## Seeing is believing – measuring is evidence.

Recently an Austrian newspaper published the graph above. It was part of an interesting story on how people viewed the different political parties. One thing is notable: The first row and the fourth row are nearly similar – except the fourth row has much more on the left side (distrust) then the first. Let’s put them together to see this:

Now check the numbers – telling the percentage of people (dis)-trusting – note how the bar on the fourth (that says 31%) is nearly as long as the one next to it saying 40%? Let’s look at it with a line helping us:

Look at this: Someone made a mistake (or intended to show a difference bigger than it really was). This is pretty clear cut and several readers noted this in the comments below the article.

### How much is it off?

Let’s find out how much it is wrong. Going back from graphs to numbers is challenging and a tricky process – I use a tool called imagej made to measure graphics (you can also do this using your graphics manipulation program). I measure the length of all the bars. Based on this and the value we can calculate whether the graph is well made. Two things are important to us: the start point (`y`

) and the scale (`x`

). The scale tells us how many pixels were used per unit, the start point at which value the graph started.

This gives the following formula for any bar: `L=y+x*V`

(L is the length in pixels, V the value of the data-point). Since we do have two unknowns we need a second value/length pair to do the calculation `L1=y+x*V1`

– transforming this tells us `x=(L-L1)/(V-V1)`

and `y=L-x*V`

. This way we can calculate both scale and starting point. I did this in a spreadsheet for all the bars next to each other – since your measuring will be slightly inaccurate `x`

and `y`

will vary. I simply took the median of all `x`

and `y`

as their final values. Now we can calculate the expected length for each value point and the difference it has to the measured length: Most of the bars are about the right size (I do think this is measurement mistakes) – however the bar in question is 13-14 pixels too long. Gotcha sloppy data journalist.

Want more: @adrianshort did this for uk election advertisements