Did the ZLF Bring More Visitor to the Oktoberfest?

Since the ZLF is at the same location as the Oktoberfest a lot of farmers and other visitors who maybe would normally not come to the Oktoberfest are going there in order to see the exhibition. This could have an influence on the mean daily visitor count. We will further investigate this hypothesis by looking at our data. In order to adjust for the duration we will use the mean daily visitor count for our analysis:

We can see that the mean daily visitor count varies around 388 thousand. There was a huge drop in 2001 which could be due to the terror attacks at the World Trade Center which took place a few weeks before the start of the Oktoberfest. Two other big drops compared to the previous year can be found in 1988 and 2016. For 2016 one could also argue that this drop is due to the shooting in Munich on July 22nd in the same year and because of the general fear of terror attacks around that time. Actually my research did not find any reasons for the drop in 1988. Even the weather was good during the Oktoberfest in that year.

Looking at years the ZLF took place, we can not tell whether the total visitor count is greater or less in general. It looks like, though, that the general mean daily visitor count has been varying around a lower level since 2001 (9/11 year). We are going to investigate this hypothesis later.

But first, let’s have a closer look at the total visitor count distribution for years with and without the ZLF:

It looks like both box plots are quiet similar. The median of ZLF years is sligthly higher. Nevertheless, we need to be careful, as we have fewer data points for ZLF years than we do for normal years.

We will continue with testing the null hypothesis:
“ZLF years do not have an impact on mean daily visitor count”

To do so we first start with a test for normal distribution in order to select a proper statistical test for comparison. We are going to use the Shapiro-Wilk test for that purpose. It tests the null hypothesis that the data is normally distributed.

# test for normal distribution of ZLF years
shapiro.test(dt[dt$zlf == 1,]$visitors_day)

## 
##  Shapiro-Wilk normality test
## 
## data:  dt[dt$zlf == 1, ]$visitors_day
## W = 0.9461, p-value = 0.6473

# test for normal distribution of normal years
shapiro.test(dt[dt$zlf == 0,]$visitors_day)

## 
##  Shapiro-Wilk normality test
## 
## data:  dt[dt$zlf == 0, ]$visitors_day
## W = 0.96318, p-value = 0.4814

The outcome of the Shapiro-Wilk test suggests that both groups have normal distributed values. The quantile-quantile plot also supports this, except of a few outliers at the ends:

We will assume that our data is normally distributed and continue with a t-test to compare the means of the two groups:

t.test(visitors_total ~ zlf, data = dt)

## 
##  Welch Two Sample t-test
## 
## data:  visitors_total by zlf
## t = -0.50553, df = 12.282, p-value = 0.6221
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -454537.6  282982.0
## sample estimates:
## mean in group 0 mean in group 1 
##         6292000         6377778

The outcome of our tests confirms the null hypothesis (the difference in means is equal to 0).

This means that, given this results, the mean daily Oktoberfest visitor count in ZLF years is not statistically different to normal years

Did the Visitors Consume More Beer in ZLF Years?

Now that we know that the ZLF did not bring more visitors to the Oktoberfest, we could ask whether the visitors consumed more beer in ZLF years. We are going to take a part of the beer consumption plot from part 1 and color the ZLF years:

At a first view we cannot see any differences in years with and years without the ZLF. They both follow a similar development. We are going to use the same procedure as above to test for differences. But first a look at the box plots:

Both box plots look similar again but the ZLF year data seems to be split. We now start with a test for normal distribution and continue with a proper statistical comparison test:

# test for normal distribution of ZLF years
shapiro.test(dt[dt$zlf == 1,]$beer_cons_per_visitor)

## 
##  Shapiro-Wilk normality test
## 
## data:  dt[dt$zlf == 1, ]$beer_cons_per_visitor
## W = 0.87501, p-value = 0.139

# test for normal distribution of normal years
shapiro.test(dt[dt$zlf == 0,]$beer_cons_per_visitor)

## 
##  Shapiro-Wilk normality test
## 
## data:  dt[dt$zlf == 0, ]$beer_cons_per_visitor
## W = 0.91753, p-value = 0.04502

The outcome of the Shapiro-Wilk test again suggests that both groups have normal distributed values. Nevertheless the p-value is way smaller than before.

The quantile-quantile plot shows us why: The lower and higher quantiles don’t fit the line well.

We could again assume a normal distribution, but in my opinion we should try a non-parametric test here. We are going to use the Mann-Whitney-U-test to compare the groups. In R this test can be performed using the wilcox.test() function.

wilcox.test(beer_cons_per_visitor ~ zlf, data = dt, conf.int = T)

## 
##  Wilcoxon rank sum test
## 
## data:  beer_cons_per_visitor by zlf
## W = 132, p-value = 0.4652
## alternative hypothesis: true location shift is not equal to 0
## 95 percent confidence interval:
##  -0.1009945  0.1783459
## sample estimates:
## difference in location 
##             0.04383077

The test result suggests that there is no statistical difference in beer consumption per visitor between ZLF and normal years.

Did the Visitors Consume More Hendl in ZLF Years?

In the last part of our analysis of the ZLF and its influence we are going to look at the hendl consumption. The analysis is going to be performed the same way as above.

Again, we start with a colored plot of the hendl consumption development and two box plots:

The data distribution looks not very similar for years with and without ZLF. The ZLF boxplot is a little bit more widespread than the other. Nevertheless, we are going to perform our tests as before:

# test for normal distribution of ZLF years
shapiro.test(dt[dt$zlf == 1,]$hendl_cons_per_visitor)

## 
##  Shapiro-Wilk normality test
## 
## data:  dt[dt$zlf == 1, ]$hendl_cons_per_visitor
## W = 0.89192, p-value = 0.2088

# test for normal distribution of normal years
shapiro.test(dt[dt$zlf == 0,]$hendl_cons_per_visitor)

## 
##  Shapiro-Wilk normality test
## 
## data:  dt[dt$zlf == 0, ]$hendl_cons_per_visitor
## W = 0.88421, p-value = 0.008449

This time the test for normal distribution suggests that at least the normal year data is not normally distributed. That means we definitely need a non parametric test to compare the group means.

wilcox.test(hendl_cons_per_visitor ~ zlf, data = dt, conf.int = T)

## 
##  Wilcoxon rank sum test
## 
## data:  hendl_cons_per_visitor by zlf
## W = 102, p-value = 0.7014
## alternative hypothesis: true location shift is not equal to 0
## 95 percent confidence interval:
##  -0.01888336  0.01236117
## sample estimates:
## difference in location 
##           -0.001684179

The Wilcoxon test confirms our impression that there is no statistical difference between the mean hendl consumption of both groups.