• Connect the lecture idea of comparing two population means to R code.
• Calculate grouped descriptives with summarise().
• Run an independent-samples t-test with t.test().
• Extract t, df, p, and the confidence interval from the t-test object.
• Use pt() to understand how a t-value and df become evidence about statistical significance.
• Use mu = ... when the null hypothesis is not a zero difference.

Check the online lecture before the workshop. Complete the Week 3 problem set after this workshop.

The lecture asks whether two samples give evidence that two population means differ.

• Sample means describe the data we observed.
• Population means are the quantities we want to learn about.
• Null hypothesis: the population mean difference is 0.
• t-value: the observed difference expressed relative to its uncertainty.
• p-value: probability of a result as or more extreme, assuming the null hypothesis is true.
• Independent groups: each person is in one group only; the two group means come from different people.

Workshop focus: describe the groups, run the test, and understand the output.

For each independent two-group analysis, use the same workflow:

1. Identify the numeric outcome and the grouping variable.
2. Calculate mean, SD, and n for each group.
3. Run the t-test.
4. Extract and interpret the result.

Running the code is only the first step. The important part is knowing what the output says about the research question.

Work from inside the RStudio Project folder you created in Week 1.

1. Download the Week 3 exercise script from NOW: week_03_workshop.R.
2. Move week_03_workshop.R into your RStudio Project folder.
3. Check that the workshop_data folder is also inside your RStudio Project folder.
4. Open your .Rproj file for this module.
5. Open week_03_workshop.R from inside RStudio.

For learning R, run one line at a time and inspect the console after each line.

Part A uses the Blomkvist data from the workshop_data folder.

blomkvist <- read_csv("workshop_data/analysis_blomkvist.csv")
blomkvist <- drop_na(blomkvist, rt, age_group)

Each row is one participant. Today we ask:

Is mean hand reaction time different for participants aged 60 and over versus participants under 60?

The Blomkvist data are adapted from a reaction-time and aging study using the Nintendo Wii Balance Board (Blomkvist et al., 2017).

Calculate the descriptives that make the t-test easier to interpret. The n = n() line also checks how many participants are in each group:

summarise(blomkvist,
  mean_rt = mean(rt),
  sd_rt = sd(rt),
  n = n(),
  .by = age_group
)

Which age group has the slower mean reaction time?

For an independent-groups t-test in R, the formula has this structure:

outcome ~ group

For the Blomkvist example:

rt ~ age_group

• rt is the numeric outcome.
• age_group defines the two independent groups.
• The outcome goes on the left of ~; the group goes on the right.

m_age <- t.test(rt ~ age_group, data = blomkvist, var.equal = TRUE)
m_age

var.equal = TRUE matches the equal-variance t-test introduced in the lecture.

The printed output is useful, but saving the test as an object lets us extract the exact values we need.

In R, the dollar sign operator $ extracts a named value from an object.

Read m_age$statistic as: from the object m_age, extract the named value statistic.

Open week_03_workshop.R.

The same area-under-the-curve idea explains where the p-value in a t-test comes from.

t_value <- abs(m_age$statistic)
df_value <- m_age$parameter

2 * pt(t_value, df = df_value, lower.tail = FALSE)

m_age$p.value

This recreates the two-sided p-value stored in the t-test object.

Open Part C of week_03_workshop.R.

The three moves are: below with pt(), above with lower.tail = FALSE, and between two values with subtraction.

The usual t-test tests whether the population mean difference is 0.

Use mu = ... to test a different hypothesised difference:

t.test(rt ~ age_group, data = blomkvist, mu = 200, var.equal = TRUE)

This is the same model, but the comparison value is no longer zero.

Recommended reading: Andrews (2021), Chapter 8, Statistical Models and Statistical Inference.

Problem-set reminder: complete the Week 3 problem set after this workshop on Friday. Focus on explaining what each result means, not only on running the code.

Before the problem set, you should be able to:

• create grouped descriptives with summarise(..., .by = group).
• run t.test(y ~ group, data = d, var.equal = TRUE).
• extract t, df, p, and CI using the dollar sign operator $.
• explain how pt() links a t-value and df to a p-value.
• use mu = ... when the null hypothesis is about a non-zero difference.