psyc 4165, spring 2016 laboratory 0 introduction to...

PSYC 4165, Spring 2016

Laboratory 0

Introduction to Experimental Methods in Perception Research:

The Oblique Effect

Part 1: Collecting Data

Psychology of Perception Lewis O. Harvey, Jr.–Instructor Psychology 4165-100 Scott M. Schafer–Teaching Assistant Spring 2016 Vincent Mathias–Learning Assistant 11:00–12:15 TR Steven M. Parker–Consultant

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Lab Overview

Classical methods of psychophysics involve the measurement of two types of sensory

thresholds: the absolute threshold, RL (Reiz Limen), the weakest stimulus that is just

detectable, and the difference threshold, DL (Differenz Limen), the smallest stimulus

increment away from a standard stimulus that is just detectable (also called the Just-

Noticeable Difference, the JND). Gustav Theodor Fechner (1801–1887), in Elemente der

Psychophysik {Fechner, 1860 #508} introduced three psychophysical methods for

measuring absolute and difference (JND) thresholds: the method of adjustment; the

method of limits; the method of constant stimuli. In the method of constant stimuli, a

standard stimulus is compared a number of times with test stimuli of slightly different

orientation. When the difference between the standard and the comparison stimulus is

large, the subject nearly always can correctly judge the difference between the test

stimulus relative to the standard. When the difference is small, however, errors are often

made. The difference threshold is the transition point between differences large enough to

be easily detected and those too small to be detected.

The purpose of this laboratory to provide participants (you) with an introductory

experience to the method of constant stimuli, and also to introduce you to the software

tools that we’ll be using throughout the semester (PsychoPy and R). We will use these

software tools to observe the “Oblique Effect,” a well-known and reliable phenomenon in

visual perception {Appelle, 1972 #40}. This effect, that perception is often better for

vertical and horizontal stimulus orientations than for oblique orientations, has been

studied extensively {McMahon, 2003 #3195;Westheimer, 2003 #4787;Meng, 2005

#4789;Freeman, 2011 #4785;Nasr, 2012 #4786}. Today’s lab activities present the entire

lifecycle of a perception experiment in a single lab session, beginning with reading a

classic review paper on the Oblique Effect, using PsychoPy to perform an experiment

designed to observe the Oblique Effect, and finally tabulating and analyzing data in “R.”

Throughout this lab you will find sample text provided as a model of each of the lab

competencies. You will learn to:


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• Download “Lab Tools” folders from the class website and run scripts in PsychoPy and R.

• Generate, save visualize (graphs) and analyze data in R.

Lab Instructions The experiment will be run under computer control using PsychoPy, a popular program

written in Python by Jonathan Peirce, at the University of Nottingham, England {Peirce,

2007 #4349;Peirce, 2009 #4350}. PsychoPy allows you to run experiments with carefully

controlled visual and auditory stimuli and to collect response data and reaction times.

You’ll need to download, then run the experiment file.

1. Download “Lab 0 Tools” from the course website:

1. In a web browser, navigate to the course webpage (or click the link below): http://psych.colorado.edu/~lharvey/P4165/P4165_2016_1_Spring/Main Page 2016_Spring PSYC4165.html 2. Move Lab 0 Tools.zip from the Downloads folder, to the Desktop 3. Unzip the Lab 0 Tools.zip by double-clicking the file. PROTIP: Keep all your working files in the Lab 0 Tools folder on the Desktop, that way you won’t overlook a crucial file when you logout!

2. Start PsychoPy2 application 1. In the applications folder, double-click on the PsychoPy2 icon (shown in Figure 1) to launch the PsychoPy application.

Figure 1. PsychoPy2 icon

3. Execute the Orientation JND Exp.py script: 1. From the File menu, Open (⌘O) Lab0_Tools > Orientation JND Exp > Orientation JND Exp.psyexp 2. Run the experiment script by clicking the Run button in the toolbar (it’s green with a silhouette of a running person; see Figure 2). Or you can use the keyboard shortcut ⌘R.


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Figure 2. PsychoPy Builder View

4. Enter your information in the info dialog. 1. You will be shown the “info dialog,” as shown in Figure 3. 2. Enter your own initials in the observer field 3. Verify that the value 10 is in the repeats field. This number tells PsychoPy how many blocks of trials to run. 4. Click OK to begin the experiment.

Figure 3. info dialog

5. Follow on screen instructions to do the experiment. Consider setting the number of repeats to 1 or 2 and running the experiment as a practice session. Then chance repeats to 10 and run the complete experiment.

The computer will randomly decide which of the two orientations to test first: 0

or 45 deg. On each trial you will first be presented with the standard stimulus (either 0 or


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45 deg, depending on the condition) followed by a test stimulus. The test will be rotated

slightly counterclockwise or clockwise relative to the standard. You must judge which by

pressing the left arrow key (if you think the second stimulus is counterclockwise) or the

right arrow key (if you think it was clockwise). On each trial the computer will record

your responses. Some of the judgments will be easy and some will be difficult. The

whole experiment should not take more than 30 minutes. On the cover of this lab are two

examples of Gabor patches: one is oriented at 0.0 degrees (vertical) and the other is tilted

clockwise by 2.0 degrees. Can you see the difference?

Your experimental data will be saved in a text file in the data folder whose name is

your initials with the date and time added to it. The file extension is .csv, for comma-

separated values. If you double click on the file name, it will open in Excel. Do not

modify this data file. It represents a lot of judgments and work on your part. Using a web

browser, log onto Desire2Learn (D2L) at https://learn.colorado.edu, and upload your data

.csv file to the lab0 csv data file dropbox.

Individual Data Analysis

There an R script in the Lab_0_Tools folder that will analyze your individual data:

lab0_glm.R. It contains all the R commands needed to completely analyze your

individual data {R Core Team, 2015 #4926}. Later in the semester you will be writing

more and more R commands on your own. There are three basic steps to any data

analysis, and the lab0_glm.R script performs all of these steps for you.

1. Data Preparation: import & organize data for analysis.

2. Data Visualization: create graphs of your results.

3. Fit Model: Fit a statistical model to your data and assess the fit.

The goal of this individual data analysis phase is to figure out how well an

individual (in this case, you) performed on the orientation discrimination task. We do this

by regressing response probabilities (dependent or measurement variable) onto the

various orientation offsets (the independent or predictor variable). The section below

deals entirely with interpreting the analysis.


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Compute dependent/measurement variables (JND). 6. Execute the lab0_glm.R script:

1. Open the R application from the Application menu. 2. From the File menu, Open (⌘O) the file lab0_glm.R in the Lab0_Tools folder. 3. Execute the entire script by selecting all of the text in the lab0_glm.R script window (Ctrl-A), then pressing ⌘Enter. Alternately, you can select the script window, then press ⌘E. 4. A “Choose File” dialog box will appear. Select your data file: Lab0_Tools > Orientation JND Exp > data > [initials] [timestamp].csv, and click “Open.”

R PROTIP: Organize your windows so that you can see both the script window, and the console window. Alternately, you can use RStudio, an application that has a much more organized interface.

In general, the best thing to start with is to visualize your results in a graph. This

script prepares four graphs that illustrate your results. In the R-script lab0_glm.R, the two

graphs are encapsulated in functions, plot1(), plot2(), plot3() and plot4() so you can

redraw them any time by giving either command.

7. In the R console, call up the function plot1()

1. In the R Console, scroll to the bottom of the screen. 2. At the prompt (>), type the name of the function: plot1() 3. Press enter.

8. Save the graphic as plot1.pdf 1. Select the Quartz 2 [*] window 2. From the File menu, select Save As… (⇧⌘S) 3. In the Save Quartz to PDF File dialog box, change the filename from Rplot.pdf to “plot1.pdf” PROTIP: I strongly recommend saving all lab files to a folder labeled “Lab 0” on the Desktop. That way, when you logout you won’t overlook any files you’ve worked so hard on!

9. Insert plot1.pdf into this table 1. Drag the file plot1.pdf from the Finder onto this document window 2. The cursor shows where the file will appear when you release the mouse button.


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plot2() shows the same response probabilities as plot1(), but as normally distributed

probability density functions. Representing our data in this way will be more important to

use later in the semester. For now, save plot2() using the same steps you used for plot1().

10. 1. In the R console, call up the object plot2() and insert plot2.pdf here:

Visualizations are great and all, but we need to compare precise numeric results to

make solid conclusions. The results of the analysis are stored in objects glm.00 and

glm.45, and the R objects mu.00, sd.00, mu.45, and sd.45 respectively. The sd (standard

deviation) objects correspond to the JNDs.

Compute, interpret, & report summary statistics (graph, prose). 11. In the R console, call up the object glm.00:

1. In the R Console, scroll to the bottom of the screen. 2. At the prompt (>), type the name of the object: glm.00 3. Press enter.

12. Copy/paste the output of glm.00 here:

13. Copy/paste the output of glm.45 here:

14. What was the value for object mu.00?

15. Object mu.45? 16. Object jnd.00?

17. Object jnd.45? 18. Compare the JNDs for both conditions. Under which orientation condition were you

more sensitive to small differences in orientation?

With these JND values, you can conclude under which viewing condition you were

most sensitive to differences in orientation. But are these results typical?


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Group Data Analysis

The goal of the sample, or group, data analysis phase is to figure out how well all

of the observed subjects performed on the orientation discrimination task. Under typical

lab conditions, you would upload your data file to D2L so that we can perform a proper

group data analysis using all students currently enrolled in the lab. But cleaning and

compiling all the data files takes a while, so in the interest of time, you have been

provided with actual experimental data from a prior semesters lab section. Use the R

commands listed in the file lab0_lmer.R in the R Scripts folder to carry out the next phase

in the data analysis. Just like the individual data analysis, there are three basic steps:

1. Data Preparation: Import and organize your data for analysis.

2. Data Visualization: Make graphs of your results.

3. Fit Model or models to your data.

19. Execute the lab0_lmer.R script:

1. Open the R application from the Application menu. 2. From the File menu, Open (⌘O) the file lab0_lmer.R in the Lab0_Tools folder. 3. Execute the entire script by selecting all of the text in the lab0_lmer.R script window (Ctrl-A), then pressing ⌘Enter. Alternately, you can select the script window, then press ⌘E. 4. A “Choose File” dialog box will appear. Select your data file: Lab0_Tools > Orientation JND Exp > data > lab_1_group_data_wide_Spring_2015.csv, and click “Open.”

Compute, interpret, & report summary statistics (graph, prose).

20. In the R console, call up the function plot4() & plot5(). Save the plots as PDF files.

21. Insert plot4.pdf here:

22. Insert plot5.pdf here:

23. Which of these plots (plot4, plot5) is more relevant to report?

From these data, we can calculate statistics that summarize this dataset (means,

standard deviations), so called summary statistics. The lab0_lmer.R script did not store


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these values separately, so you’ll need to provide the code to calculate them. We’ll use

the mean() function to compute the means of columns in the df.wide data frame.

24. Compute the mean JND values for the vertical condition.

1. In the console, type mean(df.wide$sd00) 2. Copy/paste the result here:

25. Compute the mean JND values for both the oblique condition. 1. In the console, type mean(df.wide$sd45) 2. Copy/paste the result here:

26. Use the mean() function repeat to calculate the means for the columns mu00, mu45, aic00, and aic45.

27. What was the mean value for mu00?

28. Column mu45?

29. Compare the means of sd00 and sd45. Under which orientation condition were subjects in our sample more sensitive to small differences in orientation?

Here’s an example of how to report relevant summary statistics:

“The average JND values for both the vertical (M=1.73 deg) and oblique standard orientations (M=9.03 deg) show that as a group, subjects appeared to be far more sensitive to deviations from the vertical standard.”

Inferential Statistical Tests

So far, we have observed and analyzed the pattern of an individual’s responses,

and the responses made by a sample of college students (N=35) to find that subjects tend

to be much more sensitive to deviations from vertical standard orientations than oblique:

in other words, the oblique effect is clearly present in our sample. Further statistical

analysis is only necessary if we were interested in estimating how likely the observed

effect is also present in the [unobserved] general population. Said another way: If all we


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cared about was how well our observed sample of 35 subjects performed on this task,

then we would halt our analysis right here!!!

Select, perform, and report appropriate statistical contrasts to test hypothesis (graph, prose).

The lab0_lmer.R script uses a Linear Mixed-Effects model {Bates, 2015 #5425}, to test

the hypothesis that the oblique effect is present in the general population of persons with

normal vision. Mixed-effects refers to the fact that the statistical model contains both

fixed and random effects. More likely than not, all of the statistical tests you studied in

your statistics classes were fixed effects statistical tests (t-tests, F-test, ANOVA, etc.). The

statistical model that tests our hypothesis can be found in lab0_lmer.R on line:

mod.jnd <- lmer(sd ~ standard * order + (1 | subject), data=df)

There is a lot to unpack at this level of analysis, but for now let’s just focus on the

analysis germane to our hypothesis.

30. Call up the object mod.jnd 1. In the console, type summary(mod.jnd) 2. Copy/paste the output of summary(mod.jnd) here:

32. Examine the line standard45. Was our observed effect statistically “significant”?

Here is an example of how to report the results of this statistical test: “On average, the Just Noticeable Difference for the oblique

condition (M=7.71 deg) was significantly greater than the vertical condition (M = 1.09 deg) [t(1, 31)=4.59, p=.0001], showing that humans possess a clear advantage when detecting small changes in vertical orientation.”

To this point, we’ve generated results from our data at 3 levels: individual data

analysis, group data analysis, and inferential statistics. A following discussion section is

where we would tie it all together and report our findings.


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PSYC 4165, Spring 2016

Laboratory 0


The Oblique Effect

Part 2: Analyzing the Results


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Lab 0 Results Walkthrough

Quantitative research is the systematic empirical investigation of observable

phenomena via statistical, mathematical or computational techniques (cite). Put another

way: We collect numbers (data), analyze those numbers (results), and make conclusions

(findings) based on the analysis of those numbers. Unfortunately, terms like data, results,

and findings are frequently used interchangeably. It is crucial to keep in mind that these

terms refer to very different phases in the research process.

• Data are [raw] measurements of behavior. In cognitive psychology, data are

numerically coded judgments, and in some experiments are paired with response

times (RT). [Raw] data are almost never reported in research publications but are

often deposited in an on-line repository where anyone can download them for

detailed analyses..

• Results are numerical summaries of the data. These can be summary statistics

(e.g., means, standard deviations), and statistical tests (e.g., t-tests, F-tests,

confidence intervals, standardized effect sizes). Importantly, figures, graphs, and

plots should also be considered “Results.” Relevant results are reported in the

Results section of APA publications.

• Findings are what the researcher concludes after a logical examination of the

results. Said another way, Findings are what the Results mean. In APA

publications, findings are reported as shorter statements in the Results section,

and as longer descriptions in the Discussion sections. Reporting findings is

discussed in more depth below.

First and foremost, in experimental psychology, data analyses are always performed

with the goal of assessing and interpreting subject performance on the experimental task

in question. Data analysis generally follows the trend in which mathematical models are

fitted to larger and larger sets of data to answer theoretical questions. An important

feature of perception experiments is that many have within-subjects designs, which allow

perception researchers to use very powerful statistical techniques when analyzing their

data (more on those techniques later). In most experiments with within-subjects designs,

data sets can be analyzed, and even limited conclusions made, at 3 levels: individual,


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sample/group, and population. All of our lab activities will involve analyzing and

reporting results at these 3 levels.

Individual Data Analysis

Our individual data analysis follows two basic steps: Compute response

probabilities for all of the test stimuli offsets, then fit a psychometric function to these

probabilities. An example of response probabilities for each of the orientation offsets is

shown in Figure 1. For now, we’ll deal only with data for the oblique (45 deg) condition.

Figure 1. Single subject response probabilities for the oblique (45 deg) viewing

condition only.

In Figure 1, the abscissa (i.e., horizontal or “x-axis”) represents the difference in

degrees between the standard (e.g., “-10” indicates test stimuli that were rotated 10

degrees counterclockwise relative to the standard stimulus, and the “0” point is where test

and standard stimuli were identical, with no difference in orientation). The ordinate (i.e.,

vertical, or “y-axis”) represents the probability of responding that the test stimuli were

rotated clockwise (→) relative to the standard stimuli . You can see from this plot that this


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subject made never made a clockwise response when the test stimuli were rotated

counterclockwise 5 or more degrees (all of these are “correct”). Similarly, when the test

stimuli were rotated 10 or more degrees, the subject always responded clockwise (also

correct). At first glance, this response asymmetry suggests that this subject was more

sensitive to counterclockwise orientations, shown by the perfect accuracy when rotated

counterclockwise more than 5 degrees. One might even conclude that this subject is

“twice as good” at detecting counterclockwise orientations than clockwise orientations,

as evident by the 100% accuracy for rotations > -5, compared with the 100% accuracy for

> +10 degree offsets. However, such a conclusion does not account for response bias.

Although we’ll deal more fully on the topic of response bias later in the semester, the

above pattern of responses does show a clear response bias.

What we’re really after is to calculate “the minimal difference between two stimuli

that leads to a change in experience:” the Just Noticeable Difference, the JND

{Macmillan, 2005 #3304}. The JND is statistical, rather than an exact quantity: from trial

to trial, the difference that a subject notices between standard and test stimuli will vary,

and it is necessary to conduct many trials in order to determine the JND. The JND is the

“statistical criterion,” the condition where a subject makes a response a certain proportion

of times. In this lab, the JND is set at ±1 standard deviation. Said another way, the JND is

the orientation where the subject responds clockwise 84% of the time. To calculate the

JND, the primary analytical technique we’ll be using is to use fit a smooth S-shaped

curve to our data, specifically a probit function, which is used to model dichotomous or

binary dependent variables (e.g., probability of counter-clockwise (←), or clockwise (→)

responses). The mathematical technique to compute the fit uses a so-called generalized

linear model or glm. In R, the routine we will use is glm().


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Figure 2. Single subject response probabilities and fitted psychometric function for

the oblique (45 deg) viewing condition only.

Figure 3. Fitted psychometric function with Just Noticeable Differences (JNDs) and

Point of Subjective Equality Shown.


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It can be helpful to read these types of plots from “left to right:” In the lower graph,

Figure 3, the middle horizontal dotted line runs from the 0.50 probability of a clockwise

response on the ordinate, to the psychometric function, and drops down to the abscissa to

show us the orientation that the model predicts “chance performance.” This is sometimes

called the point of subjective equality, where the standard and test stimuli are

indistinguishable. In this example, the point of subjective equality was rotated clockwise

2.04 deg relative to the 45 deg standard (47.04 deg).

The upper and lower dotted lines show the probabilities that correspond to +1 SD

(0.84) and -1 SD (0.16), respectively. From this fitted function we can calculate the JND

in two ways: One way is to compute the reciprocal of the steepness of the best-fitting

psychometric function. The steepness is given by the glm coefficient corresponding to

testOrientation (remember to get these values using the summary() command). So the

steeper the function, the smaller the JND. Computed this way, one JND is equivalent to

one standard deviation of the Gaussian distribution underlying the psychometric function.

The second, equivalent method, is to use the difference, in degrees, between the

orientation corresponding to the 0.84 point on the ordinate, and the orientation

corresponding to the 0.16 point on the ordinate divided by 2.0. The JND for the data

shown in Figure 3 is 3.51 deg (rounded from 3.507991). If we compare this JND to the

JND under the vertical condition, we can determine to which viewing condition this

subject was more sensitive. Data points and models are shown for both conditions in

Figure 4.


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Figure 4. Orientation Discrimination Psychometric Functions.

The psychometric function for the vertical viewing condition (0.0 deg) is shown in

RED, and the oblique (45.0) in BLUE. We can see from these functions that this subject

was far more sensitive to orientation differences from vertical (JND = 0.54 deg), than to

differences when oblique (JND = 3.51 deg). Because the JND is calculated from the

same statistical threshold (±1 SD), we can directly compare the JNDs for both conditions .

In this example, both JNDs are the number of degrees at which this subject judged

clockwise 84% of the time. When interpreting JNDs, remember that a smaller JND

indicates more precise performance.

Group data analysis

plot5() is included as a way of inspecting our data for unintended effects, such as

systematic ordering-effects. In this experiment, the first viewing condition was randomly

assigned by the PsychoPy script. There is always a possibility that subjects assigned to

one condition before another may perform differently than subjects for which the

conditions were reversed. The strip-plot and box plots both show that mean JNDs appear

to be unaffected by the order of conditions that subjects took the experiment. plot1()

has two panels that represent the JNDs in two ways for both standard orientations, a strip


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plot (left) and a box plot (right). Both plots show a clear relationship between standard

orientation and JND.

Inferential statistical tests

Fitting mixed-effects models to experimental data is a powerful statistical technique

{Bates, 2015 #5425;Kuznetsova, 2015 #5426} that needed where repeated measurements

are made on the same statistical units (within-subjects experiments, or longitudinal

studies), or where measurements are made on clusters of related statistical units. It’s

helpful to think of our fitted model as a straight line that connects the mean JNDs of the

vertical and oblique conditions (M = 1.09 and 7.71 respectively). The model mod.jnd is

shown as a line in the right panel of Figure 5.

Figure 5. mod.jnd shown as a regression line


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The left panel shows the JNDs for all subjects for both the vertical (00) and oblique

(45) standards. The right panel shows the same data, but with Dummy Codes substituted

for the factor levels (0=“00”, 1=“45”). The BLACK line shows the fitted model (y = 1.09

+ 6.62*x). The BLUE line indicates the value of the Intercept (where x=0), which here is

the mean JND of the vertical standard (M=1.09 deg). The ORANGE dashed line shows

the mean value of the 45 standard condition (M=7.71 deg; value of the intercept + value

of the slope). Among other things, calling up that statistical model reports the intercept

and slope of that line. To make this clear, look at the results of that test stored in the

object mod.jnd by typing its name in R. R is also able to report the results in the form a

an analysis of variance (ANOVA) table using the anova command. Here is the output of

anova(mod.jnd):

Analysis of Variance Table of type III with Satterthwaite

approximation for degrees of freedom

Sum Sq Mean Sq NumDF DenDF F.value Pr(>F)

standard 813.20 813.20 1 31 59.967 9.774e-09 ***

order 26.15 26.15 1 31 1.928 0.1748

standard:order 4.95 4.95 1 31 0.365 0.5500

---

Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

You can see that the effect of the standard (0 deg vs 45 deg) gives a large value of the F-

ratio. The probability of an F of 59.967 or larger is very small. On the other hand, the

effect of testing order and the standard:order interaction is very small. These conclusions

are consistent with the strip plots and box plots of the jnd. Examine these graphs carefully

to fully understand the meaning of each of the four panels.


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Psychology of Perception Psychology 4165-100, Spring 2016

Laboratory 0


The Oblique Effect

Part 3: Writing a Report


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Page


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Introduction Section

Describe a perceptual phenomenon using prior research literature.

Before any experimentation, researchers must begin by ensuring that they clearly

understand the phenomenon of interest by reading prior relevant literature on the topic.

Review articles are especially useful in this regard in assembling relevant literature and

critiquing the current scientific understanding, state of the art, of a particular topic or

phenomenon. For today’s experiment we will use a classic review article, Appelle to

begin our understanding of the Oblique Effect phenomenon {Appelle, 1972 #40}. This

phenomenon has been studied extensively {McMahon, 2003 #3195;Westheimer, 2003

#4787;Meng, 2005 #4789;Freeman, 2011 #4785;Nasr, 2012 #4786}

1. Open the Appelle (1972).pdf.

Appelle, S. (1972). Perception and discrimination as a function of stimulus

orientation: The oblique effect in man and animals. Psychological Bulletin, 78(4), 266–278.

2. In prose, how does Appelle {, 1972 #40} describe the oblique effect? (Hint: it’s

on page 266)

Identify a “Gap”; formulate a problem statement.

Following the literature review, a quality research article will clearly provide a

compelling motivation for the current study in the form of a problem statement. For

example:

“Throughout the literature, the oblique effect has been described as a near universal characteristic of animal visual systems; however, I have not yet observed the oblique effect myself under controlled conditions.”


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Formulate a purpose statement to address the problem statement. The purpose explicitly tells the reader that (a) the purpose of the current project is to

solve the stated problem, and (b) how. For example:

“The purpose of this experiment was to demonstrate the presence of the oblique

effect in human visual perception. To do so we used the method of constant stimuli to compare orientation discrimination under two different visual orientation conditions.”

Formulate a clear, testable/falsifiable hypothesis.

Crucial to any scientific endeavor is clearly determining and stating the

hypothesis to be tested. Here is an example:

“We tested the hypothesis that visual orientation discrimination for vertically oriented stimuli (0.0 deg) would be superior to discrimination for obliquely oriented stimuli (45 deg).”

The logical “If, Then” statement is a particularly useful way to explicitly state how we’ll

determine if hypothesis is true in terms of subject performance. For example:

“If the Just Noticeable Difference (JND) for the vertical condition

(0.0 deg) was less than the JND for the oblique condition (45.0 deg) then we could conclude that the oblique effect was present.”

But what does it look like when we assemble all these elements together? Below, the

text from 1.3, 1.4, 1.5, and 1.6 are concatenated into a complete paragraph as might be

seen in an APA-formatted publication:

“Throughout the literature, the oblique effect has been described as a near universal characteristic of animal visual systems; however, I have not yet observed the oblique effect myself under controlled conditions. The purpose of this experiment was to demonstrate the presence of the oblique effect in human visual perception. To do so we used the method of constant stimuli to compare orientation discrimination under two different visual orientation conditions. We tested the hypothesis that visual orientation discrimination for vertically oriented stimuli (0.0 deg) would be superior to discrimination for obliquely oriented stimuli (45 deg). If the Just Noticeable Difference (JND) for the vertical condition (0.0 deg) was less than the JND for the oblique condition (45.0 deg)


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then we could conclude that the oblique effect was present.”

Method Section

Design & describe an experiment to investigate behaviors (human judgments) under contrasting perceptual conditions. The Method section describes the actions you took to test the hypothesis at a level of

detail necessary to the reader to understand the logical connection between those actions

and your theoretical question, and if needed, replicate the experiment. All experiments

involve the manipulation of one or more independent variables to observe the effect on

some outcome (dependent variable). There are many ways to design experiments in

experimental psychology, but one of the things that makes perception experimentation

different than other domains of psychological research, is the heavy reliance on within-

subjects designs, rather than between-subjects designs: Experiments are often designed so

that subjects perform the same judgment task under two or more conditions. Here is a

sample description of our experimental design:

“To demonstrate the presence of the oblique effect, we used the method of constant stimuli (Fechner, 1860) to compare the ability of participants to detect small orientation differences from vertical (0.0 deg) and oblique (45.0 deg) standard stimuli. Each participant was tested in both vertical and oblique standard orientation conditions, with the order of tasks randomly counterbalanced across participants. Both conditions involved judging the direction test stimuli were rotated relative to standard stimuli (clockwise, counterclockwise). Linear mixed-effects regression was used to analyze responses. Factors were ‘orientation” (vertical, oblique), ‘testing order’ (00-45, 45-00), and ‘subject’ as a random effect. The dependent variable was the Just Noticeable Difference (JND), equal to 1 standard deviation of the Gaussian distribution underlying the psychometric function.”

Describe participants to a level of detail appropriate to the experiment.

Descriptions of participants help the reader understand to whom any findings may be

generalized. For example:

“Participants were students enrolled in an undergraduate Psychology of Perception course (N=35), and were 18–26 years of age (M ︎ 21.2). All participants had normal or corrected to normal vision.”


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Design & describe Materials and Apparatus used to measure a behavior.

Careful descriptions of stimuli and apparatus should allow another interested researcher

to replicate your experiment. Here is an example:

“Viewing distance was not fixed, but was the typical distance when viewing a desktop computer. The stimuli were Gabor patches: Sinusoidal gratings with a Gaussian envelope. The Gabor patches had a spatial frequency of 0.8 cycles per degree (cpd), with and were sized to be approximately 16 deg in diameter from the typical viewing distance of a desktop computer. Stimuli were presented on a 27 in. RGB Apple monitor, in the center of the screen on a grey background (RGB (128, 128, 128)). For both standard orientation conditions, 19 test stimuli were prepared that were rotated to vary from the standard orientations in increments of 0.5 deg. The computer program PsychoPy 1.83.03 {Peirce, 2007 #4349;Peirce, 2009 #4350} used present stimuli and record participant responses.”

Design & describe a task procedure to measure a behavior.

The procedure should be limited to describing the events between the beginning of the

experiment (Clicking “Run” in PsychoPy), and when the participant is “Thanked” at the

end. Here is an example:

“Participants were tested individually during class. To start, participants were shown brief task instructions. The time course for each trial consisted of a standard stimulus briefly displayed for 0.5 seconds, a blank grey field for 1.5 seconds, followed by a test stimulus also displayed for 0.5 seconds. Subjects responded with the left arrow key (←) if they judged the test stimuli was rotated counter-clockwise relative to the standard, and the right arrow key (→) if they judged the test stimuli was rotated clockwise. The 19 test stimuli were presented in a different random order in each of 10 blocks of trials, for a total of 380 trials (190 trials x 2 standard orientation conditions). Subjects could take a brief break between standard orientation conditions. After completing the experiment, participants were thanked. The entire experimental procedure took approximately 30 minutes.”

Discussion Section

The goal of a discussion section is to summarize your experiment and explain to the

reader what your results mean. Very often readers are overwhelmed with information by


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the time they get to the discussion section, and have more than likely forgotten the

important contextual information from the introduction. Well-written discussion sections:

• Restate the purpose of the experiment.

• Restate the hypothesis/expected results.

• Explicitly state your findings in prose.

• Explicitly compare/contrast your findings to the prior literature (discussed in your

literature review).

• Discuss any unexpected results.

• Discuss methodological limitations in the present study.

• Discuss practical implications of your findings.

Restate the purpose of the experiment.

This reminds the reader what the whole experimental endeavor was about. Here is the

purpose statement from above:

“The purpose of this experiment was to demonstrate the presence of the oblique effect in human visual perception.”

Restate the hypothesis/expected results.

Restating the hypothesis/expected results serves a similar function to the reader. Here

is our hypothesis combined with part of the purpose statement:

“To do so we used the method of constant stimuli to test the hypothesis that visual orientation discrimination for vertically oriented stimuli (0.0 deg) would be superior to discrimination for obliquely oriented stimuli (45 deg).”

Explicitly state your findings in prose.

Remember: Findings are what the researcher concludes after a logical examination of

the results. Do not report any new results (numbers), just explain what the numbers mean.

“Our results supported our hypothesis; subjects were far more responsive to small deviations from vertical orientations than differences from oblique orientations.”


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Explicitly compare/contrast your findings to the prior literature (discussed in your

literature review).

Did you observe a similar effect as reported in a prior study? This is where you point

out similarities and differences to the experiments you cited in the introduction section.

“Our findings are in line with numerous prior investigations into the oblique effect in humans (as reviewed in Appelle, 1972).”

Discuss any unexpected results.

If warranted, this section is very helpful to the reader, especially when proposing

follow-up experiments. But, keep in mind that the “unexpected results” should probably

be connected with your original hypothesis somehow.

“Although the presence of the oblique effect was expected, what was not expected was its magnitude: On average, subjects required an orientation difference seven times larger when detecting differences from the oblique standard than for the vertical standard.”

Discuss methodological limitations in the present study

This should be an honest critique of the methods used, but don’t go crazy here.

Remember the old adage, “It’s easy to criticize.” Every experiment has limitations, but

smart researchers limit their criticisms to aspects of the study that might have changed the

finding of the study.

Discuss practical implications of your findings

Finish with what your finding means in the real world It’s helpful to think of this as

making recommendations for some kind of real-world task or problem. These sections are

patently speculative, so authors are often afforded a wide latitude in this regard.

“The robust presence of the oblique effect implies that the confidence that structural engineers develop from detecting misalignment of vertical supports should not be generalized to detecting similar faults in diagonal bracing. Non-vertical structural elements should always be inspected using well-calibrated measurement instruments, such as protractors, trammels, or rafter squares.”


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References

Appelle, S. (1972). Perception and discrimination as a function of stimulus orientation: The oblique effect in man and animals. Psychological Bulletin, 78(4), 266–278.

Bates, D. M., Mächler, M., Bolker, B. M., & Walker, S. C. (2015). Fitting linear mixed-effects models using lme4. Journal of Statistical Software, 67(1), 1–48. doi: doi:10.18637/jss.v067.i01

Fechner, G. T. (1860). Elemente der Psychophysik. Leipzig, Germany: Breitkopf and Härtel.

Freeman, J., Brouwer, G. J., Heeger, D. J., & Merriam, E. P. (2011). Orientation Decoding Depends on Maps, Not Columns. The Journal of Neuroscience, 31(13), 4792-4804. doi: 10.1523/jneurosci.5160-10.2011

Kuznetsova, A., Brockhoff, P. B., & Christensen, R. H. B. (2015). lmerTest: Tests in linear mixed effects models (Version R package version 2.0-29). Retrieved from https://CRAN.R-project.org/package=lmerTest

Macmillan, N. A., & Creelman, C. D. (2005). Detection theory: A user’s guide (2nd ed.). Mahwah, New Jersey: Lawrence Erlbaum Associates.

McMahon, M. J., & MacLeod, D. I. A. (2003). The origin of the oblique effect examined with pattern adaptation and masking. Journal of Vision, 3(3), 230–239.

Meng, X., & Qian, N. (2005). The oblique effect depends on perceived, rather than physical, orientation and direction. Vision Research, 45(27), 3402-3413. doi: http://dx.doi.org/10.1016/j.visres.2005.05.016

Nasr, S., & Tootell, R. B. H. (2012). A Cardinal Orientation Bias in Scene-Selective Visual Cortex. The Journal of Neuroscience, 32(43), 14921-14926. doi: 10.1523/jneurosci.2036-12.2012

Peirce, J. W. (2007). PsychoPy--Psychophysics software in Python. Journal of Neuroscience Methods, 162(1-2), 8-13. doi: 10.1016/j.jneumeth.2006.11.017

Peirce, J. W. (2009). Generating stimuli for neuroscience using PsychoPy. Frontiers in Neuroinformatics, 2(January), 1–8. doi: 10.3389/neuro.11.010.2008

R Core Team. (2015). R: A language and environment for statistical computing. Vienna, Austria: R Foundation for Statistical Computing. Retrieved from https://www.R-project.org/

Westheimer, G. (2003). Meridional anisotropy in visual processing: implications for the neural site of the oblique effect. Vision Research, 43(22), 2281-2289. doi: http://dx.doi.org/10.1016/S0042-6989(03)00360-2

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