## Thursday, March 27, 2008

### Statistics lie!

I've always told my students - statistics lie.

I'm amazed at how subtle little massages to the data or even to the way the data is presented can create an illusion that conveys to the reader what is intended. While reading the newspaper today, I came across this little notice on the straits times that the electricity tariffs are going to go up again. Usual suspect for the rise in tariffs - high fuel price. It then proceed to put a table, after which a chart is drawn.

Guess which one of the 3 below is shown in the straits times?

I copied the data and put it on an excel spreadsheet. While the data values remain the same, the scale of the graph is different for all 3. Hence, for anyone who didn't take a closer look at the scale of the graph, they would have made some major error in their quick perusal of the charts.

1. In the first chart, it seems that the electricity tariffs are shooting up faster than the fuel oil price.

2. In the second chart, it seems that the electricity tariffs are climbing as fast as the fuel oil price, but resting slightly below it.

3. In the third and last chart, it seems that electricity tariffs are pretty constant while the fuel oil price fluctuates wildly.

No prizes for guessing which of the chart above is used for the straits times :)

#### 7 comments :

fergus said...

Actually I think the first 2 is more misleading because you didn't start the graph axis from 0 for both..

But anyway, I think % change from a benchmark date might be a much better chart rather than absolute figures..

Any thoughts?

la papillion said...

Hi Fergus,

You misunderstood me. I didn't say that the first 2 is less misleading. I'm saying that all 3 can be misleading. Depending on whose interests is at stake, different graphs will be used.

Starting from 0 doesn't make it less misleading. I can equally start the first 2 graphs from 0 but instead of using cts/kWh, I can use cts/Wh or \$/mWh or any other more subtle changes.

Of course if you read the chart as it is, there is nothing misleading. It's only when a laymen looks at the chart without questioning, without looking at the axis, without taking a closer look...then he/she will be mislead.

% change is not a good idea to me too. 100 to 200 is a 100% increase. But 200 back to 100 is a 50% decrease. It could even be potentially more misleading.

Good discussion nevertheless!

Cheng said...

Hi LP,

Statistics are sure misleading. I never read the ST today, so im guessing it to be either graph 1 or 2.

Graph 3 shows a fairer picture of comparing prices of oil to tariffs as their price axis are of the same range.

It is good using graph 2 to compare how well tariffs react to oil prices movements only.

Since ST is fully garmen controlled, if they want to tell the citizens that their tariffs increases are faster than the increase in oil prices, then I think they will use graph 1. It is really misleading if one didnt look at the price axis and range carefully. Would have thought that the garmen so good, increase the % in tariffs more than the increase in % of oil prices.

Good article to educate fellow investors. :D

Cheers for you,

Cheng

la papillion said...

Hi Cheng,

Haha, you guessed wrongly :)

I think you made a mistake? Electricity tariffs is the amount that we paid for our electricity per kWh, so the lower it is, the better it'll be. If ST is fully garmen controlled, then they should support the garmen by saying that as the oil prices increase, electricity tariffs DIDN'T rise as much,and is in fact fairly constant despite the fluctuations of the oil price. This will convey the message that electricity pricing in singapore is fair to consumers.

By now you should have guessed which graph ST used :)

Actually does it make it fairer to put both on the same range? Or even starting from 0? Oil prices have their own range (in tens of dollars) while electricity tariffs have their own (in tens of cents). The only purpose of putting two graphs together is to look at the trends and see how each graphs respond to each other. The purpose should never be to compare both in terms of the same scale. THAT is my discontentment.

Perhaps I'm an extremist with radical views :) I believe the more raw the data is, the less chances of misleading (but it makes it harder to understand).

Thks for your comments cheng :)

Cheng said...

Ahhhhhhh, I confused the term on tariffs, thought it is something like subsidy. Hope other readers dont make the same mistake as I do. Thanks for your valuable lesson.

ST used graph 2. :D

In your opinion, how to make the comparison fairer?

la papillion said...

Hi Cheng,

Haha, wrong again :) They used graph 3, the one where it shows that the electricity tariffs remained more or less constant while oil prices fluctuates. As I said, I believe this will cause a casual reader of the graph to interpret that while oil prices moves a lot, the electricity tariffs (which is the price per kWh that residents pay) remained fairly constant.

In my opinion, to make it fairer, how about finding a ratio between the two for a start? I'll use the ratio of electricity tariffs to fuel oil price, then see how this ratio varies across different times.

By doing that, we end up with only 1 graph of which the values represent how much the electricity tariffs changes according to fuel oil price.

Sounds interesting...i'll post it up and see what funny trends we get :P

Hee hee, you probably don't pay the electricity bills? :)

fergus said...

One graph that I did, which is more similar to how they measure CPI is to have a benchmark year, then all subsequent years are a % of that year..

Again like you said, different ways of presenting information usually depends on who's purpose you intend to serve :) There is no such thing as a neutral way in that sense.. It's more of presenting it as a fair way.. but definitely it won't be neutral, because there are many 'fair' ways of presentation.