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Assignment 4: Creating graphs for your data

To create graphs for my data, I choose a reasearch question with the gapminder dataset: Does alcohol consumption or urban rate influence the breast cancer rate ?

Therefore I had the three variables urbanrate, breastcancerper100TH and  alcconsumption available.

All of them are quantatative variables, so I choose to group them into the percentage groups with new secondary variables created out of them to show a graph for categorical variables, too.

I than started by using the univariate function to examine the means and standard deviation for the values, made bar charts for the group and original variables as univariate graph, and at last I made a scatterplot for the corresponding variables breastcance100th and the two others, urbanrate and alcconsumption.

SAS Code:

By looking at the results of the univariate function, we see how the mean and standard deviation looks like. This way, the range of the observations can be examined, for example in the urbanrate:

The univariate graphs look the following, showing that all are unimodal, while the urbanrate peaks at around , breastcancerrate and alcohol consumption rate are both skewed right distributions.

For the scatterplots showing the connection between breast cancer rate and either alcohol consumtion or urbanrate, a small positive correlation/trend between the two variables could be observed.

So this visualizing of our data helped to understand the disctibution and to draw conclusions out of them.

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Assignment 3: Making Data Management Decisions

To manage my used data in the question of how excessive alcohol usage can be examined, I had to adjust my data in appropriate ways to work with it and get meaningful results.

First I labeled the needed variables and coded out missing data from those quantitative reasearch questions (answer Unknown or Never)

Afterwards I recoded the used variables wih more specific quantitative values, as the codebook uses different time sets (once a year, 2 times a week and so on).

I recoded all values to a number refered to days a month that apply (USMONTH).

Afterwards I was interested in the real number of beer drank in this month time period.

As the dataset I am using only tells me the number of days with 5+ beer, I included a factor for this quantity (QTYFACTOR) and with this I set a secondary variable describing the usual quantity of beer drank in a month (USQTY)

Then I only included data of intereset for ages between 25 and 55 and for persons that drank at least once alcool in the past 12 month.

For a better overview I grouped the ages in this range in a way, that a “Young”, a “Middle age” and an “Old” group is created, with the cut for every group at around 1/3rd of the percentage of used values.

For interpretation I sorted the output by ID-Number, checked with a PROC PRINT if the calculated secondary variable is correct and printed frequency tables for my used variables with a PROC FREQ procedure.

By checking the result, we see that the filters and management options are functionable, as only data of interest is included and the sorting into age groups is done, too.

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Assignment 2: First SAS programm

For my reasearch question codebook, the relevent data was defined to answer if any correlation between alcohol abuse and living region is related already.

To begin, I set my dataset to the NESARC-pds data.

To now check how the distribution of the variables is within the interesting  variables I first labelled all the data accordingly and filtered only for subsets that are interesting for me (age between 25 and 55, Drank at least 12 alcoholic drinks last year: Yes)

To do so, I included LABEL statement and IF functions to my programm.

I then used the SORT procedure to sort the results by ID-Number and let SAS create distribution tables by using the PROC FREQ function with tables for all interesting variables.

Code looks the following:

By checking the results, I see it worked, as only data for age 25 to 55 is included and the table for S2AQ2 only includes data for the value of “1″, meaningt at least 12 alcoholic drinks were consumed in the last 12 month.

The percentages add up to 100%.

My program an successfully.

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Assignement 1:Getting Your Research Project Started

For the course I want to dive deep into the topic, if beer drinking is related to the area people are living in.

I observed the NESARC dataset as it includes various data on Alcohol and Related Conditions in the USA, so it would be a perfect match for my research question:  Is beer drinking related to the living area?

First hypothesis: There should not be a significant difference.

For the living area details, I look into the codebooks: Background Information area and choose the variable CENDIV as categorical variable for the living region to include in my personal codebook:

Then I checked alkohol consumption and choose to only include thoose that drank at least 12 alkoholic drinks in the last 12 month (S2AQ2 = 1)

For defining a more specific second topic within this research question, I focussed on beer consumption, excessive beer consumption in particular.

So I checked how the codebook provides information about that and it does with the variable S2AQ5G, telling how often 5+ beers were drank in one day during the last 12 month:

Also it was interesting to see, if alkohol dependence is present or not.

The variable that resembled this question the most for my hypothesis is ALCABDEP12DX, so I included it, too:

With this personal codebook I have enough data to find a relation between Census region and excessive beer drinking / alcohol abuse.

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Week4: Testing a potential moderator

When comparing the relation between the urban rate “urbanrate” and the breast cancer rates “breastcancerper100TH” using the gapminder dataset to perform a Pearson correlation, it is shown that there is a moderately strong positive relation with a very high significance (r=0.57; p>0.0001).

But is this the case for all subsets of variables used here?

If we want to know if another variable has an effect of the outcomes of our statistical test, we repeat the process and introduce a third variable as moderator.

The moderator variable can devide the examined data into subsets matching its criteria and look at the outcome one by one.

For my example, I want to know that the overall seen significance of the urbanrate and breast cancer rate might be different in countries that have a low, mid and high urban rate.

Therefore I sorted the urban rates into 3 groups from urban rate 0% to 35% (group1 = low urban rate), 35% to 70% (group2= mid urban rate) and 70% to 100% (group 3== high urban rate).

In my SAS-code, I created a new categorical variable “urbangrp” as explained above, it used it as moderator for the correlation coefficient procedure.

I excluded invalid values, sorted the data by urban group and then ran the procedure first without moderation (for comparison reasons), and than with the variable urbangrp as moderator.

The results show the following:

So we see, that for the group 1 (low urban rate) the correlation is r= -0,25 and not significant (p=0.12>0.05).

For group 2 r=0.34 and significant (p=0.0016). So a moderate positive correlation is examined.

And for group 3 the r=0.29 and also significant (p=0.037). A moderately weak positive correlation was found.

Visually this would give us such a graph when looking at the three groups in the scatterplot:

So by looking at different parts of the correlation, we found different results.

Result: The used of urbangrp as a moderator indeed moderated the test results.

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Week 3: Generating a Pearson Correlation Coefficient

The process of generating a correlation coefficient is used to examine the dependence between a quantative explanatory variable and a quantative response value.

Q->Q

For this course, I will perform a Pearson correlation and analyze the results.

A correlation can be made visually with a scatterplott. With this one can see a general form /shape of the value mid line.

A pearson correlation coefficient is generally useful only when looking at linear shaped scatterplots, for curved it gives no good significant findings.

The coefficient “r” can range from -1 to +1, while a value next to (+/-)1 indicates a perfect relation between the variables, whilst a value near 0 indicate a very weak connection between the variables examined.

For my test I will use the gapminder dataset, as it already contains several quantative variables sorted to different countries of origin for the collected data.

I will examine to correlations, first between braest cancer rate “breastcancerper100TH”  and alcohol consumption rate “alcconsumption”, second between breast cancer rate and rate of individuals living in urban areas “urbanrate“.

To perform that with SAS this code is used:

The Proc Corr statement provides the correlation between (in this case 3) variables in an output table.

For visuallizing I included scatterplots for both relations I try to examine (breastcancer100TH as explanatory variable on the x-axis for both plots).

The output is the following:

We find for relation between breast cancer and alcohol consumption a r=0.493 with a p-value of <0.0001 indicating a moderate positive relation.

For the relation between breast cancer and urbanrate a r=0.57 with a p-value of <0.0001 indicating a moderately strong relation between the variables.

 When we square the examined r value, we get Coefficient of Determination (RSqaure) which tells us, how many values of the second variable we can predict with the first variable.

Here r-square for breastcancer and alcconsumption is 0.243, so we could predict about 24.3% of the breast cancer cases with the alcohol consumption rate.

The r-square for breastcancer and urbanrate is 0.325, so we could predict about 32.5% of the breast cancer cases with the urban rate.

So we can say that the higher the urbanrate or the alcohol consumption rate, the higher the breast cancer rate will be.

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Week 2: Performing a Chi-Square test of independence

The Chi-Square (X²) test of independence can be used when comparing a categorical explanatory variable (e.g. the absence or presence of major depression) to another categorical explanatory value (e.g. ethnical group).

C->C

For this course we use a categarical explanatory value and compare it to a categorized originally quantative explanatory variable.

For my test I choose to compare for regular chewing tobacco users if there is a dependency between the use of chewing tobacco and the presence of symptoms for lifetime nicotine dependence.

I categorized the usage frequency in 6 groups sorted by the usual times in a month cheweing tobacco is used. It results in the groups “1″, “2.5″, “5″, “14″, “22″ and “30″ days monthly use.

The null hypothesis here is:

Ho: There is no significant difference between those categorys.

While the alternative hypothesis then is:

Ha: There is a sinificant difference in those categorys.

For performing the Chi-Sqaure, I only include relevant data of those who used chewing tobacco in the last 12 month, sort the data by ID-Number and perform the test using the Proc Frey function, followed by /CHISQ, pairing the categories:

“used chewing tobacco when experiencing symptoms for lifetime nicotine dependence” + “Usual usage frequency of chewing tobacco” 

As we have 6 different response categories who all need to be compared pairwise to another, we have in sum 15 paired comparisons involved in the test.

To ensure, that we do not have a type 1 error, we need to adjust our used alpha with the bonferroni procedure: To do this we divide the original alpha of 0.05 with the amount of comparisons:

p (adjusted): 0.05/15 = 0.0033

The result of the hi Square showed a value of 54.38 and a p<0.0001 So it looks like we have a significant finding, as the p value is way smaller than the used, adjusted p value.

But to ensure that we do not have a type one error, we perform a post hoc by comparing all of the possible pairs one by one, catergorize the results and check for significant differences.

We do this by using the CHISQ Porc FREQ function, but only include the date for two of the frequency categories at a time. This is repeated 15 times for all possible pairs, see for example:

The results show some different outcomes and tell us, that there are several comparisons without significant findings, for example comparing “14″ to “30″ we have a p-value of 0.065: no definite significance.

To compare the results in an easy an short overview, I put them in a table:

When looking at this, we only see significant differences between the pairs 1+30, 2.5+30 and 5+30. All other comparisons show no significant differences via the p-value that is greater than our adjusted p-value of 0.0033.

That means, that the post hoc does not give enough evidence to reject the null hypothesis.

So we still need to think, the Ho might still be true.

The post hoc protected us against a possible type 1 error successfully.

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Running an ANOVA with Post Hoc

With the nesarc-dataset and by using the method “Analysis of Variance” “ANOVA“ it is possible to conclude several hypotheses between a categorical explanatory variable (as for example the state an american citizen is living in) and a quantative response value (as for example the numbers of cigarettes smoked a week).

For doing this, we first set our null hypothesis, in my case I assume that there is no difference in the numbers of beers consumed in excessive beer drinking in one sitting (5+ beers in one sitting) for the categorical variable as “Census division” where the test persons are originated.

Meaning if the null hypothesis Ho is true, the means of excessive beer drinking quantities per census division should be the same for all 9 divisions.

Ho = µ1 = µ2= µ3= µ4= µ5= µ6= µ7= µ8= µ9

The alternative hypothesis resulting out of it is:

Ha = not all means are equal.

For performing the test I used the Data Analytics tool “SAS” and the nesarc dataset.

At first, I include the dataset and import the used variables for this test.

I defined the labels of thes used variables and explain what kind of data from the nesarc base should be used running the test.

To get a meaningful quantative responsible variable, I include the number of days with excessive beer drinking (min. 5 a day), calculate a value for the monthly use and multiply it with the minimum amount of beers in those sittings to get the variable USQTY (usual quantity)

Then I only include data of interest in filtering for middle aged people (25 to 55 years old) who at least once drank beer in the last year.

Finally the data is sorted by ID-number of the nesarc participants and the ANOVA itself is run.

I also included the “Duncan's new multiple range test” as unction of the SAS tool to perform a post hoc test on the results of the ANOVA.

This shows if there really are significant differences in the means of more than two categorical variables and therefore shows, if the results of the ANOVA are valid for the used test case.

The Results are the following:

The 9 different CENDIVS with values 1 to 9 were used as categorical explanatory values.

With the included data, 13713 arguments were looked at, while 4048 match the criteria and were used for the test.

The test results in an F-statistic value of 3.42 and a p-value of 0,0006. It is way lower than our alpha value of 5%.

Therefore we can reject the null hypothesis and accept the alternative hypothesis: Not all means are equal.

The Duncan Post Hoc treatment also shows the same:

There are three different groups of means that are not significantly different to another, but to the other groups.

This tells us, that it is true to reject the null hypothesis and protects us against type 1 errors (rejecting the null hypothesis, although it is true).