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Rules-of-Thumb-for-Sample-Size-and-Power Research Proposal


  1. No title page – put student name, number and actual date of submission in footer.
  1. Page numbers belong in header, top right, start on first page.
  2. Place title at top of first page of your introduction.
  3. Use 12 pt Times Roman font throughout body of the paper. Some flexibility on font size in schematics (tables, matrices) and also in Appendix (ces). Sometimes it’s just easier to understand when it all fits inside the rows and columns neatly. Please no text smaller than 10 point anywhere in schematics or appendices.
  4. Use 2.54cm margins all around (top, bottom and sides, this document has correct margins).
  5. Double-spaced throughout body of paper. Appendices and schematics can be single- spaced.
  6. This is a proposed study, so write in the future tense to the extent possible. This might get tricky when writing the Discussion section, which will be based on what you say you found. Okay then to switch to past tense. Aim for clear and coherent writing, so I have a clear understanding of your main ideas.
  7. Okay to use first person, active tense E.g. “I will…” or third person, passive E.g. “Students will be recruited…”
  8. Maximum 8-10 pages for main body NOT including references, note: I will stop reading at 10 pages.
  9. Up to 2 additional pages for Appendices, for table, chart, questionnaire, sample questions, visuals, other materials- must NOT be used for additional text describing study!
  10. Use APA format for citations in text and for References section only!!!

You do not have to format the whole paper in APA style (so no title page, abstract, running head).

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Suggested Length of Sections

Introduction – 3 to 4 pages

Methods and proposed results – 3 to 4 pages

Discussion – 3 to 4 pages

Proposed Study Template

The following pages provide a template that you can populate with the specifics for your proposed study, with suggestions by section. You are responsible for describing the details of your proposed study clearly. So if there is a sub-heading or section that you need to add, please tailor the template to suit the details of your particular study. Just keep the main headings, in the same general order as presented here, as I will be looking for this information when I am marking your papers. Scientific writing is highly ritualized. You may use this template in subsequent content courses when writing any quantitative research proposal.



Introduction (3 to 4 pages)

Meaningful Title Goes Here – centered

Be specific. Identify the sample (e.g. elementary, grades 4 to 6, middle school, adolescents, undergraduates, adults, aging adults), state the constructs of interest (i.e. what you are measuring). A statement or a question are both okay for the title.

Example of a not great title: Teacher Education and Student Mental Health

Example of a Better Title, statement style:

Teacher Mental Health Education Improves Teacher Identification

of Anxiety and Depression in Secondary Students

Example of a Better Title, question style:

Does Teacher Mental Health Education Improve Teacher Identification

of Anxiety and Depression in Secondary Students ?

Ask yourself if your study will speak to the title. Titles that start with “How…” are not easily answered by quantitative studies. You are not describing something, you are asking if a manipulation has an impact on an outcome (s) or if variables are systematically related i.e. if they predict an outcome (s).

Note: No need to write the word “Introduction”

First Paragraph:

State your topic, say why it is important. What are the implications for individuals? For Education? For policy, practice, society? These should NOT be the only two sentences in this paragraph. It is not enough to simply say it is important or to cite someone else who says it is. Make your own case, clearly. Act as if you are convincing a funding agency to fund your study. Why should they choose your study to fund?

Intervening paragraphs (3-5 suggested, but this is just a suggestion):

Review previous, relevant work, identify limitations, say if the findings are conflicting. Each paragraph should have a theme or a main point. Order the paragraphs so that you build an argument that leads up to your last paragraph where you will outline a specific research question that your proposed study will address. By the time the reader gets to your last paragraph they should have some idea as to what you are going to propose for your study.

This section should be based heavily on previous, primary source, peer-reviewed, quantitative research. Use your own argument to seam this work together to build towards your research question or hypothesis.


Last paragraph:

Present Study (suggest you keep this subheading)

State the purpose of the proposed study in general terms. Refer to constructs (elementary student mental health, self-regualtion, math achievement and so on). State a clear research question. Be specific – it should be clear what age/demographic group you will be targeting, what if anything you will be manipulating, what you will be measuring.

E.g. The present study will investigate…

E.g. The proposed study asks if grade 3 students who are taught with reading program X will show significantly greater growth in reading achievement compared to their peers who are taught with the business-as-usual reading program.

Alternatively,  you could state as a straightforward question.

E.g. Do grade 3 students who are taught with…?

If you are making a prediction, do so here…

E.g. I predict that grade students who receive program X reading instruction…

If you are taking an exploratory approach…

E.g. Given the mixed results from previous research with program X, it is not clear which approach to reading instruction will be more effective for improving grade 3 reading achievement.


At issue, was whether program X reading instruction or the business as usual reading instruction would lead to greater growth in math achievement over the school year.

Method (3-4 pages)


Describe the sample. Give the sample size. Provide age, grade, distribution of gender. Say if the sample will be ethnically or socioeconomically diverse, give as much detail as you can. Provide any other demographic information that will be important to help make sense of the study question, design, results and discussion.

Describe how they will be recruited.

Say that you will obtain signed consent and from whom you will obtain it.


Keep as brief as you can, no narrative sentences, name the task or measure and then very briefly describe it. For established measures, cite the authors using APA style.

Describe any behavioural tasks like the Day/Night Stroop task or any computerize tasks.

Describe what kind of grades, marks, GPA etc. you will obtain and where will you get them from.

Describe any questionnaires or scales you will use.

For each task, instrument, questionnaire here it should be clear what data you will obtain.

e.g. The last sentence might be “The X scale will yield a verbal and non-verbal IQ score” or for something like the Day/Night Stroop “Participants are awarded one point for each correct trial for a total score out of 16”

Here’s an example:

Fictitious Reading Achievement Scale (FRAS; Solomon & Ganea, 2018). A standardized scale measuring reading fluency comprising 3 short paragraphs. For each paragraph, students read the passage and then answer 4 multiple choice comprehension questions. One point is awarded for each question answered correctly, for a total score out of 12. See Appendix A.

Refer to any Appendices as Appropriate

Study Design

I am inserting this section here, because at this point you will already have described your participants and the materials/measures/instruments you will use, so you can refer to them here. But you can choose to move this section to the beginning of the methods section before participants if that makes more sense for your study. If you choose this, then when you refer to the measures etc. you can say “…(see below)”.

Whether you are doing an experiment, quasi-experiment (like an experiment but without random assignment) or association study (correlation, regression, other association models), it should be clear what are your independent variables or predictors and what are you dependent variables or outcomes. Describe any counterbalancing if appropriate to your study.

For an Experiment or Quasi-Experiment

This is where you should show a schematic of your study design as we discussed in class.

For an experiment (random assignment) or quasi-experiment (you have different groups but no random assignment) your schematic should be a matrix showing what you will manipulate.

Your schematic should be called Figure 1 and it should have a title. You can also include a legend. Title and legend go below the figure. Describe the in the text making reference to the figure.  You can insert the sample sizes into each cell but you do not have to do this if it will be clear from the text. You can leave the cells empty. See example below.

    Reading Program X Reading Program Y Nutrition Program

(control group 1)

No New Program

(control group2)

Grade 2 Boys n = 12 n = 12 n = 12 n = 12
Girls n = 12 n = 12 n = 12 n = 12
Grade 4 Boys n = 12 n = 12 n = 12 n = 12
Girls n = 12 n = 12 n = 12 n = 12

Figure 1. Overview of the study design. You may place a brief figure legend here if you like.

E.g. Grade and reading program will be between subjects factors. The outcome will be children’s scores on the Fictitious Reading Achievement Scale.

For an Association Study

This is where you should insert a table (called Table 1). It should have a title. You can include a legend. Title goes above the table, legend goes below. Show your predictors in the first column, any control or moderator variables in the second column, show your outcome variables in the last column.

Table 1. List of predictors, controls/moderators and outcome measures.

Predictors Control/Moderator Variables Outcome Measures
Time Spent on Social Media Years since first use of social media Anxiety Scale Score
Gender IQ Beck Depression Inventory Score
Current Age

You may place a brief table legend here. Everything in the table should be mentioned in the text. There should not be anything surprising in your table.

Procedure  (keep very brief)

How will the data be collected? When? Where? What will happen to collect the data?

E.g. “Participants will be tested individually in a quiet area of their school. They will receive all of the tasks at baseline (on the same day) and again one week later.”

E.g. “Participants will create a logon code for the study site. They will login, complete a brief demographic questionnaire and then complete all four mental health questionnaires online before logging off. Three months later, they will receive an email requesting that they login and complete the same four mental health questionnaires again.”

Anticipated Results

Plan for Analysis

This is not required, but good if you can include this. E.g. “I will analyze the data to determine if there is a main effect of reading program, a main effect of gender and a reading program by gender interaction on growth (or change, or improvement) in children’s reading achievement scores over the school year.

Note, that you should name the independent variables and the outcome variable (s), as I did in the example above.

You may say something like, “I will repeat the same analysis for growth in math achievement to determine if the effects for reading program A were specific to reading achievement rather than to growth in academic achievement more generally”, if this is appropriate for your study.

Results (if only using results, no plan for analysis, centre “Results” here)

Say in words (no statistical procedures required) what you expect to find.  Make it easier on yourself and say that you will find what you predicted.

E.g. “I anticipate that I will find that grade 3 students taught with reading program  A…”

If your study was exploratory i.e. you did not make any clear predictions, then you will have to commit to an outcome here, so that you can discuss it below.

You may use figures (graphs, tables and so on) to show fictitious data here or in an appendix, but this is not required.


Remember, no causal language for an association study. Also, stay away from saying that anything was “proven”!!!! Say “The results show…” or “My findings suggest…”

First paragraph:

Summarize the purpose of your study.

E.g. “In this study, I investigated…I was interested in whether or not children who received reading program X…”


E.g. “This study examined the relation between time spent on social media (including Facebook, Instagram and Twitter) and frequency, duration and intensity of self-reported anxiety and depression in adolescents in grades 10 and 11. It was predicted that…”

Second paragraph:

Summarize what you found. Discuss how your results relate to your research question, your hypothesis (es), did you confirm your prediction?

E.g.  “I found that grade 3 students who received …”

E.g. “I found that the more time adolescents in grades 10 and 11 spent on social media in the preceding month, the likely they were to report…”

Next paragraph:

What do your results mean? E.g. if you found that reading program A was significantly more effective than the business as usual approach to reading instruction, then the study results suggest that the key ingredient in reading program A might be a more effective way to…”

Next paragraph:

What if you do not find what you predicted results? Briefly state what a different outcome might look like. E.g. “If I find that there is no difference between reading program A and the business as usual approach to reading instruction on children’s growth in reading achievement it could be that…” E.g. maybe your reading measures were not sensitive enough to tap any changes in children’s reading skill, perhaps the programs have more in common than not, perhaps reading program A is not effective for your target age group, even if in previous studies it was found to be effective for children in other age groups. Maybe your sample is different from that in previous studies that found different results.

Next paragraphs:

Discuss the strengths of your study such as random assignment to conditions or treatments, a large, diverse, representative sample, what you controlled for…

Discuss any limitations of your study such as that your measures may have been too insensitive to detect subtle improvements in depression scores or that the study duration may have been too short for effects to take effect or it is not possible to know if the effects you found will be enduring.


Broaden out a bit. You can make connections to the broader literature here but this is not required. Connections could be made to previous work on the same topic, to other related topics, to theory.

What are the broader implications of your results (relates to why your study is important as you outlined in the introduction).  For individuals? For communities? For society?

What are potential real-world applications of your results?

Suggest any directions for future studies.

Have a concluding sentence. “Given the long-term implications of early reading skills, reading program X may be a worthwhile investment”.

Appendix A

Appendix B

(each Appendix on a separate page)

You can use up your 2 Appendix pages any way you like. E.g. one page could contain sample questions from multiple measures. Just be sure this is clear and you include references for the measures.


Starts on a separate page, be sure to use APA style, at least 15 primary sources altogether, at least 12 quantitative studies including those cited in your literature review. Up to 5 qualitative studies fine, but these should not be the basis for your study. Additional references e.g. narrative review, theoretical paper welcome but remember these are NOT primary sources. Avoid popular publications like magazines, blogs and so on.


I strongly suggest that you consult the following website:



Here are some examples of how to cite original research using APA style:

In the Main Text

List all of the authors and the year (in parentheses) in the main text the first time you cite

the paper. E.g. “Smith (2002) showed that”… or “Klein and Smith (2000) found that…” or “Research

with grade one students showed that…(Klein, Adams, Portman, Pearce & Smith, 2000).

If two authors, list both along with year (in parentheses) every time you cite the paper. If

more than two authors, then on the 2nd and remaining times you cite the paper you can list the first

author, then “et al.”. Always include the year (in parentheses). E.g. On the 2nd time you cite the Klein

paper above, you can just say “Given than Klein et al. (2000) found that…”. Or previous work on

children’s understanding of proportion indicates…(Klein et al., 2000).

In the Reference List (use 12 point font throughout the reference list, it is larger than what is shown below)

List all papers under “References” (title on new page, at top and centered, as on this page). First line

of each reference is left justified, all subsequent lines are indented, as in examples below.

Example for single author paper

Vasilyeva, M. (2002). Solving spatial tasks with unaligned layout: The difficulty of dealing with

conflicting information. Journal of Experimental Child Psychology83, 291-303.


“Author Last Name, Author Initial. (year). Title of article, only first word begins with an upper case

letter. Journal Name in italicsvolume in italics, page X – Y.”

Example for two author paper

Sophian, C. & Kailihiwa, C. (1998). Units of counting: Developmental changes. Cognitive

Development13, 561-585.


“1st Author Last Name, 1st Author Initial & 2nd Author Last Name, 2nd Author Initial (year). Title of

article, only first word begins with an upper case letter. Journal Name in italicsvolume in

italics, page X – Y.”

Example for more than two author paper

Williams, B. R., Ponesse, J. S., Schachar, R. J., Logan, G. D. & Tannock, R. (1991). Development of

inhibitory control across the life span. Developmental Psychology35, 205-213.


“1st Author Last Name, 1st Author Initial., 2nd Author Last Name, 2nd Author Initial.,” etc. listing all

authors in this way, then “& last Author Last Name, Last Author Initial. (year). Title of article,

only first word begins with an upper case letter. Journal Name in italicsvolume in italics,

page X to Y.

From the syllabus:

Policies and Procedures


Writing at the University of Toronto

If you are not familiar with APA style of referencing sources: Please go to the following websites for excellent descriptions and examples:




Writing support is available at the University of Toronto:  You may visit the OISE Student Success Centre http://www.oise.utoronto.ca/ss/OISE_Student_Success_Centre_(OSSC)/

OR http://www.writing.utoronto.ca/advice for general resources on writing OR http://www.sgs.utoronto.ca/currentstudents/Pages/ELWS-Workshops.aspx for useful workshops.

ACADEMIC INTEGRITY:  Please make sure you are aware of the guidelines set forth by the School of Graduate Studies on: http://www.sgs.utoronto.ca/facultyandstaff/Pages/Academic-Integrity.aspx It is particularly helpful to review this document: http://www.writing.utoronto.ca/advice/using-sources/how-not-to-plagiarize Please also note that you should not submit the same written material for assignments in different courses, even if the topic is similar.

Students agree that by taking this course all required papers may be subject to submission for textual similarity review to Turnitin.com for the detection of plagiarism. All submitted papers will be included as source documents in the Turnitin.com reference database solely for the purpose of detecting plagiarism of such papers. The terms that apply to the University’s use of the Turnitin.com service are described on the Turnitin.com web site.


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