2. Week 2 - Measuring, describing, and visualising psychological concepts

Written by Carly Anderson and featuring lectures from John Towse

Overview

This week we focus on two strands of learning:

  1. Psychological measurement - how we turn psychological concepts into measurable data, and how we can summarise those data using numbers.
  2. Variability and distributions - why differences between people and observations matter, and how we can measure and visualise information that a single average might hide.

The materials we have prepared to support your learning are arranged in four parts:

  • Lectures
  • Reading
  • Pre-lab activities
  • Lab activities

You can navigate to each in the side bar on the right

Lectures

Last week, you looked at some of the bigger questions that sit behind psychological science: how theories are linked to observable evidence, why our observations provide estimates rather than direct access to the “truth”, and why the complexity and variability of human behaviour matter.

This week, we move from those ideas to some of the practical tools that allow us to gather and make sense of evidence. We’ll look at how psychological concepts can be represented as data, and how choices about measurement, summary and visualisation shape the evidence we use to evaluate scientific claims.

The lectures are grouped into section A and B (relating to the two strands of learning stated above). Each section is split into short videos so you can work through them at your own pace. It’s a good idea to take notes as you go and to have a 10-minute break between section A and section B.

A note about the recordings

The recordings were originally delivered by Prof John Towse and have been selected and reorganised for this week’s teaching. If you hear references to a different week or to something covered “last week” don’t worry about these references! I’ve reviewed the materials and you will never be expected to know anything that you haven’t yet covered. All questions should be posted on the discussion forum and will be answered by Carly. Please do not contact John about his content.

Questions?

Make a note of questions as you work through the material. These might be answered later in the recordings, or in your lab. Otherwise, please bring them to the live online Q&A session on Friday or post them on the Q&A forum on Moodle.

Section A: Psychological measurement and central tendency

You can watch the lecture for the video using the video playback windows shown next. Section A is broken into three parts that should be watched in sequence:

  1. Types of data
  2. Scales of measurement
  3. Central tendency and notations

Download the slides for sections A and B in one go here. The transcript for all the videos is here.

Downloading files

If the file doesn’t download when you click on it, try right-clicking on it instead. You should than see multiple options and you can select ‘Download linked file’.

1. Types of data (~10 minutes)

What types of data can we use to measure psychological concepts that we are interested in? This includes nominal and numerical data.

2. Scales of Measurement (~9 minutes) Four different scales that we commonly use to measure our data. These include nominal, ordinal, interval, and ratio.

3. Measures of central tendency and key notations (~10 minutes) Why measurement matters, and how to describe your data using numbers and appropriate measures. This includes the mean, median and mode.

Take a break!

Before continuing, we recommend you take a 15-minute break away from your computer. Remember to note down any questions to bring to the Q&A, lab or discussion forum whilst you’re watching the lectures.

Section B: Variability and distributions

Section B is broken into four parts that should be watched in sequence:

  1. Variability in numbers
  2. Variability in words
  3. The standard deviation and distribution curves
  4. The normal distribution curve

1. Variability in numbers (~19 minutes) Why does variability or ‘spread’ in our data matter? How can we measure and express variability using numbers? This includes range, interquartile range, deviance, variance and standard deviation.

2. Variability in words (~5 minutes) A short reflection on what numerical measures of variability can actually tell us about our data.

Formulae and calculations

John has just introduced the notion of using calculations to measure variability and the broader concepts behind them. You can download the key formulae for calculating variance and standard deviation and other measures here You may come across slightly different versions of these formulae (computational and conceptual) so it is useful to be aware of them. You do not need to memorise these formulae. The important thing is to understand what each measure tells us about our data and the basic idea behind how it is calculated. In the next recording, John will take you through a worked example of calculating a standard deviation.

3. The standard deviation and distribution curves (~15 minutes) An example of how to calculate standard deviation, and how we can look at variability visually using histogram plots. An overview of the shape of data distributions, with features including symmetry, skew, and bimodality.

4. The normal distribution (~9 minutes) Basic properties of the normal distribution curve and linking central tendency and standard deviation to the normal curve.

Reading

Easy access to readings

All reading is accessible via the library. You can go to Moodle -> Library Resources -> Resource List or you can follow this link. Readings have one of the following tags:

  • Essential: We expect you to be familiar with these reading. You will be assessed on this.
  • Recommended: We highly recommend these readings. They often provide a different perspective, or explain things in a different way.
  • Optional: Further readings for those interested.

The reading list is divided into multiple sections:

  • Reading associated with statistics: this contains links to readings useful for the development of statistical concepts and skills. The main textbook Fundamental statistics for the behavioral sciences by Howell (Essential) lives here.
  • Reading associated with psychological research principles and design: this contains links to readings that provide a good basis for foundational knowledge around research design.
  • Reading associated with Open Science principles and practices: this contains links to key literature on the Open Science movement.
  • Week by week: these contain links to key reading for that week that are not listed on any of the more general lists above.

For week 2, the reading is:

  • Keck, S., & Tang, W. (2020). Enhancing the wisdom of the crowd with cognitive-process diversity: The benefits of aggregating intuitive and analytical judgments. Psychological Science, 31(10), 1272-1282. Essential
  • Lorenz, J., Rauhut, H., Schweitzer, F., & Helbing, D. (2011). How social influence can undermine the wisdom of crowd effect. Proceedings of the National Academy of Sciences of the United States of America, 108(22), 9020–9025. Recommended
  • Howell, D. C. (2017). Fundamental statistics for the behavioral sciences (9th ed.). Cengage Learning. Chapters 2, 4, 5 and 6. Recommended

Pre-lab activities

The lecture material is designed to deliver important ideas and procedures for learning about psychological science and analysis. Pre-lab material is then designed to help consolidate this learning, or enhance, expand and apply it in ways that set the scene for the lab session activity. We want to prepare you to be ready to go in the session itself and make the most of your time there.

Pre-lab activity 1: From psychological claims to measurements

Last week, you considered psychological claims that we might encounter in everyday life. One example is the claim that “screen time negatively impacts mental health in adolescents”. Before we could investigate this claim, we would need to decide what we actually mean by screen time and how we could turn that concept into something we can observe and measure.

One simple approach might be to ask people: “Approximately how many hours did you spend looking at a screen yesterday?”

Imagine we asked a small group of adolescents and received the following sample of responses:

6 8 5 9 7 4 11 6 7 8 10 5 6 12 7 8 4 9 6 7 14 5 8 6 10 7 3 9

Take a moment to think about what these numbers actually represent.

Pre-lab question 1
  1. What scale of measurement best describes the number of hours of screen time reported here?
  1. Nominal
  2. Ordinal
  3. Interval
  4. Ratio

d. Ratio. Time measured in hours has equal intervals, and zero hours represents the absence of the measured quantity. This means that differences and ratios between values are meaningful.

Once we have collected observations like these, how can we describe them in a useful way? One way is to summarise the data to find the mean or average value. You’ll learn how to do that in RStudio during the lab, but for now, have a look at the website app: Describing and Exploring Quantitative Variables: https://istats.shinyapps.io/EDA_quantitative/. The website should open in a new window. You may be offered a free trial of the ‘Art of Stat Mobile App’; you can dismiss that.

Choose the following options:

  • Under ‘Enter Data’, select ‘Your Own’
  • Under ‘Name of Variable’, enter a sensible label (such as ‘Screen time’)
  • Under ‘Enter observations’, add the numbers of the observations
  • Under ‘Choose Type of Plot’, click the box to select a ‘Histogram’.

Now have a look:

  • On the right, you’ll see key descriptive statistics such as the mean and the standard deviation (Std. Dev.).
  • Below it, you can see a histogram. If the histogram looks funny, try adjusting the bin size.
What is a histogram?

A histogram is a graph that shows how the values of a continuous (or finely measured) variable are distributed. The values are divided into consecutive, equal-width intervals called bins, and a bar is drawn for each bin with its height showing how many observations fall inside it (or the proportion or density). Because the bins are adjacent, the bars touch, which distinguishes a histogram from a bar chart of separate categories. Histograms make it easy to see the shape of a distribution, including its centre, spread, skew, and any outliers or multiple peaks.

Play around:

  • What happens if you add more observations? How does it change the mean and the standard deviation? What happens to the histogram?
  • Try adding 10 observations of lower screen time values.
  • Try adding an impossibly large observation, like 89. That is, of course, far larger than there are hours in the day, but data entry errors like that do happen. How does it effect the mean and the standard deviation?
  • You can also click the option to see a boxplot as well as a histogram. Can you work out how key descriptive statistics are represented in a boxplot?
Pre-lab question 2
  1. The mean reported screen time in this sample was approximately 7.4 hours. Which of the following would NOT be justified from these data?
  1. Participants reported an average of 7.4 hours of screen time.
  2. There was variation in reported screen time between participants.
  3. Adolescents who use screens more have poorer mental health.
  4. Some participants reported more screen time than others.

c. Here, our measure of screen time is self-reported hours of screen use on one day. We have not measured mental health, so these observations cannot tell us whether greater screen use is associated with poorer mental health. Our measure of “screen time” is also only one possible way of representing a complex behaviour. For example, it does not distinguish between different activities or content, such as studying, gaming, messaging friends or watching videos. This illustrates an important challenge in psychological science: the questions and theories we are interested in are often complex, while the data we collect are particular observations produced by the choices we make about what and how to measure. So, even when we can accurately describe a set of observations, we still need to be careful about what those observations allow us to conclude.

Pre-lab question 3
  1. If two sets of data have exactly the same mean, what can we conclude about their variability?
  1. They must have the same variability
  2. They must have the same standard deviation
  3. One must have a larger range
  4. We cannot tell from the mean alone

d.

Pre-lab activity 2: Revisit the video on how to get started in RStudio

RStudio is the software that we’ll use to work with data, visualise data and analyse data. It is an important tool when learning to do psychological science.

If you haven’t watched it yet, or would like to remind yourself, please revisit last week’s video on How to work with RStudio.

Pre-lab activity 3: Make sure your device is connected to the eduroam Wi-fi

Most people find it easier to use a laptop to engage in the lab activities.

  • If you don’t have a laptop, you can borrow one from the locker in the Levy lab with your Lancaster University ID card.
  • If you prefer to use your own device, please make sure you have set it up to be connected to eduroam Wi-fi before you come to your lab session. Instructions on how to do that can be found on this website: https://portal.lancaster.ac.uk/ask/connect-eduroam/.

Lab activities

Lab activity 1: Getting setup in RStudio (Recap - skip if completed succesfully last week)

Background

If you have not succesfully logged into the R-server yet, let’s get this sorted before you do anything else. If you have succesfully logged into the R-server, you can skip this and start the next lab activity.

Aims of the activity

  1. Login to the R-server
  2. Setup RStudio

Step 1: Login

Navigate to the website for the RStudio server: https://ps-rstudio.lancaster.ac.uk/ and log in by clicking on the Single sign-on button. You may have to put in your Lancaster University username and password. Once your credentials have been checked, you should get to the RStudio server window.

Step 2: Revisit the video on how to get started in RStudio

RStudio is the software that we’ll use to work with data, visualise data and analyse data. It is an important tool when learning to do psychological science.

If you haven’t watched it yet, or would like to remind yourself, please revisit last week’s video on How to work with RStudio.

Lab activity 2: Calculating descriptive statistics

Background

Last week, we worked with some publicly available data from a research project on mind wandering. Anna Schubert and colleagues (Schubert et al., 2024) conducted a study in which they created a 12-item questionnaire that measures how often your mind wanders without meaning to, how often you let it wander on purpose, and how aware you are when it happens. You can have a look at the questionnaire here. This week, we’ll revisit how to create a histogram and then calculate descriptive statistics for the questionnaire responses.

Reference

Schubert, A.-L., Frischkorn, G. T., Sadus, K., Welhaf, M. S., Kane, M. J., & Rummel, J. (2024). The brief mind wandering three-factor scale (BMW-3). Behavior Research Methods, 56(8), 8720-8744. https://doi.org/10.3758/s13428-024-02500-6

Aims of the activity

We are going to:

  1. Download the files
  2. Setup the appropriate bits and pieces in RStudio
  3. Read in the data
  4. Build a histogram
  5. Calculate the mean, median and standard deviation
  6. Create a new variable that combines responses from several questions
  7. Build a histogram and calculate descriptive statistics using the combined score.

Step 1: Download the files

To complete this lab activity you will need two files:

  1. We’ll work with an example script called 4141_wk2_lab.qmd. This is a Quarto document.
  2. We need a data file called data_bmw3.csv. This is a file that contains the responses of the participants in one of the studies reported on in the paper by Schubert et al. (2024). It is a file of the type .csv. This means that individual bits of data are separated by comma’s. We’ll often use .csv files.

You can download the files here: 4141_wk2_lab.zip. Usually they will be saved in your ‘Downloads’ folder.

Next, upload the zip-folder as it is to your Files space on the R-server (bottom right quadrant; no need to extract the files first).

Finally, open the example script by clicking on the file called 4141_wk2_lab_act2.qmd in the Files space on the R-server.

Steps 2 to 7

For steps 2 to 7, you’ll be working in RStudio.

Lab activity 3: Get started on collecting SONA credits

Background

Gaining experience with psychological research as a participant plays an important role in becoming a researcher.

Why take part in research as a participant?

Taking part in psychological research is one of the most direct ways to understand how research works. A textbook or lecture can only take you so far. Experiencing a study from the inside shows you things that are hard to appreciate otherwise.

As a participant, you see how researchers turn abstract ideas into something measurable: how instructions are worded, how tasks are designed, how conditions are manipulated and how responses are recorded. You may notice how your own expectations shape what you do. These are the same issues you’ll need to think critically about in your own designs, such as demand characteristics, operationalisation and measurement validity.

You also see research ethics in practice, from information sheets and informed consent to the right to withdraw and debriefing. Knowing what it feels like to be on the receiving end helps you design studies that treat participants with care.

Finally, participation shows you why sample size and representativeness matter, and why your own research will depend on others being willing to take part. Seeing a range of studies can also spark ideas for your own projects, including your dissertation.

In short, being a participant helps you become a better researcher. It connects what you learn in class to real practice.

Aims of the activity

  1. Get setup on the SONA system
  2. Take part in your first study and collect 2 SONA credits

Step 1: The background

Sections 1 to 3 on the SONA page explain:

  1. Why research participation is important
  2. What SONA is and how you go about collecting SONA credits
  3. How SONA credits contribute to your grade

Action: We went through sections 1 to 3 during the first part of the in-person lab in week 2, so if you attended that, you can skip this step. If you didn’t attend or you’d like to review the information, please watch the videos on the SONA page, starting in section 1.

Step 2: Get setup and collect your first SONA credits

Section 4 on the SONA page talks you through how to set up your account and take part in your first study.

Action: Please navigate to the SONA page, watch the video in section 4.1, login to SONA and complete your first study.

Once you’ve done that, there is another video with tips on how to collect your SONA credits on time (section 4.2).

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