0% Chad Observed 1687580 2320423 4008003 Expected 1822616.26 2185386.74 4008003.00 % of chisq 1.4% 1.2% 2.5%

Congo Brazzaville Observed 666086 872255 1538341

Expected 699551.70 838789.30 1538341.00 % of chisq 0.2% 0.2% 0.4% Congo Kinshasa Observed 174347 213091 387438 Expected 176185.20 211252.80 387438.00 % of chisq 0.0% 0.0% 0.0% Ethiopia Observed 168336 192885 361221 Expected 164263.17 196957.83 361221.00 % of chisq 0.0% 0.0% 0.0% Ghana Observed 57849 77603 135452 Expected 61596.02 73855.98 135452.00

August 23, 2011


% of chisq 0.0% 0.0% 0.1% Kenya Observed 120399 129842 250241 Expected 113795.65 136445.35 250241.00 % of chisq 0.1% 0.0% 0.1% Sudan Observed 168948 193586 362534 Expected 164860.25 197673.75 362534.00 % of chisq 0.0% 0.0% 0.0% South Africa Observed 725511 886735 1612246 Expected 733159.57 879086.43 1612246.00 % of chisq 0.0% 0.0% 0.0% Swaziland Observed 506724 619330 1126054 Expected 512066.57 613987.43 1126054.00 % of chisq 0.0% 0.0% 0.0% Tanzania Observed 1894582 2368228 4262810 Expected 1938488.27 2324321.73 4262810.00 % of chisq 0.1% 0.1% 0.3% Uganda Observed 64675 86759 151434 Expected 68863.74 82570.26 151434.00 % of chisq 0.0% 0.0% 0.1% Zambia Observed 67892 79448 147340 Expected 67002.02 80337.98 147340.00 % of chisq 0.0% 0.0% 0.0% Zimbabwe Observed 538168 688355 1226523 Expected 557754.26 668768.74 1226523.00 % of chisq 0.1% 0.1% 0.2% Total Observed 145907436 174948607 320856043 Expected 145907436.00 174948607.00 320856043.00 % of chisq 54.5% 45.5% 100.0% 721377.60 chi-square 76 df 0.00E+00 p-value

August 23, 2011


Documents

Ecostat Paper (Acne Statistics)