Collecting and showing data
Introduced| English | Meaning |
|---|---|
| tally table/ˈtælɪ ˈteɪbl/ | A counting table using tally marks to record frequencies. |
| two-way table/tuː weɪ ˈteɪbl/ | A table showing frequencies or other data classified by two categorical variables. |
| correlation/ˌkɒrɪˈleɪʃn/ | A statistical association between variables, which does not by itself establish causation. |
| causation/kɔːˈseɪʃn/ | A relationship in which a change or event helps bring about another change or event. |
| qualitative/ˈkwɒlɪteɪtɪv/ | Describing qualities or categories rather than numerical measurements. |
| quantitative/ˈkwɒntɪteɪtɪv/ | Based on numerical values, measurements or counts. |
| discrete/dɪˈskriːt/ | Consisting of separate, distinct values rather than a continuous range. |
| continuous/kənˈtɪnjuːəs/ | Changing without a break or jump, or taking every value within an interval. |
"Statistics" — the word that means both data and lies
- "There are three kinds of lies: lies, damned lies, and statistics." — often attributed to Mark Twain.
- Good statistics tells the truth about data. Bad statistics misleads. The skill is telling them apart.
Data handling cycle
Follow a statistical question from collection to display.
Tally tables 计数表 and two-way tables 双向表
- A tally table records each value with a mark ($\mid$), grouping them in fives for easy counting.
- A two-way table sorts data by two features at once (e.g. boys/girls against walk/bus/car).
A two-way table of 60 students by gender and transport might show: 15 boys walk, 10 boys take the bus; 12 girls walk, 23 girls take the bus. Each cell is a count.
Data is collected from people, a sample drawn from a population
A two-way table sorts data by how many features at once?
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A two-way table cross-tabulates two features (e.g. gender vs transport).
A table where you make a mark for each value, then count, is a ______ table.
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A tally table records each value with a mark before counting.
Reading data honestly
- Only draw conclusions the data actually supports.
- Don't assume a trend that isn't shown, or causes that aren't proven.
- Correlation 相关性 is not causation 因果: two things can rise together without one causing the other.
Check the axes. A graph with a truncated $y$-axis can make small differences look huge. Always check the scale before drawing conclusions.
A Galton board shows how data piles up into a distribution
You should only draw conclusions that the data really supports.
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Over-claiming beyond the data is a common exam error to avoid.
If two quantities both increase together, one must cause the other.
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Correlation does not prove causation. Both could be influenced by a third factor.
Types of data
- Qualitative 定性 (categorical): colours, opinions, brands.
- Quantitative 定量 (numerical): height, age, score.
- Quantitative data is discrete 离散的 (counted: number of siblings) or continuous 连续的 (measured: height, time).
The number of siblings a student has is what type of data?
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Number of siblings is counted (not measured), so it is discrete quantitative.
Height is an example of ______ quantitative data.
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Height is measured (not counted), so it is continuous.
Why data matters
- Governments use census data to plan schools and hospitals. Companies use sales data to decide what to stock. Medical researchers use trial data to approve new drugs.
Two-way tables split data into parts, just like a bar model splits a total into proportional sections.
Complete and interpret a two-way table
- In a survey, junior bus 6, junior walk 4, senior bus 3 and senior walk 7 give row totals 10,10; column totals 9,11; grand total 20. Check totals in both directions.
- To compare two samples, use both an average and a spread. Scores A: $4,6,8$ and B: $5,6,7$ have equal means 6 but ranges 4 and 2. B is more consistent in this sample; three scores per group cannot establish a general population claim.
A survey has junior bus 6, junior walk 4, senior bus 3, senior walk 7. Find the total who walk.
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Add the walk column: 4 + 7 = 11.
You've got it
- a tally table counts values with marks; a two-way table sorts by two features at once
- only conclude what the data actually shows — correlation $\neq$ causation
- data types: qualitative (categories) or quantitative (numbers: discrete or continuous)