Grade by Grade
E. Culminating Data Management Investigation · Culminating Data Management Investigation

Background Research and Hypotheses

E1.1 E1.2About 65 minutes
Learning goals
  • I can do background research on my question using reliable sources and record them properly.
  • I can write operational definitions so that every variable is measured the same way.
  • I can identify the explanatory, response and possible lurking variables in my question.
  • I can write a clear hypothesis with reasons, and the predictions it makes about the data.
  • I can state in advance what pattern in the data would support or contradict my hypothesis.

Words to know

background research
Reading what is already known about a question (guidelines, published data, studies) before collecting data, so the investigation builds on it.
operational definition
An exact description of how a variable will be measured or recorded, for example "sleep = hours from falling asleep to waking on a usual school night, to the nearest quarter hour".
hypothesis
A clear, testable statement of the answer you expect, with a reason, made before you look at the data.
null statement
The "nothing is going on" version of a hypothesis: no difference between groups, or no relationship between variables. Your evidence is weighed against it.
explanatory and response variables
The explanatory (independent) variable is the one you think may explain changes in the response (dependent) variable.
lurking variable
A variable not included in the study that is related to both variables and may create, hide or change an apparent relationship.

Don't start from zero

Scientists, journalists and government analysts never collect data without first reading what is already known. Background research tells you whether your question has already been answered, which definitions experts use, what results would be surprising, and which variables might get in the way.

The curriculum asks you to pose a significant problem and perform the appropriate background research. In this lesson you will do that research, sharpen your definitions, and write a hypothesis: your best prediction of the answer, with reasons, written down before you see your data.

Where to look, and how to judge it

  • Statistics Canada: articles (for example in its journal Health Reports or its daily release, The Daily) and data tables on almost every topic about Canadians. Note the survey name, the year and the exact definitions.
  • Government and professional guidelines: for example, health guidelines from national organizations.
  • Other reliable databases: Environment and Climate Change Canada (climate), sports leagues (official statistics), the Bank of Canada (economics), municipal open data.
  • University research and reputable news: good for ideas; trace any statistic back to its original source.

For each source, record who published it, when, how the data were collected, and the full citation (you will need it for your report). Prefer sources with clear methods and no reason to favour a particular result.

What is known?guidelines, studies,published dataWhat is missing?the gap your datacan fillHypothesisyour predictedanswer, with reasonsPredictionswhat the datashould show if trueBackground research comes first: it shapes the hypothesis and tells you what counts as a surprise.
From background research to hypothesis. Each step narrows what you expect to see in your own data.

Operational definitions

Everyday words are slippery. "How much do you sleep?" Does napping count? Weekends? Time in bed or time asleep? An operational definition says exactly how a variable will be measured, so every response means the same thing.

Good operational definitions:

  • name the unit (hours, dollars, kilometres) and precision (nearest quarter hour, nearest dollar);
  • name the time frame (a usual school night, the 2025 season, the last 7 days);
  • match the definitions in your background sources where possible, so you can compare your results with theirs.

Variables and hypotheses

In a question about a relationship, the explanatory variable is the one you think might explain changes in the response variable. Think about lurking variables too: things related to both that could create or hide an association. You met these in Two-Variable Data Analysis and Validity.

A hypothesis is a clear, testable statement of what you expect, with a reason. For each hypothesis, also write its null statement (no difference, or no relationship). Your analysis weighs the evidence: do the data look very different from what the null statement predicts?

A strong hypothesis:

  1. is specific (which group, which direction, which variable);
  2. is testable with the data you plan to collect;
  3. comes with a reason from your background research;
  4. turns into predictions about your summaries ("the mean will be lower", "r will be negative").
Explanatory variablehours of paid work per weekResponse variableschool-night sleep (hours)association?Possible lurking variableshomework, sports, screensHeld constant: same grade, same schoolA lurking variable linked to both could create or hide an association.
The variables in Amira's question. Dashed arrows show lurking variables that could affect both work hours and sleep.
Worked example

The model investigation, Stage 2: background research

Amira researches sleep and teen employment before writing her survey. What does she record, and how does it change her plan?

  1. Health guidelines: the Canadian 24-Hour Movement Guidelines for Children and Youth recommend 8 to 10 hours of uninterrupted sleep per night for youth aged 14 to 17. Most of her population is 17, so she adopts 8 hours as the benchmark: "meets the guideline" means 8 or more hours on a usual school night.
  2. Statistics Canada: she searches its website for articles and tables on youth sleep and on employment of students. She notes for each source the survey, the year and how sleep or work was defined, and saves the citation. She does not copy numbers without their definitions.
  3. Operational definitions: sleep = hours from falling asleep to waking on a usual school night (Sunday to Thursday nights), to the nearest quarter hour. Work = usual hours of paid work per week during the school year (0 if no job). This excludes volunteering and chores, and she will say so in her report.
  4. Lurking variables to keep in mind: homework load, sports and other activities, screen time at night, commuting time. She cannot control them all, but she adds one question about evening activities so she can discuss them later.
  5. What would surprise her: if students with jobs slept as much or more, perhaps because students who choose to work are more organized, or work only on weekends.

Background research gave Amira a benchmark (8 hours), precise operational definitions, a list of lurking variables and a reason for her prediction. All of these go into her report.

Worked example

The model investigation, Stage 3: hypotheses and predictions

Write Amira's hypotheses, their null statements and the predictions they make.

  1. Hypothesis 1 (comparison): Grade 12 students at Pinecrest who have part-time jobs sleep less on school nights, on average, than students without jobs, because work hours compete with time for homework and sleep.
  2. Null statement 1: there is no difference in the mean school-night sleep of the two groups.
  3. Predictions if Hypothesis 1 is true: the mean and median sleep of the job group will be lower; the job group's box plot will sit to the left; a smaller proportion of the job group will meet the 8-hour guideline.
  4. Hypothesis 2 (relationship): among students with jobs, more hours of work per week is associated with less sleep.
  5. Null statement 2: there is no linear relationship between hours worked and sleep; the correlation coefficient would be close to 0.
  6. Prediction if Hypothesis 2 is true: a scatter plot sloping down to the right, a negative correlation coefficient r, and a regression line with a negative slope.

Two hypotheses, each with a null statement and specific predictions about means, medians, box plots, proportions, r and the slope. Writing them now prevents "finding" whatever pattern happens to appear later.

Worked example

Example 3: Operational definitions for other projects

Write an operational definition for each variable. (a) "Snowfall" in a study of winters in Sudbury. (b) "Home-team advantage" in a study of a hockey league. (c) "Screen time" in a survey of students.

  1. (a) Total snowfall in centimetres from November 1 to March 31 each winter, as recorded at one Environment and Climate Change Canada station (name the station), from the historical climate data.
  2. (b) The proportion of regular-season games won by the home team (including overtime and shootout wins) in one named season, from the league's official results.
  3. (c) Self-reported minutes per day spent on a phone, tablet, computer, TV or game console for anything other than school work, on a usual school day, to the nearest 15 minutes.

Each definition names a unit, a time frame, a precision or rule and a source, so anyone could repeat the measurement.

Write it down before you look

Date your hypothesis in your project log before you collect or open your data. It is fine if the data prove you wrong. Reporting a hypothesis that was not supported, and explaining why, is honest science and earns full credit. Changing the hypothesis afterwards to match the data is not.

Just for fun

Why did the hypothesis bring a jacket? It heard the data might be cold to it. (Dress warmly: a well-made hypothesis survives either way.)

Hands-on activity

Your investigation, step 2: research log and hypothesis

You need: a computer with Internet access and your project log.

  1. Find three reliable sources related to your question. At least one should be from Statistics Canada, a government agency or another reliable database.
  2. For each, record: author or organization, title, date, web address, date accessed, how the data were collected, and the one or two facts most useful to you.
  3. Write an operational definition for each of your variables (unit, time frame, precision, source).
  4. Name your explanatory and response variables (if your question is about a relationship) and list at least two lurking variables.
  5. Write your hypothesis (with a reason), its null statement, and three predictions about your summaries.
  6. Date the page.

If your project is a probability game: your "background research" is the theory. Record the sample space and the rules, and write a hypothesis such as "the game favours the organizer, with an expected profit of about 0.75 tickets per play".

Your turn

1

Give two reasons to do background research before collecting data.

2

Write an operational definition for "hours of homework".

3

In "Is outdoor temperature related to ice cream sales at a store?", name the explanatory and response variables.

4

Write the null statement for: "Students who eat breakfast have a higher mean test score than students who do not."

5

Amira's hypothesis 2 predicts that r will be ______ .

6

Why should you record how a secondary source collected its data?

More practice: warm-up

1

True or false: a hypothesis should be written after you look at the data.

2

What benchmark did Amira choose for meeting the sleep guideline?

3

Name one Statistics Canada publication where you can find articles.

4

What is a lurking variable?

5

Should a hypothesis include a reason?

More practice: on your own

1

A student hypothesizes, "Sports affect marks." Improve the hypothesis.

2

Give two lurking variables for "Students who own more books get higher reading scores."

3

Why did Amira define work as paid work only? What effect might this choice have?

4

For a probability project on a two-spinner game, what plays the role of background research?

5

Write a hypothesis and null statement for a secondary-data project: "Has the mean January temperature in Winnipeg changed between 1960 to 1989 and 1990 to 2019?"

Challenge

1

Explain why a hypothesis that predicts no direction ("work hours and sleep are related") is weaker than Amira's directional hypothesis, using the idea of predictions.

2

Two background sources report different percentages of teens getting enough sleep. Give three reasons that could explain the difference without either being wrong.

3

Amira's population is Grade 12 students at one school. Explain why her background benchmark (for ages 14 to 17) still fits, and what she must say about the few students who are 18.

Check your understanding

Quiz

1.

Which is the best operational definition of "exercise"?

2.

In Amira's study, hours of paid work per week is the:

3.

The null statement for "students with jobs sleep less" is:

4.

Why is homework load a possible lurking variable in Amira's study?

5.

When should a hypothesis be written?

6.

What does background research NOT usually provide?

For parents and teachers

Big idea (E1.1, E1.2): good investigations build on what is already known. Background research supplies definitions, benchmarks and a reason for the hypothesis, and the hypothesis is written down before the data are seen.

How to help: Ask your teen to show you one source and explain who made it and how its data were collected. Play "define it": pick a word from their question ("active", "screen time", "cold winter") and ask how exactly it will be measured. Remind them that a hypothesis that turns out wrong is not a failure.

Health benchmark used in the model: the Canadian 24-Hour Movement Guidelines for Children and Youth recommend 8 to 10 hours of uninterrupted sleep per night for ages 14 to 17.

Common difficulties:

  • Copying statistics from a website without their definitions or year.
  • Hypotheses with no direction or no reason ("X affects Y").
  • Vague definitions that let respondents interpret questions differently.
  • Forgetting lurking variables, which later leads to claims of cause and effect.