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for my term paper, I want to compare broadband internet price data in the US. There are three datasets, each represent retail prices from 2016, 2017 and 2018. All data is clustered into 6 download speed classes and four product classes (itnernet only, internet with fixed telephony, internet with television, internet with fixed telephony and television). This gives me 24 subsets of data per year.

My research question is "have broadband retail offer prices changed significantly from 2016 to 2018 across the different speed classes?" and I am not very familiar with these tests for significance and absolutely new to statistics. But at it's core I need to compare the mean prices of all products in the different speed clusters. Which tests and methods should I apply here?

I started reading about one and two-sided t-tests, Wilcox, Shapiro-Wilk, KS-tests and many more but find it a bit confusing and hard to understand what they are actually used for and which could be relevant for my research question.

A second question: If i changed my research question from "changed significantly" to "improved significantly" (i.e. less expensive in 2018 compared to 2016), how would that affect the choice of statistical tests?

I hope someone can bring some light into this or refer to some useful and easy-to-understand literature. The analysis is supposed to be done using R.

Cheers

###Update

My data looks something like this:

2016

OfferID Price Product SpeedCluster
NY001   20    Single  1
NY002   34    with FT 2
NY003   25    Single  1
NY004   40    with TV 3
NY005   42    Single  5
NY006   60    All     4
NY007   50    All     4

2017

OfferID Price Product SpeedCluster
NY001   19    Single  1
NY002   37    Single  2
NY003   24    Single  1
NY004   45    with TV 3
NY005   40    with TV 2
NY006   56    All     4
NY007   50    All     3

In every year, different price offers were collected directly from the Website of Internet Service Provider during two weeks. Time of year did not change over the years.

From this data, I did subsets, so all offers with internet only in speed cluster 1 are together, all offers with internet only in speed cluster 2, all offers with internet only in speed cluster 3, ...., all offers with internet and telephony in speed cluster 1, all offers with internet and telephony in speed cluster 2, ... and so on.

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  • $\begingroup$ It seems that what you want to find out is whether there is a dependence of price on year, while adjusting for speed and offer type. As Demetri points out, a linear regression is suitable for this, though it will assume a linear effect of year on price. $\endgroup$ – aocall Feb 6 at 14:29
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If I have understood your question correctly, it might be as simple as doing a linear regression.

Combine the datasets for the three years, and add a column indicating to which year the data are from. Then your model will look like

$$ y = \beta_0 + \beta_1\text{years since 2016} + \beta_2 \text{speed class} + \beta_3 \text{includes telephone}$$

The coefficient of $\beta_1$ should tell you if the price of internet has increased over the years. If you hypothesize that internet has become more expensive over time, then you should conduct a one sided t-test for $\beta_1$.

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This is an issue with problem formulation.

The tests you have mentioned are mainly related to inferential statistics where sampling is involved from a population. Here sampling from a population concept is not present.

Also, Most likely you have a date in your data.

Since we dont have access to your data, you can possibly take the following routes:

  1. Simple regression
  2. Time Series because the main feature here is time.

Providing the datasets features will help with more accurate answers.

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  • $\begingroup$ I dont think there is a linear interdependency between time and price. So you are suggesting an univariate time series analysis? $\endgroup$ – Luke666 Feb 5 at 16:14
  • $\begingroup$ time is more likely a important feature. you would have offerid and their start and end dates. so you could expand and replace offerid with date. offerid becomes a useable feature after conversion to date. also having datasets 2016 2017 and 2018 in a way makes time as categorical. instead converting offerid to date makes it continuous. along with date, you could use speedcluster also as another feature. $\endgroup$ – solver149 Feb 5 at 17:01
  • $\begingroup$ Sorry if I forgot to mention it, but there is no "date" as such. Each year, data was collected within a fixed timeframe (2 weeks of October) and represents the available offers per Internet Service Provider in each State and corresponding prices for the whole year. I dont have data on how expensive each single offer is for each week of the year. $\endgroup$ – Luke666 Feb 5 at 17:08
  • $\begingroup$ what is your sample size then?? $\endgroup$ – solver149 Feb 5 at 17:31
  • $\begingroup$ 2016: 1200, 2017: 1540, 2018: 1600. And between between 20 and 110 for each subset. $\endgroup$ – Luke666 Feb 5 at 18:01

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