As a part of one of my latest courses ‘Applied Statistics – from data to results’, we were asked to find any kind of large data set and apply at least one hypothesis test on it.

My group and I found a data set consisting of 130.000 wine tasting reviews on Kaggle.com and went to it. We worked hard on the data analysis and visualisation as a team and actually ended up learning a lot about applying hypothesis testing to real life data and the programming of it, but probably even more about the importance of considerate data visualisation.

We ended up doing a presentation of our findings in front of all course participants (selected projects were asked to present).

In this post, I will summarise our presentation together with an outline of findings and methods, and later on I will connect this post with specific guides to each procedures. In case you’re wondering, the wine bottle word cloud was also generated from our data set.

# Introducing the data

The data was retrieved from Kaggle.com, and was scraped in November 2017.

The data set consisted of 129.971 rows of data with 14 parameters of various type. There were numbers, Nan-values, or strings describing e.g. price, rating, or wine descriptions.

### Next: reduction and sorting of data

A rough discarding of non-descriptive data had to be done. Our main hypotheses revolved around relations with either price or rating of a wine, so we dropped all rows with Nan-values in these columns.

We then extracted the vintage of the wine from the wine description, as that was not a parameter.

After this, we had 120.975 rows of data, and 15 parameters.

# Choosing hypotheses

Any sorting in the data set (i.e. choosing reviews for a city, choosing reviews for 1 reviewer, or similar fixation of parameters) meant a serious reduction in the available data. The hypotheses were therefore reviewed a couple of times. We ended up investigating:

1. If ratings would be normally distributed.
2. Potential correlations between prices and ratings.
3. Bias in tasters.
4. Application of machine learning algorithms to predict either wine ratings or prices.

# H1: Normally distributed ratings

To test the normality, we made a histogram, and constructed a reference normal distribution based on the data’s mean and variance.

To actually test the normality of the distribution, we then performed a Kolmogorov-Smirnov test between these two statistics which returned a test-value of 0.9999.. The closer the test-value is to 1, the more normal the data is. The ratings were therefore concluded to be normal.

# H2: Price and rating correlations

To test the correlation between prices and ratings in an attempt to see if expensive wines are rated lower or higher based on their price, we plotted the mean price in each point-group and the variance.

While it could seem that there might be a higher-order or exponential correlation in the higher point ranges, it seems that the lower point ranges could consist of a linear correlation.

In the end, we remain on the conclusion that there is some positive correlation between the rating of a wine and its price, but it is non-trivial and can only be fitted with high degree polynomia which is likely to just overfit the data. A closer look at the data, however, showed that this was not the case, so we ended the analysis there.

# H3: Taster’s bias

### Joe Czerwinski

We drew the reviews from a single reviewer, Joe Czerwinski, and analysed his ratings of German and French wines. To eliminate fluctuations in the ratings due to price, we transformed the measure to one of points per dollar. Then we compared the histograms of these ratings using a Kolmogorov-Smirnov test again.

The Kolmogorov Smirnov test revealed a statistic of $$3.8 * 10^{-9}$$ which means the distributions are not at all alike. In comparison with this, we tested the distributions of all reviews of German and French wines, were the KS-test indicated greater similarity with a test-value of 0.47.

We therefore concluded that Joe was inclined to prefer French wines with a larger point per dollar.

### 19 reviewers

Using the points-per-price index, we made an overview of 19 different tasters, and their mean ratings (with standard deviation showing their ‘experience’ – at least in the data set)

# H4: Machine learning predictions

We applied two machine learning algorithms in order to use as much data as possible to predict either wine ratings based on the other informations, or the price of the wine based on the other informations.

Both methods actually proved to be almost equally good at predicting ‘correctly’ – meaning according to the actual data we withheld and had the algorithms estimate the parameter for (although some distributions might seem closer to the original one, measures of variation showed that they deviate equally).

This goes to show, that the complexity of a data set can weigh heavily on a researcher. Fixating one parameter value could seriously reduce the amount of data you look at – so with 15 parameters, ~121k rows of data might not be that much anyways.

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