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

Organization of Data for Analysis: Unit Review

C1.1 C1.2 C1.3 C2.1 C2.2 C2.3 C2.4 C2.5About 40 minutes
Learning goals
  • I can explain the role of data in statistical studies, the sources of variability and the different types of data.
  • I can describe populations, samples, sampling techniques and the sources of bias.
  • I can design experiments and surveys that follow the principles of control, randomization and replication, and that are ethical.
  • I can find, collect, clean and organize primary and secondary data to answer a question.

Words to know

parameter / statistic
A number describing a population / a number calculated from a sample.
bias
A systematic error that pushes results consistently in one direction.
randomization
Using chance to select a sample or assign treatments.
tidy data
One record per row, one variable per column, one value per cell.

Let's review!

In this unit you learned how statisticians get good data before any analysis begins. You saw why data matter and why studies can disagree, why data always vary, and how to classify data in many ways (categorical or numerical, nominal or ordinal, discrete or continuous, primary or secondary, experimental or observational, microdata or aggregate). You studied populations and samples, five random sampling techniques, and the many kinds of bias. You designed experiments with control, randomization and replication, wrote fair survey questions, considered ethics and privacy, and organized data in tables, spreadsheets and databases, including data from Statistics Canada.

The next units, One-Variable Data Analysis and Two-Variable Data Analysis and Validity, analyse the data you have learned to collect. This review has a few questions from every lesson. Try each one, then press Show answer to check.

How to use this review

Work through one or two lesson sections at a time. Write full answers: for "name the bias" questions, say the type, how it pushes the results and how to fix it. For calculations (stratified samples, randomized response, estimates of totals), show each step. For every question you miss, note which lesson it came from and reread that lesson's examples. Finish with the 10-question quiz.

Data concepts (C1)role of data, variability,types of data (lessons 1 to 4)Populations and samples (C2)sampling methods, bias(lessons 5 to 7)Designing data collection (C2)experiments, surveys, ethics(lessons 8 to 10)Organizing data (C2)tables, spreadsheets, databases,secondary sources (lessons 11, 12)Next: One-Variable Data Analysis and Two-Variable Data Analysis and Validity
How the lessons in this unit fit together: from understanding data, to choosing a sample, to designing collection, to organizing the results.

The Role of Data in Statistical Studies

1

List the five steps of the statistical inquiry process in order.

2

Give three reasons two studies of the same relationship can reach different conclusions.

3

A study found that towns with more libraries have higher graduation rates. A councillor says building libraries will raise graduation rates. Is the conclusion justified?

Variability in Data and Sampling Variability

1

Name the three main sources of variability.

2

What happens to the spread of sample proportions when the sample size is multiplied by 4?

3

Is "the mean mass of 30 randomly chosen apples from an orchard" a parameter or a statistic?

Variables and Types of Data

1

Classify: number of goals scored; wait time at a clinic; T-shirt size; province of birth.

2

Is "Does outdoor temperature affect hot-chocolate sales?" one-variable or two-variable? Name the response variable.

3

Why is a phone number categorical?

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

1

Classify in three ways: you randomly assign 30 classmates to two keyboard layouts and record each person's typing speed.

2

Two schools have mean marks of 75 (300 students) and 81 (100 students). Find the combined mean.

3

Give one reason aggregate data cannot answer every question.

Populations, Samples and the Census

1

A survey randomly selects 500 of a city's 64 000 households from a property list; 140 have an electric vehicle. Estimate the number of households with one.

2

In that survey, what is the sampling frame, and who might it miss?

3

Give two situations where a census is a better choice than a sample.

Which sampling method chose the shaded units?123456789101112131415161718192021222324252627282930
Units 1 to 30 in order. The shaded units are the sample.

Sampling Techniques

1

Which method chose the shaded units in the figure above? State the interval and start.

2

A company has 1800 hourly workers, 900 salaried workers and 300 managers. Find a proportional stratified sample of 150.

3

Name the method: randomly select 8 of 40 apartment buildings and survey every household in them.

4

Name the method: randomly choose 5 schools, then 2 classes in each, then 6 students in each class.

Bias in Sampling and Surveys

1

Name the bias and its likely direction: a survey on exercise habits done at a fitness centre.

2

Name the bias: "Wouldn't you agree that our overcrowded roads need a new highway?"

3

Name the bias: only 12% of mailed surveys are returned.

Principles of Primary Data Collection: Control, Randomization and Replication

1

Name the three principles of experimental design and what each protects against.

2

A teacher compares a new method in her morning class with the old method in her afternoon class. Name a confounding variable.

3

What is the difference between random selection and random assignment?

Designing Effective Surveys and Questionnaires

1

Fix this question: "How often do you read? (sometimes / a lot)"

2

With the coin method of randomized response, 31% answer Yes. Estimate p.

3

What is the difference between anonymity and confidentiality?

Designing Experiments and Ethical Data Collection

1

Twenty volunteers each try two pillow types for a week, in a random order. Name the design.

2

Why is a double-blind design used in drug trials?

3

Give three things an ethics review would check in a student survey.

Organizing Data: Tables, Spreadsheets and Databases

1

State the three rules of tidy data.

2

Write a formula for the mean of column E for rows where column B is "Grade 12" (rows 2 to 101).

3

A Province field contains Ontario, ontario, ON and Ont. What should you do?

Finding and Using Secondary Data: Statistics Canada and Other Databases

1

Name a good source for each: (a) monthly unemployment rates, (b) daily snowfall in Sudbury in 2010.

2

What does the symbol x mean in a Statistics Canada table?

3

List four elements of a data citation.

Just for fun

Unit summary in one sentence: collect it randomly, ask it fairly, measure it carefully, organize it tidily, and cite it properly. Then, and only then, may you make a graph.

Check your understanding

Quiz

1.

Which is a parameter?

2.

Which variable is categorical, ordinal?

3.

A survey randomly selects 20 students from each grade of a school. This is:

4.

For a systematic sample of 75 from a list of 3000, the sampling interval k is:

5.

A survey of Internet habits is done only by landline telephone. The main problem is:

6.

A larger sample reduces:

7.

Which study can best show that a new fertilizer causes taller plants?

8.

Using the coin method of randomized response, 45% of respondents answer Yes. The estimated proportion with the trait is:

9.

Which question is double-barrelled?

10.

In a tidy spreadsheet, each column should hold:

For parents and teachers

Use the review to find what to revisit:

  • Confusing association with cause, or vague statistical questions → Lesson 1 (The Role of Data in Statistical Studies).
  • Mixing up parameter and statistic, or expecting samples to match the population exactly → Lesson 2 (Variability in Data and Sampling Variability).
  • Misclassifying variables (labels treated as numbers, discrete versus continuous) → Lesson 3 (Variables and Types of Data).
  • Primary/secondary, experimental/observational or microdata/aggregate errors, or unweighted means → Lesson 4 (Primary and Secondary... Microdata and Aggregate Data).
  • Population versus sampling frame, or estimating totals → Lesson 5 (Populations, Samples and the Census).
  • Naming sampling methods, systematic intervals, stratified sample sizes → Lesson 6 (Sampling Techniques).
  • Naming biases or their direction → Lesson 7 (Bias in Sampling and Surveys).
  • Control, randomization, replication, lurking variables → Lesson 8 (Principles of Primary Data Collection).
  • Flawed survey questions, overlapping categories, randomized response algebra → Lesson 9 (Designing Effective Surveys and Questionnaires).
  • Block and matched-pairs designs, blinding, ethics and OCAP® → Lesson 10 (Designing Experiments and Ethical Data Collection).
  • Tidy tables, spreadsheet formulas, two-way tables, cleaning → Lesson 11 (Organizing Data).
  • Choosing and judging secondary sources, quality symbols, citations → Lesson 12 (Finding and Using Secondary Data).

Looking ahead: the sibling units One-Variable Data Analysis and Two-Variable Data Analysis and Validity analyse data like those collected here, and the Culminating Data Management Investigation asks your teen to plan, collect and organize data for a study of their own, using every skill in this unit.