From a research question to an analysis plan
Before a treasure hunt, you decide what you are looking for and how you will know you found it. Before a research project, you decide what you will measure and how you will work out the answer, so the numbers cannot trick you later.
- Before this course: Experiment Design: variables and controls (course 15.9.2), which came after The Scientific Method & Science Fair Projects (course 15.9). You already know independent, dependent and controlled variables, control groups, trials, random order, blinding, random and systematic error, mean and range. This course adds statistics: how to describe, compare and trust your data.
- Two big kinds of data:
- Numerical data are measured or counted numbers: time in seconds, height in cm, number of seeds that sprouted.
- Categorical data are labels or groups: brand A, B or C; yes or no; colour.
- Descriptive statistics summarise the data you have (mean, median, spread, graphs). Inferential statistics use a sample to say something about a bigger group, with a measure of uncertainty (confidence intervals, tests).
- Population and sample: the population is everything you want to know about (all paper helicopters of this design); the sample is the ones you actually measure. Statistics tell you how far the sample might be from the truth.
- Kinds of research question and the tool that fits:
| Question | Data | Main tool (this course) |
|---|---|---|
| What is typical, and how much does it vary? | One numerical variable | Mean or median, standard deviation (Lesson 2) |
| Is group A different from group B? | Numerical result, two groups | Difference in means, t-test, effect size (Lesson 5) |
| Do two measurements go up or down together? | Two numerical variables | Scatter plot, correlation, regression (Lesson 6) |
| How common is something? | Categorical | Counts and percentages, bar chart (Lesson 3) |
- Analysis plan: write it before you collect data: the question, the variables, the sample size, the graph, the statistic or test you will use, and what you will do with odd results. Deciding after you see the data makes it easy to fool yourself.
- Running example in this course: paper helicopters dropped from a fixed height. The dependent variable is fall time in seconds; one independent variable is wing length in cm.
- Write your research question in one sentence.
- List each variable and mark it numerical or categorical, with its unit.
- Use the table to choose your main tool (describe, compare or relate).
- Write how many items or trials you will measure per group, and why.
- Write which graph you will draw and which statistic or test you will report.
- Write what you will do with odd results: report all, explain, or repeat and report both (course 15.9.2, lesson 5).
- Date the plan and ask your teacher or an adult to check it.
- Check: someone else could read your plan and know which numbers you will calculate before any data exist.
Videos by other creators on YouTube, for reference. They are not made by or affiliated with The Future Market.
Read the video script
[Host holding a paper helicopter] "Before I drop a single helicopter, I write down what I will calculate."
[Text on screen: Numerical vs categorical] "Is my data a number with a unit, or a label? That decides the tools."
[Screen: table matching questions to tools] "Describe, compare, or relate. Each question has its own tool."
[Host] "Plan the analysis first. Then the data cannot talk you into a story you wanted."
Write a one-page analysis plan for a project you could do in a week: question, variables with types and units, sample size, graph, statistic or test, and your rule for odd results.
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I'm learning "Research Projects: statistics" on The Future Market. Lesson 1: "From a research question to an analysis plan". What the lesson teaches: - Before this course: Experiment Design: variables and controls (course 15.9.2), which came after The Scientific Method & Science Fair Projects (course 15.9). You already know independent, dependent and controlled variables, control groups, trials, random order, blinding, random and systematic error, mean and range. This course adds statistics: how to describe, compare and trust your data. - Two big kinds of data: - Numerical data are measured or counted numbers: time in seconds, height in cm, number of seeds that sprouted. - Categorical data are labels or groups: brand A, B or C; yes or no; colour. - Descriptive statistics summarise the data you have (mean, median, spread, graphs). Inferential statistics use a sample to say something about a bigger group, with a measure of uncertainty (confidence intervals, tests). - Population and sample: the population is everything you want to know about (all paper helicopters of this design); the sample is the ones you actually measure. Statistics tell you how far the sample might be from the truth. - Kinds of research question and the tool that fits: The exercise I'm working on: Write a one-page analysis plan for a project you could do in a week: question, variables with types and units, sample size, graph, statistic or test, and your rule for odd results. --- I'm stuck. Please: 1. Explain the main idea in plain, simple words with one everyday example. 2. Walk me through the exercise one small step at a time. Ask me what I've done so far before giving the next step. 3. Don't just give me the final answer. Help me do it myself, and check my work when I share it.
I'm a parent helping my child (about 8 years old) with a lesson called "From a research question to an analysis plan" from the course "Research Projects: statistics". Here's what the lesson says: Before a treasure hunt, you decide what you are looking for and how you will know you found it. Before a research project, you decide what you will measure and how you will work out the answer, so the numbers cannot trick you later. The activity: Write a one-page analysis plan for a project you could do in a week: question, variables with types and units, sample size, graph, statistic or test, and your rule for odd results. --- Please explain this so an 8-year-old understands: short sentences, a fun everyday example, and no hard words. Then give me 3 simple questions I can ask my child to check they understood, and a way to do the activity together, one tiny step at a time.
Describing data: centre and spread
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Graphs that tell the truth
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Samples, uncertainty and confidence intervals
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Comparing two groups: t-tests, p-values and effect size
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Relationships: correlation and regression
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Public data, honest reporting and your research report
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Final project
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Quiz
What is the difference between numerical and categorical data?
Numerical data are measured or counted numbers; categorical data are labels or groups.
Why write the analysis plan before collecting data?
So you cannot choose the method after seeing the results and fool yourself.
What are the mean and median of 12, 15, 11, 18 and 14?
Both are 14.
Which is less affected by one big outlier, the mean or the median?
The median.
Why does the sample standard deviation divide by n - 1?
To correct for the sample mean being closer to its own data than the true mean is.
What does the IQR measure?
The spread of the middle half of the data (Q3 - Q1).
What must a caption say about error bars?
Whether they show the SD, the standard error or a confidence interval.
What is the standard error of the mean?
SD divided by the square root of n; how much the mean would vary from sample to sample.
How many times more data do you need to halve the standard error?
About four times as many.
Does a p-value tell you the probability that your hypothesis is true?
No; it shows how well the data fit a model of no difference, and it does not measure effect size.
What does a p-value of about 0.40 with small groups tell you?
The data cannot tell the groups apart; it is not proof that there is no effect.
What does an r close to +1 mean?
A strong positive straight-line relationship.
Does a strong correlation prove that one thing causes the other?
No; a third variable or coincidence could explain it; a controlled experiment is the strongest test of cause.
Why should you read your own fair's rules?
Science fair rules differ by country and by fair.
Final exam
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Certificate
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