What Does That Mean?

Community Development workers work in communities, with people, right?  Right.  So why should community workers know something about statistics?

As most community workers will have discovered, in their work they will be involved in surveys, studies, research and demographics.¹  If not carrying out such work, community workers are likely attempting to understand and apply such work.  It’s important to know what it all means.  That’s a good place to start – the mean.²

Mean and Median

In statistical terms the mean is what many people think of as the average – a term that most will understand.  The mean (average) is often used in surveys.  For example: the mean wage in the Statville³ community is $35,000.  To get that figure, the wages of every person in Statville are added together and then the result is divided by the total number of people in Statville.  Certainly, that does tell us something.  However, the figure could be quite misleading.  It could be skewed by a small sector of Statville obtaining very high wages, thus increasing the average wage.

One way of discovering whether the mean is unrepresentative is to find out the median wage.  The median is the point at which half the population earn a higher wage and half a lower wage.  Suppose there are 10,000 people in Statville.  If all those people are ranked according to their income, then the wage of the 5,000th person would be the median.  In our fictitious community of Statville suppose the median wage is $20,000 – significantly less than the mean of $35,000. 

What does that mean?  It certainly suggests that most people in that community earn significantly less than the average wage, and also suggests that there is an inequality of incomes in that community.

Errors and Deviations

An aspect of statistics that appears to be poorly understood is that of errors and deviations (more correctly known as Margin of Error and Standard Deviation). Because these are poorly understood, they can be used and misused easily and even deliberately, especially by politicians, decision-makers and lobbyists intent on using statistics to their own ends.

In any population there will be a variation from the mean.  Returning to our mythical community of Statville.  We know that the mean wage is $35,000.  We also know that there will be some who earn more than this and some who earn less.  But, how far from the mean will those variations be?  The standard deviation gives us a measure of this.  Without going into the mathematics of it, standard deviation gives us a measure of how close (or far) from the mean the majority of the population is.

Suppose we are told that the standard deviation is $3,000.  Then we know that around 68% of the population will have an income of between $32,000 ($35,000 – $3,000) and $38,000 ($35,000 + $3,000).  If we widen the number of standard deviations to three standard deviations (ie 3 x $3,000 = $9,000) then we would know that 99.8% of the residents earned between $26,000 and $44,000.

Margin of error is closely related to standard deviation: it is approximately twice the standard deviation.⁴  Margin of error relates to estimating the true mean of a whole population by determining the mean of a sample of that population.  In Statville we could do a survey of the entire population of 10,000, but that is likely to be time consuming, costly and cumbersome.
 
Instead we could survey a random sample of those residents.  Now let’s suppose that sample survey found that 40% of them believed that the government was doing a good job.  What does that tell us about the percentage of the total population?  Do 40% of the total population of 10,000 believe that the government is doing a good job?  The margin of error tells us how close we are.

The researcher tells us that the margin of error for their survey is 5%.  That tells us that with a high degree of confidence⁵ we can say that somewhere between 35% and 45% of the entire population believe that the government is doing a good job.  (i.e. 40% ± 5%)

Now comes the bit where politicians and others are prone to mislead with statistics.  Back to Statville again where one year 40% of the sample said they believed the government was doing a good job.  The following year the researchers ask the same question of another randomly selected sample.  This time, 43% of the sample say that they believe the government is doing a good job.  The researcher again says that the margin of error is 5%.

“Hurrah” cries the government, “survey shows that the percentage of people who have confidence in us is increasing.”  They point excitedly at the two figures – 43% this year, up from 40% last year.

Hang on, hang on.  The catch is in that figure often mentioned at the end of the article, sometimes in fine print, and never mentioned by the politician: margin of error 5%.

The two figures really prove nothing.  They neither prove that confidence has increased, nor do they prove a decrease in confidence.  Why’s that?

Consider this.  In the first year the true proportion of those believing the government was doing a good job could have been as high as 45% (40% plus the margin of error of 5%).  Similarly, this year the true proportion of those having confidence in the government could be as low as 38% (43% less the margin of error of 5%).  As you can see, because of the margin of error, it is not possible to make a definitive statement either way.

Be wary of claims like the one in this example.  They are very common.

A community development worker one does not need to add statistics to their tools of trade.  However, just understanding some basic concepts such as those mentioned above will mean you are less likely to have the wool pulled across your eyes.

1. Demographics are statistical characteristics of specific populations, e.g. gender, age, ethnicity, income etc.
2. As my biography states I have been involved in community development work for over 40 years.  However, I do also have a degree in mathematics and have tutored statistics at first year University level.
3. Statville is a fictitious community name used in this post as an example only.
4. If one wanted to be pedantic, the margin of error is 1.96 times the standard deviation.
5. At the 95% confidence level (for those who want to be accurate).  I won’t go into confidence levels as that can start to get a bit confusing.