Category: Workshops

R: Linear Mixed Models in R – A case Study

Jordan Graham, MSc student in SES, presented his experiences working with Linear Mixed Models (LMM) in R.  Please review the presentation and the sample code provided.

R-Users group will continue in May.  Stay tuned for an updated list of dates and topics.  If you are interested in talking to the group about a package that you’ve been using, please contact me at oacstats@uoguelph.ca  – I welcome all suggestions!

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ARCHIVE: W18 SPSS Workshop: Creating Charts

Chart Builder in SPSS

Numbers and statistics can be fun, but sometimes putting these numbers into context with a chart or graph may reach a broader audience of understanding.  What do I mean by that?  How many of you will remember a number vs how many of you will remember a graph that shows a trend?

Building charts in SPSS is quite straightforward.  The dataset we will use for this workshop is one of the many Sample datasets that accompany your SPSS program.  For ease of this workshop, I’ve saved the DEMO dataset as an Excel file.  Please download this file and open it in your SPSS program.

Let’s start by creating a barchart for our job satisfaction variable.  We want to see a bar for each level and we want to see the count.

In SPSS:

  • Graphs
  • Chart Builder – this will open a dialogue box
    • Notice on bottom half – a gallery of all the different types of charts you can create in SPSS.
    • We want a simple barchart
      • Select bar
      • Then double-click on the first barchart listed
      • Once you do this you should see the skeleton of a bar chart appear in the top half of your dialogue box.
      • All you need to do now, is to drag and drop the variables where they are appropriate.
      • For this example:
        • Select Job satifisfaction and drag it to the x-axis
        • On the right, you may see an Element Properties dialogue box (if you do not see this – Click on the Element Properties button to open it).
        • Note that under Statistics, Count is selected – this is what we want.  But click on this to see what other statistics are available.
      • To create the graph Click OK

You should now see a very plain barchart with frequencies.

Let’s create a chart that shows the average income for each level of job satisfaction.  I’m curious to see whether the folks that are not satisfied with their job have a lower average income.

So, let’s start this again:

  • Graphs
  • Chart Builder – this will open a dialogue box
    • Select Barchart again
    • Drag and drop Job Satisfaction to the x-axis
    • Now drag and drop Household income to the y-axis
    • Notice how the Statistic changed to Mean.  This is what we want.
    • Let’s run in by clicking OK

Hmm…  now that’s an interesting graph!

One last piece missing from this graph – error bars!  Whenever you have charts with means, you should ALWAYS provide some measure of variance.  So let’s add some error bars and we’ll try standard error.

  • Graphs
  • Chart Builder – this will open a dialogue box
    • Select Barchart again
    • Drag and drop Job Satisfaction to the x-axis
    • Now drag and drop Household income to the y-axis
    • Ensure that the statistic is mean
    • Under the statistics box in the Element Properties box, check the Display Error Bars box
      • Now you have a few options, as stated above let’s use the Standard Error option – select Standard Error
      • Click Apply
    • Click OK to run chart

Providing the error bars gives the reader a “fuller” picture of the data.  Although in this case it does not change the story!

Try:

  1. Create a barchart that shows the mean household income by job satisfaction for the 2 levels of marital status.  Be sure to include error bars.
  2. What question does this barchart answer?

More types of charts

We’ll investigate different types of charts based on what you are looking for.

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Experimental Designs

What is an experimental design?

Is the process of planning a study to meet specified objectives.  An experiment that SHOULD be designed to match a specific research question.

Steps to designing an experiment

  1. Define the EXPERIMENTAL UNIT
    What is the difference between an EXPERIMENTAL UNIT and a SAMPLING UNIT?
  2. Identify the types of variables
  3. Define the treatment structure
  4. Design the design structure

Experimental Unit  vs. Sampling Unit

Experimental unit is the unit to which the treatment is applied to.

Sampling unit is a fraction of the experimental unit.

Examples of potential experimental units:

  • An animal
  • A cage with 5 birds inside
  • A plot in a field
  • A box of fruit
  • A tree
  • A pot of plants
  • A growth chamber
  • A fish tank
  • A tray of seedlings
  • A taste panelist
  • A sample of a new food product
  • A bench in a greenhouse

Examples of potential sampling units:

  • 1 bird in a cage
  • A quadrant in a plot of a field
  • 5 apples from a box
  • A branch or leaf of a tree
  • 1 plant from a pot of plants
  • A tray or shelf placed in a growth chamber
  • An individual fish from a fish tank
  • One pod of seedlings from a tray
  • A plot on a bench in a greenhouse

Experimental Error

Measure of the variation that exists among observations taken on the experimental units that are treated alike.

Sources of Experimental Error

  1. Natural variation among experimental units
  2. Variability of the measurements taken (response)
  3. Inability to reproduce the treatment conditions exactly from one unit to another
  4. Interaction between the treatments and the experimental units
  5. Any other extraneous factors that may influence the response

With any statistical analyses, what we are looking for is an estimate of the variation of the experimental error.  So, the variation between our experimental units – We need this  to test treatment differences.

Variation of observations within an experimental unit will not give us treatment differences!

Completely Randomized Design (CRD)

Treatments that are randomly assigned to experimental units.

Completely Randomized Design

Experimental unit is the individual plot/square in the design.  The statistical model is represented by:

Model for the CRD

Where:

Yij = Observation on the jth experimental unit on the ith treatment
μ = overall mean
τi = the effect of the ith treatment
εij = experimental error or residual

The experimental error is variation among experimental units on the same treatment. The unexplained variation – the residual – what’s left.

Randomized Complete Block Design (RCBD)

In any experiment we conduct, we have experimental error.  Our goal is to take control over our experimental error so we can study the effects of our treatments.  Blocking is one way to take control of our experimental error.

Blocking occurs when we group experimental units in a way where the variation of the experimental units within the blocks is less than the variation among all the units before blocking.

Diagram of a Randomized Complete Block Design (RCBD)

Each block highlighted as the different colours or the columns in the above table.  Within each block all the treatments will appear an equal amount of time.  The statistical model would be:

RCBD model

What happens though when we have more than one experimental unit/treatment in each block?  If you look at the current design – you have one measurement per treatment in each block – so there is not enough measures to see whether the treatments are doing something different across the blocks.  But when we have more than one experimental unit per treatments in a block, then you have variation to examine.  So your model would now be:

RCBD model with an interaction

Split Plot Design

A design where you have 2-3 factors or treatments of interest, yet the experimental units of each treatment are different sizes.

Split_plot design

What are the 2 sources of experimental error?

Variation between the Blocks where A was assigned.  Two blocks have the A1 treatment and two blocks have the A2 treatment.  The main plot is the A treatment.

The second source of experimental error is the variation among the experimental units.  The subplot is the B treatment.  The statistical model is:

Split_plot model

Split Block or Strip-plot

Two treatments that are applied as a strip as an example.  Here is one blockstrip_plot design

If we are interested in looking at the effect of Treatment A – what is the correct error term?  Start by asking yourself what is the experimental unit for treatment A?  Then think about the definition of experimental error – variation between experimental units that were treated the same….

What about Treatment B?

And the interaction between Treatment A and Treatment B?

The statistical model is:

strip_plot model

Let’s see how much we can get through.

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