Statistical observation: where do the numbers come from, and do we always have to count everyone?

Kamola opa owns the «Navbahor non» bakery. She wants to know three things: how much bread is sold every day, how much flour is left in the storeroom at the end of the month, and whether customers would like hot bread to come out in the evening too. The answer to all three questions is in numbers. But these numbers do not appear by themselves: someone has to collect them, at some point, by some method. This work of collecting data is called statistical observation.

What is statistical observation?

Statistical observation is the systematic collection and recording of data about mass phenomena according to a plan drawn up in advance. The word «systematic» matters: counting one day and forgetting the next is not observation. In the first lesson, Bobur writing down the customers who came to the barbershop every day for a week was a simple example of observation.

All the later work of statistics (averages, tables, charts, conclusions) relies on these collected data. If the data are collected wrongly, even the most elegant calculation gives a wrong conclusion.

Which four questions are answered before an observation?

Before starting, Kamola opa wrote down answers to four questions:

Sometimes the question «when» is answered with one exact moment. For example, Kamola opa weighs the storeroom on the last day of every month in the evening, after the bakery has closed. If she weighed part of the flour in the morning and part in the afternoon, the flour used in between could be counted twice or left out. That is why everything is counted as of one moment.

What types of observation are there?

Observation can be classified by three different questions.

1. By coverage: is everything observed or only a part?

• Complete (full) observation: every unit in the population is counted. Kamola opa takes into account all the receipts at the till. A population census is the best-known example of complete observation.
• Partial observation: only a part is studied. Its most important type is the sample: a part is chosen in such a way that conclusions about the whole population can be drawn from it.

2. By timing: how often?

• Current (continuous) observation: events are recorded as they happen. Each loaf sold is registered at the till immediately.
• Periodic observation: repeated at certain intervals. The flour in the storeroom is weighed at the end of every month.
• One-off observation: carried out once, when needed. The survey about evening bread.

3. By the method of obtaining data: where does the number come from?

• Direct observation: the observer sees, counts, weighs or measures personally. Weighing the flour sacks on scales.
• Documentary method: data are taken from ready documents. Sales volume is taken from till receipts.
• Survey: people are asked, orally or with a questionnaire. Asking customers about evening bread.

Kamola opa's three questions are distributed like this:

Why don't we always ask everyone?

About 1 400 customers come to the bakery in a week. Asking all of them would lengthen the queue and annoy customers. Kamola opa asked 70 of them, which is 70 / 1 400 = 5 percent of all customers. 49 people said «yes»: 49 / 70 = 70 percent.

A sample has a price: it may differ somewhat from the exact result obtained from the whole population. This difference is called sampling error. As the Australian Bureau of Statistics notes, a complete count has no sampling error, because the whole population is observed. As a randomly selected sample gets larger, this error usually decreases.

What errors occur in observation?

The most dangerous one is taking a one-sided sample. Kamola opa carried out the survey with 35 people in the morning and 35 people in the evening:

If she had asked only the morning customers, the result would have come out at about 51 percent instead of 70 percent, and she would have reached the wrong conclusion that «evening bread is not really needed». Yet the people who come in the evening are exactly the ones waiting for this bread. Such an error is not random: it always tilts the result in one direction and is not fixed by enlarging the sample: even if 700 morning customers were asked, the evening customers' opinion would still be left out.

Another group of errors has nothing to do with sampling at all. According to the Australian Bureau of Statistics materials, they occur at any stage of observation, both in a complete count and in a sample. The bureau names four types of them: coverage error (omitting a unit, adding an extra one or counting it twice), non-response, incorrect response and error in data processing. For example, if an employee mistakenly adds one day's bundle of receipts twice, the result comes out wrong even though all the receipts were counted.

Practical tip. Before starting an observation, run a small «trial»: ask for one day and see whether the question is clear and whether the answers are easy to record. Then most of the errors of the big observation become visible in advance.

In the next lesson

In the third lesson we will get to know the key terms of statistics: population, unit, attribute, sample and indicator.