Grade by Grade
C. Organization of Data for Analysis · Organization of Data for Analysis

Primary and Secondary, Experimental and Observational, Microdata and Aggregate Data

C1.3About 65 minutes
Learning goals
  • I can distinguish primary data from secondary data and give advantages and disadvantages of each.
  • I can distinguish experimental data from observational data.
  • I can distinguish microdata from aggregate data and explain why agencies often publish only aggregate data.
  • I can classify a data set in all three ways and choose a suitable source for a question.

Words to know

primary data
Data collected first-hand by the person or team doing the study, for that study.
secondary data
Data collected by someone else, often for a different purpose, such as Statistics Canada tables or sports statistics websites.
experimental data
Data from a study in which the researcher deliberately imposes a treatment (changes a variable) and measures the response.
observational data
Data from a study in which the researcher only observes or asks, without imposing any treatment.
microdata
Data in which each record (row) is one individual respondent, such as one person or one household.
aggregate data
Summary data produced by grouping microdata, such as counts, totals, means or percentages for a region or group.
metadata
Data about the data: who collected it, when, how, definitions of variables, and sample size.

Where did these numbers come from?

Suppose you want to know whether Ontario teenagers sleep less than they did ten years ago. You could survey your own classmates. Or you could look up a national health survey. Or you could design an experiment where volunteers try a no-screens-before-bed rule. Each choice gives a different kind of data, with different strengths.

The curriculum asks you to distinguish several pairs of data types. In the last lesson you met categorical/numerical, nominal/ordinal and discrete/continuous. This lesson covers the other three pairs: primary/secondary, experimental/observational and microdata/aggregate.

Primary or secondary?

Primary data are collected by you, for your study: your own survey, measurements or experiment.

Secondary data were collected by someone else: Statistics Canada, Environment and Climate Change Canada, a sports league, a research article, a newspaper.

Both have trade-offs:

  • Primary: you control exactly what is asked or measured, and how. But it takes time and money, samples are usually small, and you must deal with ethics and privacy yourself.
  • Secondary: often fast, free, large and professionally collected. But it may not measure exactly what you need, may be out of date, may use definitions you did not choose, and you must judge its reliability.

The same numbers can be primary for one person and secondary for another. Statistics Canada's survey results are primary data for Statistics Canada and secondary data for you.

Experimental or observational?

  • Experimental data come from a study where the researcher imposes a treatment: assigns some plants to get fertilizer and others not, or assigns volunteers to a new exercise program.
  • Observational data come from studies where the researcher only observes or asks: surveys, records of what people already do, counts of birds at a feeder.

This matters because only a well-designed experiment can give strong evidence of cause and effect. Observational data can show relationships, but other variables may explain them. You will design experiments in the lessons Principles of Primary Data Collection and Designing Experiments and Ethical Data Collection.

Who collected the data?Primaryyou collected itSecondarysomeone else didI didothersDid researchers impose a treatment?Experimentaltreatment assignedObservationaljust observedyesno
Two questions classify a data set: who collected it (primary or secondary), and whether the researchers imposed a treatment (experimental or observational).

Microdata or aggregate?

Microdata have one record (row) for each individual respondent. Aggregate data are summaries of microdata: counts, totals, averages or percentages for groups.

In the figure below, six people's records are summarized by province. Ontario's three commuters took 25, 15 and 35 minutes, so the aggregate table reports a count of 3 and a mean of 25 minutes.

Why does it matter?

  • Microdata let you do any analysis you like: you can regroup, cross-tabulate and look at relationships between variables for the same people. But they carry privacy risks, because a single record could identify someone.
  • Aggregate data are safer to publish and easier to read, but you cannot go back to individual records. A mean commute by province cannot tell you whether older people commute longer.

Statistics Canada is required by the Statistics Act to keep respondents' information confidential. It publishes most results as aggregate data tables. It also releases some anonymized microdata, called Public Use Microdata Files (PUMFs), with identifying details removed or grouped.

Microdata: one row per personIDProv.AgeCommute (min)1ON34252QC51403ON19154MB42205QC27306ON6335summarizeAggregate data: summariesProv.CountMean commuteON325 minQC235 minMB120 minindividuals can no longer be seen
Microdata (left) keep every individual's record. Aggregate data (right) summarize them by group, here by province. The summary is easier to read and protects privacy, but the detail is gone.

Other ways to describe data

You may also see cross-sectional data (many individuals at one point in time, like a census) and time-series data (one quantity measured over time, like monthly unemployment rates). Your Culminating Data Management Investigation will probably use at least one secondary source, so it is worth recognizing these terms.

Worked example

Example 1: Classifying in three ways

Classify each data set as primary or secondary, experimental or observational, and microdata or aggregate. (a) You download a table of the mean household income for each Ontario census division. (b) You randomly assign 20 bean plants to get either 4 or 8 hours of light per day and record each plant's height. (c) You survey 50 students about their screen time and keep each student's answers in a spreadsheet row.

  1. (a) Collected by someone else: secondary. Nobody imposed a treatment on households: observational. Means by region are summaries: aggregate.
  2. (b) You collected it: primary. You assigned the treatment (light hours): experimental. One row per plant: microdata.
  3. (c) You collected it: primary. You only asked, with no treatment: observational. One row per student: microdata.

(a) secondary, observational, aggregate; (b) primary, experimental, microdata; (c) primary, observational, microdata.

Worked example

Example 2: Choosing a source

For each question, would primary or secondary data be the better choice? (a) How has the population of Ontario changed over the last 50 years? (b) Do students at your school prefer the new or the old cafeteria menu? (c) Does the brand of paper towel affect how much water it absorbs?

  1. (a) Historical population counts already exist and you cannot go back in time to count: use secondary data from Statistics Canada.
  2. (b) Nobody else has this data, and the question is about your specific school: collect primary data with a survey.
  3. (c) You can easily test it yourself with a fair experiment: collect primary, experimental data (manufacturers' claims are secondary but may be biased).

(a) secondary; (b) primary; (c) primary experimental data.

Worked example

Example 3: What aggregate data can and cannot answer

A table shows only the count and mean commute time for each province (as in the figure: ON 3 people, mean 25 min, QC 2 people, mean 35 min, MB 1 person, mean 20 min). Can you answer: (a) Which province has the longest mean commute? (b) What is the overall mean commute for all 6 people? (c) Do older people commute longer?

  1. (a) Yes. Compare the means: QC has the longest, 35 min.
  2. (b) Yes, because the counts are given: total minutes = 3 × 25 + 2 × 35 + 1 × 20 = 75 + 70 + 20 = 165, and 165 ÷ 6 = 27.5 min. (You must weight by the counts; the mean of the three provincial means, (25 + 35 + 20) ÷ 3 ≈ 26.7, is wrong.)
  3. (c) No. Age is not in the aggregate table, and the link between each person's age and commute is lost. You would need the microdata.

Aggregate data answer group-level questions, sometimes with care (weighted means), but relationships between variables for individuals need microdata.

Just for fun

A statistician's favourite way to keep a secret: aggregate it. "Somebody in Ontario ate the last butter tart" is perfectly true, and it protects the guilty.

Hands-on activity

Your thermometer versus the weather station

You need: an outdoor thermometer (or a car dashboard thermometer as a backup), a notebook, and Internet access for the last step.

  1. For five days, read the outdoor temperature at the same time each day (for example 7:00 a.m.) and record it. If you do not have a thermometer, record the temperature shown on a car dashboard or a sign, and note the source. These are your primary data.
  2. At the end of the week, go to the Environment and Climate Change Canada website (search "historical climate data") and find the readings from the weather station nearest your home for the same days and times. These are secondary data.
  3. Put both sets side by side in a table and find the difference for each day.
  4. Write three reasons the two sets might differ (location, instrument, height above ground, shade, exact time) and say which set you would trust for a report, and why.

What to look for: differences of 1 to 3 degrees are common. A thermometer near a house wall or in sunshine often reads warmer. The official station is placed and maintained to standards, so it is usually more reliable for comparing with other places, but your own reading better describes your own yard.

Your turn

1

You count the cars that pass your house in 10 minutes. Primary or secondary?

2

A table of the unemployment rate for each province, from Statistics Canada. Microdata or aggregate?

3

Researchers give half of a group of volunteers a new sleep app and compare their sleep with the other half. Experimental or observational?

4

Give one advantage and one disadvantage of secondary data.

5

Why do statistical agencies usually publish aggregate data rather than microdata?

6

A health survey asks 10 000 people how many hours they exercise per week. Experimental or observational?

More practice: warm-up

1

Data collected by someone else are called ____ data.

2

Data with one row per individual are called ____.

3

In which kind of study does the researcher impose a treatment?

4

Is the mean mark for each class in a school microdata or aggregate?

5

Name one Canadian organization that provides secondary data.

More practice: on your own

1

A city table shows the number of 311 complaints in each ward for each month. Classify it in all three ways (from your point of view as a student).

2

Two classes have mean marks of 72 (28 students) and 80 (12 students). Find the overall mean mark.

3

Explain why the same data set can be primary for one person and secondary for another.

4

You want to know whether listening to music while studying improves memory. Describe an experimental study and an observational study of this question.

5

List two questions that microdata from a student survey could answer but an aggregate table of averages could not.

Challenge

1

A student wants to know whether her town's winters are getting warmer. Plan a study that uses secondary data, and name two pieces of metadata she should check.

2

An aggregate table reports, for each of three regions, the number of households and the mean number of vehicles per household: Region A 2000 households, 1.2; Region B 500 households, 2.4; Region C 1500 households, 1.6. Find the mean for all households combined.

3

Even with names removed, microdata can sometimes identify a person. Explain how, and describe two ways an agency can reduce this risk.

Check your understanding

Quiz

1.

A student downloads a table of average rents by city from Statistics Canada. These data are:

2.

Which study produces experimental data?

3.

What is the main reason agencies publish aggregate data instead of microdata?

4.

Which is an advantage of primary data?

5.

Class A (20 students) has a mean of 70 and Class B (30 students) has a mean of 80. What is the combined mean?

6.

Data with one row for each respondent are called:

For parents and teachers

Big idea (C1.3): data can be described by who collected it (primary or secondary), how it was produced (experiment or observation) and how detailed it is (individual records or summaries). Each choice affects what questions the data can answer.

How to help: When your teen chooses a topic for the culminating investigation, ask: "Will you collect the data yourself or find it? Is there an experiment you could run? Do you need each person's answers or just totals?"

Common difficulties:

  • Thinking that all secondary data are reliable because they are "official". Students should still check the source and metadata.
  • Calling any study with a comparison an experiment. It is only an experiment if the researcher assigns the treatment.
  • Averaging group means without weighting by the group sizes.
  • Not realizing that aggregate data cannot show relationships between variables for individuals.