# Overview of Writing & Submitting Assignments Conducting Complete and Efficient Analyses

Being a good researcher, and conducting good analyses, is more than getting the right numbers in the end. Your output file should be complete, concise, and efficient, so any colleagues with whom you share your data are not forced to wade through multiple analyses and unnecessary output across many files.

For most multi-week analyses, after the first week you will have an output file saved (*.spv). In later weeks, open that file in addition to the data file (*.sav), and close all other output files that may be open. This way, all new output will be added to the original file.

With some exceptions, your output file should have the following elements, in this order:

**1. Assumptions check (only required for Lab 5)**

Every statistical analysis has underlying assumptions about the data set – see your textbooks and lab assignments. You must always check your assumptions *first*, before you conduct the test itself! If these assumptions are violated, the validity of your test’s results may be jeopardized if you don’t make corrections (or choose a different test).

Because every test’s assumptions are different, they are all checked differently. However, for most of the analyses conducted in this course, running the “Explore” function (found through “Analyse” – “Descriptive Statistics” – “Explore”), and going into “Plots” and selecting “Histograms”, will usually get you what you need. Make sure you check with the specific test of the week to ensure this is really what you need, and that it will be sufficient on its own!

**2. The analysis of interest**

** **

Once you have checked your assumptions (and, in the real world, dealt with any anomalies or problems), you may proceed with the test itself. You should only run the test once, unless you have a specific reason to need multiple tests with slight variations each time. If you have made an error and need to re-run the test, make sure you delete the “wrong” output! (Select it in the outline in the left window panel, and hit “delete” on your keyboard.) Sifting through nearly-identical tests can be very confusing if they don’t all need to be there.

**3. Graphs displaying data trends**

** **

These are not always required. Sometimes they were required as part of the assumptions check, in which case they’ll be up with #1. Sometimes they are most easily gathered through options and checkboxes in the analysis itself, in which case *please do so*, and they’ll be up with #2. If neither is the case, and you need a graph to show the pattern of data, do it last.

These elements may be repeated for each week’s analysis.

PSYC 315 LAB MANUAL: FALL 2023

# Writing: What’s Expected, and Tips for Statistics

** **

You will include a write-up with every lab assignment. Each assignment will be tailored for a different audience and will include different elements, eventually culminating in a formal APA-format write-up. See each assignment for specific instructions on what is required; when you reach the full APA write-up, this is what will be involved. (However, note that APA style usually includes a Methods section, not required here.)

When writing, put yourself into the given scenario and write as if you are presenting your own research. The phrase “In this lab…” (or similar) should not appear in your write-ups!

# Introduction

– Briefly introduce the problem under investigation: What are we trying to figure out and why? Whom did we look at, and how did we go about it?

– Please don’t just copy what I’ve written as background on the assignment. Put it in your own words. – You don’t need a Methods section, so some of the more important Methods points should here.

# Results

** **

– Evaluate the assumptions of your analysis *first*. Most published articles do not mention these assumptions unless they are problematic, but I want to know you’ve done it and understand its implications. Don’t just state the assumption’s definition, assess whether our data meets it.

– Give the results of the analysis: report the descriptive statistics, then the test results.

** **

# Writing with statistics

** **

– Report the mean and standard deviation together. The standard deviation doesn’t mean anything on its own – without its mean, it’s mean(ing)less!

– In the narrative, write out the words “mean” and “standard deviation”. The abbreviations “*M*” and “*SD*” should be used in parentheses only, or after a comma at the end of the complete sentence.

– A sentence should make grammatical sense even when you skip all the material in parentheses. – When used, italicize all standard statistical abbreviations except CI and Greek letters.

– Always report numbers to 2 decimal places, except for *p*-values, which are reported to 3 decimal places.

– *State the general results of an inferential test in words, in a full and complete sentence, including significance, direction (if significant), and effect size. Then report the numerical results all together, in APA format, at the end of the sentence or phrase.*

**Bad:**

“The mean of the treatment group was *M* = 2.22, *SD* = 1.11.”

“The treatment group’s *M* was 2.22 and *SD* was 1.11.”

“The treatment group had a *M* = 2.22 and a *SD* = 1.11.”

“The treatment group had a mean of (*M* = 2.22, *SD* = 1.11) and the control group had a mean of (*M* = 4.44, *SD* = 3.33).”

“The difference between the two groups had a *t*-value of 3.33 and was significant, with a *p*-value

of .004.”

**Good:**

“The mean of the treatment group was 2.22 (*SD* = 1.11).”

“The treatment group’s mean (2.22, *SD* = 1.11) was higher than…”

“The treatment group (*M* = 2.22, *SD* = 1.11) scored higher than…”

“The treatment group had a mean of 2.22 (*SD* = 1.11), and the control group had a mean of 4.44 (*SD* = 3.33).”

“The treatment group’s mean was higher than expected, *M* = 2.22, *SD* = 1.11.”

“The treatment group scored significantly higher than the norm, though the effect was small, *z* =

2.03, 95% CI [10.98, 13.46], *d* = 0.24.”

“The treatment group scored significantly and moderately higher than the control group, *t*(19) = 3.33, *SEM* = 4.44, *p* = .004, 95% CI [1.23, 3.45],* d* = 0.49.”

# Discussion

** **

– First state the statistical conclusions (relationship, difference, etc.).

– Then state the practical conclusions, in context – interpret and apply the statistics. You may not have a full body of research to draw from, but dig into what you do have, and what you know. Use your instincts. (However, I do not expect you to conduct additional background research.)

– Relate what we’ve learned back to the problem at hand, and make some interpretations/suggestions.

– How do these results help us? What do these numbers *mean*? What have we learned from them? – How can we *apply* them towards our original research purpose?

– Address any limitations or future considerations you may see.

– For the most part, keep numbers out of the Discussion. Everything relevant should already have been reported in the Results.

– May be a few sentences or a couple of pages. Longer does not necessarily mean better!

** **

PSYC 315 LAB MANUAL:

FALL 2023

Lab 5: t-tests

32

Summary:

Lab

5a: Single sample and dependent samples t-tests

Lab

5b: Independent samples t-tests;

writing up your findings

What to submit:

Yourname-lab5.spv – Output file with

assumptions and test results for all three tests Yourname-lab5.docx – Word file with APA-style write-up

Due: Dec. 4

**Lab 5a: Single Sample and Dependent Samples t-tests**

# Test Usage

*Single Sample t-tests*: Used when you have a sample of people and you want to compare their mean score to a single population norm.

* *

*Dependent Samples t-tests:* Used when you have a single sample of people, tested twice over time or on two related measures (Within Groups or Repeated Measures design), and you want to compare the two scores to each other. Also used with Matched Groups designs.

** **

# Assumptions

The assumptions underlying single sample and dependent samples *t*-tests are:

## Assumption 1: Normality

* *

Single Sample *t*-test: The test variable is normally distributed.

Dependent Samples *t*-test: The difference scores are normally distributed.

Note that the *t*-test is robust to moderate deviations from normality, provided the sample size is large enough (*n* > 30).

## Assumption 2: Independence

* *

The cases are independent of each other. (This assumption is usually built into your research procedures. In our case, you can accept it as true.)

** **

** **

# Exercises**[1]**

## Single Sample t-Test

Download, save, and open a new data set from Moodle: **ch7exercise1.sav**.

Psychologists are interested in whether people with depression undergoing group therapy will perform a different number of activities of daily living after group therapy. Therefore, the psychologists have randomly selected 30 clients with depression to undergo a 6-week group therapy program. The typical number of activities of daily living for similar people with depression is 14.

Check the assumption of normality, and gather descriptive statistics:

1. *Go to* Analyse → Descriptive Statistics → Explore.

2. *Click* the variable “activities” and *Click* the top arrow to move it to the Dependent List window

3. *Click* the Plots button on the right

4. *Click* the check-boxes beside Histograms (to select it) and Stem and Leaf (to de-select it)

5. *Click* Continue, then *Click* OK

Conduct the Single Sample *t*-Test:

1. *Go to* Analyse → Compare Means and Proportions → One-Sample T Test

2. *Click* the variable “activities” and *Click* the arrow to move it to the Test Variable(s) window

3. *Type* the population mean (comparison point) of 14 in the Test Value box 4. *Click* OK

* *

## Dependent Samples t-Test

Download, save, and open a new data set from Moodle: **ch7exercise2.sav**.

Psychologists are interested in whether people with depression undergoing group therapy will perform a different number of activities of daily living before and after group therapy. Therefore, the psychologists have randomly selected 30 clients with depression participating in a 6-week group therapy program.

Calculate the difference scores of the participants:

1. *Go to* Transform → Compute Variable…

2. *Type* the new variable name (difference) in the Target Variable box

3. Either by *Clicking* the variable names and the arrow button, or by *Typing* the variable names, along with *Clicking* or *Typing* a minus sign between them, enter this formula in the Numeric Expression box: adlpost – adlpre 4. *Click* OK

Check the assumption of normality:

1. *Go to* Analyse → Descriptive Statistics → Explore.

2. *Click* the name of the variable “difference” and *Click* the top arrow to move it to the Dependent List window

3. *Click* the Plots button on the right

4. *Click* the check-boxes beside Histograms (to select it) and Stem and Leaf (to de-select it)

5. *Click* Continue, then *Click* OK

Conduct the Dependent Samples *t*-Test:

1. *Go to* Analyse → Compare Means and Proportions → Paired-Samples T Test

2. *Click* the variable “adlpre” and *Click* the arrow to move it into the Paired Variables box. It will be in the Variable 1 column.

3. *Click* the variable “adlpost” and *Click* the arrow to move it into the Paired Variables box. It will be in the Variable 2 column. 4. *Click* OK

** **

# Assignment

The Matching Figures Task (for memory) and Raven’s Progressive Matrices (for spatial/sequential reasoning) are tests commonly used to assess people’s cognitive development, among other things. In the Matching Figures Task (MFT), participants view a picture for 2 seconds, then 5 seconds later they must identify this picture from a set of three pictures. In Raven’s Progressive Matrices (RPM), participants view a grid of three figures with a blank bottom right corner. These figures change sequentially, and participants must choose the appropriate fourth figure in the series from a set of three choices. (See right for an example image of this test.) As both tests are multiple-choice from three options (even guessing, you have a 1 in 3 chance to be correct) and have 24 questions total, a “chance” score on either test is 8/24.

These tests are approved for use with children starting at age 5, but developmental psychologist Dr.

M’Benga wonders if they could be appropriate for 4-year-olds. In addition, one of Dr. M’Benga’s grad students is a parent of a 4-year-old child. After sending the child to preschool for a year, she noticed an improvement in his cognitive abilities.

Dr. M’Benga has therefore administered both tests to a group of 40 four-year-old children who regularly attend preschool, and to another group of 40 four-year-old children who do not.

** **

** **

# Research Questions

** **

## Single Sample t-tests

“Do 4-year-olds perform better than chance at the Matching Figures Task, and does attending preschool make any difference to this? What about Raven’s Progressive Matrices?” (Note that we will conduct 2tailed tests, as significance in the opposite direction would still be interesting.)

## Dependent Sample t-tests

“Are 4-year-olds better at the seemingly simpler memory task (MFT) than the more complex spatial reasoning task (RPM), and does this differ depending on whether or not they attend preschool?” (Also note that we will still conduct a 2-tailed test, as both directions would be important.)

** **

Download, save, and open the data set from Moodle: **lab5data.sav**.

# Procedure

* *

## Single Sample t-test

1. Divide the data file so that SPSS will analyse the two groups of children separately.

• *Go to* Data → Split File

• *Click* the radio button beside “Compare groups”

• *Click* the variable “Preschool” and *Click* the arrow to move it into the “Groups Based on:” box

## • Click “OK”

• The data will not appear to have changed, but in the lower right corner of the screen, you will see “Split by Preschool”.

• *From this point onwards, until you go back into Data – Split File and select the “Analyse all cases, do not create groups” option, SPSS will treat the two groups as two separate data files, and no data will ever be created or analysis completed that combines or compares the two groups.*

2. Conduct an Analyse – Descriptive Statistics – Explore on both tests’ scores simultaneously to evaluate Assumption 1. *Note that you should not enter “Preschool” as a Factor.*

3. Conduct a “One-Sample T Test” as described to determine if 4-year-olds perform better than chance on each test. Note that you can evaluate both tests simultaneously – put them both in the “Test Variable(s)” box, and each will have its own output line in the test results. There will also be separate test lines for children attending preschool and not.

4. Report the effect size of this difference for each test using the Point Estimate of Cohen’s *d* in the output. By convention, an effect size of ±0.20 is considered weak, ±0.50 is considered moderate, and ±0.80 is considered strong. *The actual effect size can range from negative to positive infinity.*

* *

* *

## Dependent Samples t-test

1. Use Transform – Compute to calculate the difference scores for the two tests (i.e., the difference between each child’s score on the MFT and the RPM).

2. (Ensure the Split File is still on.)* *Conduct an Explore to create histograms of the* difference scores*, to

evaluate Assumption 1. (Still ignore “Preschool” in the Explore dialogue.)

3. Conduct a “Paired-Samples T Test” on the *original variables* as described to determine if 4-year-olds perform differently on the two tests. You will receive separate results for those who do and do not attend preschool.

4. Report the effect size of this difference for each factory using the Point Estimate of Cohen’s *d* in the output. By convention, an effect size of ±0.20 is considered weak, ±0.50 is considered moderate, and ±0.80 is considered strong. *The actual effect size can range from negative to positive infinity.*

5. Save your output file as *yourname*-lab5.spv. You will submit it, with more output and a write-up, on **Dec. 4**.

APA Format & Write-Ups:

•

See “Overview of Writing” section earlier in

this manual. All of it now applies.

•

Single Sample t-test reporting format:

After

a 6-week therapy program, patients perform significantly more activities of

daily living than a typical patient, with a strong effect, t(29) = 4.63, p < .001, 95% CIdiff [1.40, 3.60], d = 0.85.

•

Dependent Samples t-test reporting format:

After a 6-week therapy program,

patients perform significantly more activities of daily living than they had

before the program, with a moderate effect, t(29) = -3.30, SEM =

0.80, p = .003, 95% CIdiff

[-4.27, -1.00], d = -0.60.

•

Report all numbers to two decimal places only! (Exception: report p to three decimal places.)

•

Do not use a leading zero in front of the p-value.

•

As much as possible, keep numbers out of the

Discussion.

**Lab 5b: Independent Samples t-tests**

# Test Usage

*Independent Samples t-tests:* Used when you have two separate groups of people, tested on the same measure (Between Groups design), and you want to compare their scores.

# Assumptions

** **

The assumptions underlying independent samples *t*-tests are:

*Assumption 1: *The test variable is normally distributed in each population. Note that the *t*-test is robust to moderate deviations from normality, provided the sample size is large enough (*n* > 30).

*Assumption 2: *The variances of the test variable for each population are equal. A rough guideline to evaluate this is if either of the two variances is more than 4x the size of the other.

*Assumption 3: *The cases are independent of each other.

# Exercise**[2]**

Download, save, and open a new data set from Moodle: **ch8exercise.sav**.

Psychologists have randomly selected two groups of clients with depression, one of which has undergone a 6-week group therapy program and the other a 6-week individual therapy program. They have measured the number of activities of daily living performed by each group, and will compare them to determine which type of therapy is more effective.

Check the assumptions of equality of variances and normality of distributions, and gather descriptive statistics:

1. *Go to* Analyse → Descriptive Statistics → Explore.

2. *Click* the variable “activities” and *Click* the top arrow to move it to the Dependent List window

3. *Click* the variable “therapy” and *Click* the middle arrow to move it to the Factor List window.

4. *Click* the Plots button on the right

5. *Click* the check-boxes beside Histograms (to select it) and Stem and Leaf (to de-select it) 6. *Click* Continue, then *Click* OK

Conduct the Independent Sample *t*-Test:

1.

*Go to* Analyse → Compare Means and Proportions → Independent-Samples T Test

2. *Click* the variable “activities” and *Click* the top arrow to move it to the Test Variable(s) window

3. *Click* the variable “therapy” and *Click* the bottom arrow to move it to the Grouping Variable window

4. *Click* the Define Groups… button

5. The group labels should be auto-filled; *Click* Continue

## 6. Click OK

** **

** **

** **

** **

** **

** **

# Assignment

** **

Dr. M’Benga is investigating whether two common cognitive tests, the Matching Figures Task (MFT) and Raven’s Progressive Matrices (RPM), are appropriate for children as young as 4 years old. He has administered both tests to 80 four-year-olds, and we have compared their scores on each test to “chance” levels and to each other.

We have compared the children’s scores on both tests to chance levels of responding (i.e., guessing), and we have compared the two tests to each other. Both times the results were divided by whether or not the children attended preschool, leading to some general interpretations in that regard but with no ability to make formal conclusions about preschool’s effects (if any). Now we would like to directly compare children’s test scores based on whether or not they attend preschool regularly.

** **

# Research Questions

“Does preschool teach 4-year-olds skills that would help them perform better on the Matching Figures Task? On Raven’s Progressive Matrices?”

** **

** **

** **

# Procedure

Open your data and output from last week: **lab5data.sav**, and ** yourname-lab5.spv**.

*If you have waited until today to complete your 5a analyses, and you have just now done so, you will need to turn the Split File function off! Go into “Data” – “Split File…”, and click “Analyse all cases, do not create groups”.*

1. The descriptive statistics and histograms you need to evaluate Assumptions 1 and 2 are already in the output, from last week’s procedures. *You do not need to repeat the analysis*, but in your write-up, you must now also look at the variances.

2. Conduct an “Independent-Samples T Test” as outlined above to answer the two research questions posed above. You can complete both at the same time by entering both dependent variables into the “Test Variables” box. SPSS will put the test results for each on a separate line in the output.

3. Report the effect size of this difference for each test using the Point Estimate of Cohen’s *d* from the Output. By convention, an effect size of ±0.20 is considered weak, ±0.50 is considered moderate, and ±0.80 is considered strong. *The actual effect size can range from negative to positive infinity.*

4. Write an APA Style write-up for the analyses conducted here and in Assignment 5a. Take the role of the researcher writing up your own study; do not talk about Dr. M’Benga in the third person.

• Be sure to cover all the sections and details included in the “Writing: What’s Expected” section of this manual, using proper APA format to present all results. Independent Samples *t*-tests are reported using the same format as that used for Dependent Samples *t*-tests (see Lab 5a section); the “Std. Error Difference” in the Output is what should be reported for the *SEM*.

• In the Results, report all means and standard deviations first – you should have four sets, one for each test for each group of children. These are the same values being tested throughout, so they do not need to be reported again after this.

• For the rest of the Results, handle each test type (single sample, dependent sample, independent samples) individually, one per paragraph.

• For each test type, report, in this order:

o outcomes of checking all *t*-test assumptions

o test results, including effect sizes and 95% CI of the difference

• The Discussion section should include an interpretation of these results in terms of the original research purpose. o When interpreting significance, use the effect size and 95% CI to augment your findings, determine practical importance, etc.

o Make some interpretations and put it in context:

o What’s going on? What’s the big picture?

o What have we learned from this, and how can we use it?

o Where are we now, and where can we go from here? What more should we look at?

o Also address any confounding factors limiting our interpretation of these results.

5. Save your output and write-up files:

• *yourname*-lab5.spv – Output of all of 5a and 5b together

• *yourname*-lab5.docx – Write-up

* *

Submit these *two files* through Moodle by midnight on **Dec. 4**.

[1] Whitley, T. W. (2009). *Study guide and computer workbook for statistics for psychology* (5th Ed.). Upper Saddle River, New Jersey: Pearson Education, Inc. Pages 69-72.

[2] Whitley, T. W. (2009). *Study guide and computer workbook for statistics for psychology* (5th Ed.). Upper Saddle River, New Jersey: Pearson Education, Inc. Pages 82, 85, & 86.