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Research Projects: statistics

Step 6 of 7 in Science Center

Next in your path: 15.3.3 Mechanics & Energy Models: modelling

What you'll be able to do
  • Write an analysis plan before you collect data, and match each question to the right kind of data.
  • Describe data with the mean, median, range and standard deviation, and know when each one fits.
  • Draw honest graphs: histograms, box plots, scatter plots and bar charts with labelled error bars.
  • Measure uncertainty with the standard error and a 95% confidence interval.
  • Compare two groups with a t-test, read a p-value correctly and report the size of the effect.
  • Measure a relationship with correlation and a regression line, without mixing up correlation and cause.
  • Use public data from official statistics agencies, report honestly, and present a graded research project.

Safety rule for this course: every example uses safe materials: paper, a ruler, a stopwatch, seeds, water, and data you collect from objects or public data sets. Drop things only from a height you can reach while standing on the floor, never from a chair, ladder, stairs or window. Surveys or tests with people need your fair's ethics rules and consent first (course 15.9.2, lesson 6). Kids: do experiments with an adult.

Words in this course 63Open the Vocabulary Hall
01

From a research question to an analysis plan

In simple words

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.

Key facts
  • 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:
QuestionDataMain tool (this course)
What is typical, and how much does it vary?One numerical variableMean or median, standard deviation (Lesson 2)
Is group A different from group B?Numerical result, two groupsDifference in means, t-test, effect size (Lesson 5)
Do two measurements go up or down together?Two numerical variablesScatter plot, correlation, regression (Lesson 6)
How common is something?CategoricalCounts 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.
Step by step
  1. Write your research question in one sentence.
  2. List each variable and mark it numerical or categorical, with its unit.
  3. Use the table to choose your main tool (describe, compare or relate).
  4. Write how many items or trials you will measure per group, and why.
  5. Write which graph you will draw and which statistic or test you will report.
  6. Write what you will do with odd results: report all, explain, or repeat and report both (course 15.9.2, lesson 5).
  7. Date the plan and ask your teacher or an adult to check it.
  8. Check: someone else could read your plan and know which numbers you will calculate before any data exist.
Watch on YouTube
How statistics can be misleadingTED-Ed · YouTube · youtube.com

Videos by other creators on YouTube, for reference. They are not made by or affiliated with The Future Market.

LESSON 01From a research question to an analysis plan
LESSON 01 / ANIMATED LESSON / AI VOICE00:00 / 01:00
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."
Try it now

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.

ClaudeStuck? Copy a ready-made prompt for Claude

Copy this, open Claude, paste it, and Claude will walk you through the lesson step by step.

For a grown-up: Claude is for adults (18+). Copy this, paste it into Claude, and use the answer to explain the lesson to your child.

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.
Open Claude
My notes
02

Describing data: centre and spread

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03

Graphs that tell the truth

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04

Samples, uncertainty and confidence intervals

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05

Comparing two groups: t-tests, p-values and effect size

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06

Relationships: correlation and regression

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07

Public data, honest reporting and your research report

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++

Final project

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??

Quiz

  1. What is the difference between numerical and categorical data?

  2. Why write the analysis plan before collecting data?

  3. What are the mean and median of 12, 15, 11, 18 and 14?

  4. Which is less affected by one big outlier, the mean or the median?

  5. Why does the sample standard deviation divide by n - 1?

  6. What does the IQR measure?

  7. What must a caption say about error bars?

  8. What is the standard error of the mean?

  9. How many times more data do you need to halve the standard error?

  10. Does a p-value tell you the probability that your hypothesis is true?

  11. What does a p-value of about 0.40 with small groups tell you?

  12. What does an r close to +1 mean?

  13. Does a strong correlation prove that one thing causes the other?

  14. Why should you read your own fair's rules?

EX

Final exam

This lesson is part of full access: every course and every level for one payment.

CE

Certificate

This lesson is part of full access: every course and every level for one payment.