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Talking about Statistics

Dr David Butler

Maths Learning Centre

University of Adelaide

March 2024

Foundations in Plant Science

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The most important thing to learn about statistics is…

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You should ALWAYS �talk to someone �about your statistics!

When to talk to someone

What to talk about

Before you collect your data

How the data will be analysed

How to set it up in your spreadsheet

Just after you start collecting data

Whether you’re entering the data correctly

Just before you analyse your data

How to analyse the data

While you are analysing your data

Whether you’re analysing the data correctly

After you analyse your data

How to interpret the results

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You should ALWAYS �talk to someone �about your statistics!

Who to talk to:

  • Your research mentor
  • Your Foundations in Plant Science lecturers
  • Other students
  • The MLC

(email first with as much detail as you can mathslearning@adelaide.edu.au )

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OUTSIDE! �For an activity with much to talk about…

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We’re back!

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The things you write down �about your experimental subjects �are called variables

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Each subject has a row of variables in the data

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Multiple measurements on the same subjects

  • Either continue the rows and put the time in the column title
  • Or make new rows with subject labels and put the time in a column of its own

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Variables come in two types

CATEGORICAL

(also known as “qualitative”)

Usually words: how far apart has no consistent meaning.

NUMERICAL

(also known as “quantitative”, “interval”, “scale”)

Always numbers: how far apart has a consistent meaning.

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What kind of variables you have �makes a difference to �the kind of statistics you can do.

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Other information about the variables�also makes a difference to �the kind of statistics you can do.

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WARNING!

(That’s what experimental design is for.)

Statistical calculations by themselves NEVER tell you whether anything CAUSES anything else.

Statistics CAN help you CALCULATE what you expect one variable to be, from other variables.

BUT

Explanatory variable

Outcome variable

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Categorical variables belong to subjects in different ways

Independent groups

Repeated measures

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Numerical variables have different distributions

The distribution of a variable is all the things it can possibly be and how likely all those options are.

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approximately normal

not normal

more likely

in the middle

less likely on either side

just as likely one side as the other

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Information about the variables�changes the statistical calculations you can do

  • How many variables are involved
  • What kind of variables they are
  • Categorical variables �– whether there are two categories or more than two
  • Categorical explanatory variables �– whether they go with independent groups or repeated measures
  • Numerical outcome variables �– whether the distribution is normal

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Hypothesis tests help decide answers �to yes-or-no questions

    • Almost always, the question is �“Are these variables related?”
    • Sometimes the question is �“Is this unknown number equal to this value?”

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Thirteen common hypothesis tests

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Independent samples t-test

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Independent samples t-test

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Paired t-test

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Chi-squared test (for association)

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Chi-squared test (for association)

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McNemar’s test

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ANOVA �(ANalysis Of VAriance)

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(Simple) Regression

Note: technically answers a “predict” question, but produces hypothesis tests along the way

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Mann-Whitney U-test

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Wilcoxon signed ranks test

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Kruskall-Wallis test

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Two-way ANOVA

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Multiple Regression

Note: technically answers a “predict” question, but produces hypothesis tests along the way

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Multiple Regression

Note: technically answers a “predict” question, but produces hypothesis tests along the way

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One sample t-test

Note: helps to answer the question of whether the mean is equal to a specific number.

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One sample z-test for a proportion

Note: helps to answer the question of whether the proportion of people in one category is equal to a specific number.

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The most important thing to learn about statistics is…

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You should ALWAYS �talk to someone �about your statistics!

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WARNING!

That’s what experimental design is for…

Statistical calculations by themselves NEVER tell you �whether anything CAUSES anything else.