In academic writing, using literal word choices whenever possible is of the utmost importance.  As the writer, you want the explanation of your research to be shown as exact and true in regard to your findings, and although some expressions and words may popularly and colloquially mean one thing, their true definitions may mean another.  When editing dissertation content, be on the lookout for the following 5 words to make your intention of meaning as clear as possible.

–since/because

The word since denotes the passage of time—something occurred in the period since something else occurred.  The word because denotes cause and effect—the result of X is because of Y.

Incorrect: The researchers included only participants in their area since the experiment required a small sample size.

Correct: The researchers included only participants in their area because the experiment required a small sample size.

 

–while/although

In its literal sense, while should be used to refer to X occurring while Y occurs. However, writers regularly use it in the place of although, though, or even though depending on your intent.

Incorrect: While the limitations are reasonable, the research is practical.

Correct: Although the limitations are reasonable, the research is practical.

 

–regard/regards

Regard, typically preceded by the preposition in, should be used to denote X concerning Y. Regards is typically a valedictory, or the closing section of a letter, such as sincerely.

Incorrect: In regards to past findings, the researcher came to similar conclusions.

Correct: In regard to past findings, the researcher came to similar conclusions.

 

–affect/effect

When it comes to the difference between affect and effect, most writers know there is a difference—it’s just a matter of remembering what that difference is that trips them up. The difference can be subtle at times, but in its simplest form, affect is a verb and effect is a noun (except in rare cases where effect means to create a result; you can usually ignore this case). A trick you can use to remind yourself is: “The effect is the result of affect.” Also, if an article (a, an, the) precedes affect/effect, you should most often expect the correct usage there to be effect (an effect, the effect).  This will be helpful when editing dissertation content.

 Incorrect: The affect of this managerial style on employees is well documented.

 Correct: The effect of this managerial style on employees is well documented.

 

–impact/influence, effect, affect

When editing dissertations, the misuse (and overuse) of the word impact is undoubtedly the word-choice error I see the most as a copy editor. In academic writing, impact should be reserved to mean a literal collision. Depending on the construction of the sentence, influence, affect, or effect can usually be used in its place to convey a precise connotation.

Incorrect: Roberts et al. (2013) described the impact of socioeconomic status on youths in inner-city Tampa.

Correct: Roberts et al. (2013) described the effect of socioeconomic status on youths in inner-city Tampa.

Train yourself to think critically about the words you are writing. If it seems a word could have more than one meaning, take the time to look it up, and remember that using literal word choices is a key to academic writing that increases the reliability and trustworthiness of your research. To quickly scan for and correct word-choice issues when editing dissertation content, you can use ctrl+f on the Windows platform or command+f on the Apple platform to find and replace.

The resulting margin of error is what we will add or subtract from our guess to create our confidence interval.  What is the critical value?  The critical value is a cut-off value that tells us how far from the sample mean we can vary and remain confident—usually one standard deviation from the mean.  We usually look it up in a z table or t table, although we can also compute it.  For our example, for a large sample size of 2,500 and a 95% level of confidence, our critical value would be ±1.96.

What do we mean by standard error?  Well, standard error is to a sample what standard deviation is to a population.  To compute it, per Smith (2009), we estimate the population proportion (a number between 0 and 1).  Our statistic is 75%, so as a proportion that would be 75 / 100 = .75.  We might call this p but we don’t know p for sure, so we use p̂ (pronounced p-hat).  Now we’re ready to calculate standard error using our statistic (.75).  The formula is just:

             SE = sqrt (p̂ (1 – p̂) / n)

Where:  SE stands for standard error, p̂ is our estimated population proportion, and n is our sample size.  Substituting our values we get:

SE = sqrt (.75 (1 – .75) / 2500) = .0087

Now let’s use our complete formula (margin of error = critical value * standard error)

            E = 1.96 * sqrt (p̂ (1 – p̂) / n) = (1.96 * .0087) = .017

To get our interval, all we need to do is subtract from or add to our guess (while rounding to 2 decimal places):

= (p̂ – (1.96 * SE),  p̂ + (1.96 * SE) ) = (.75 – .017),  (.75 + .017) = (.73,  .77)

So, our margin of error, at a 95% confidence level, would be M = 75,  95% CI (based on Smith, 2009; Sullivan, 2006).


References

Smith, R. L. (2009). Point and interval estimates. Available at http://www.unc.edu/~rls/s151-09/class19.pdf

Statistics Solutions. (2013a). Margin of error. Available at https://www.statisticssolutions.com/margin-of-error/

Statistics Solutions. (2013b). Why do we have margin of error in statistics? Available at https://www.statisticssolutions.com/why-do-we-have-margin-of-error-in-statistics/

Sullivan, L. M. (2006). Estimation from samples. Circulation, 114(5), 445-449. doi:10.1161/​CIRCULATIONAHA.105.600189

U.S. Department of Education. Institute of Education Sciences, National Center for Education Statistics. (2012). Table 223: Total fall enrollment in degree-granting institutions, by control and level of institution: 1970 through 2011. In U.S. Department of Education, National Center for Education Statistics (Ed.), Digest of Education Statistics (2012 ed.). Retrieved from http://nces.ed.gov/programs/digest/d12/tables/dt12_223.asp

It is difficult to understate the value of the correlation coefficient to descriptive statistics.  Use of the term “correlation coefficient” is almost always a short-hand phrase for the Pearson product-moment correlation coefficient.  There are several other well known correlation coefficients such as Spearman’s rho rank correlation coefficient but it usually a safe assumption the correlation being referenced is a Pearson correlation coefficient since it is the most commonly used measure of bivariate association.  It is appropriate to use the Pearson correlation coefficient when the two variables of interest are scored using interval or ratio measures while the associations of ordinal or nominal variables should be compared using alternative methods.  However, all statistical packages will calculate the Pearson correlation coefficient for ordinal or nominal variables (assuming the categories are given numerical values) but the justification for using this statistic relies on assumptions which are either untested or questionable; the resulting value of the statistic may not make real world sense.

Before calculating a Pearson correlation coefficient it is essential and good practice to first visually inspect the relationship between two variables by means of a scatterplot graph.  A bivariate scatterplot allows the researcher to gain better sense of the overall variability of the data but also visualize any systematic relationships the correlation coefficient would be describing such as a general positive or negative linear trend.  A non-linear association e.g., a curvilinear relationship may be present but this would not be described well by the Pearson correlation coefficient.  Also, oftentimes extreme values are readily apparent and may represent outliers or data errors to which Pearson’s correlation coefficient is sensitive.  If the distribution of either of the variables is skewed or contains outliers then transforming the data or using an alternative measure of association may be warranted.  Ignorance regarding the potential presence of these factors may obscure the sample’s true correlation coefficient and ultimately mislead the researcher when making inferences about the target population’s true Pearson correlation coefficient.

The use of Greek letters in statistics is common and the Greek letter rho, symbolized by ρ, represents the Pearson correlation coefficient for a population.  A researcher wants to know rho but in practice it is typically impossible to collect a census (sample the entire target population) so instead a smaller sample is taken from the target population and the sample’s Pearson correlation coefficient is calculated and labeled with a lower case r.  The value of the correlation coefficient always ranges from negative one to positive one.  These values describe perfect negative and positive linear relationships, respectively, while a coefficient value equal to zero indicates the two variables have no linear relationship. Regardless of the calculated value of the Pearson correlation coefficient the researcher is not able to infer causation.  The confusion may be a result of the language and notation used when discussing the correlation of two variables.  For example, it may be said knowing the values of one variable allows the researcher to “predict” the values of the other variable as though one caused the other but this type of prediction is not analogous to causation.  Also, the labeling two variables as X and Y may be mistakenly interpreted as a dependent, independent variable relationship that is customary with regression but for the purposes of calculating correlation coefficients it does not matter which variable is labeled X or Y.

Writing the literature review for your dissertation can be a daunting process. Students are told, “You should find everything published about your topic and review it.”  That can be overwhelming, as your dissertation may be centered on a broad or thoroughly researched topic where there is no shortage of literature.  There are things you can do to make this process much easier – here are five:

1.  Do your research!  This sounds simple, I know.  However, it is imperative that you include the necessary background research to show the reader why this variable is of interest to you and, more importantly, why it is important enough to be studied in this project.

2. Cite primary sources.  When doing your research, you want to find the primary (or original) source.  It can be extremely frustrating and confusing as a reader to read a sentence that says, “Roberts and Johnson (2004, as cited in Lee, 2009) said …” In this example, it seems that the author was too lazy to find the original source.  If your sentence was “Roberts and Johnson (1912, as cited in Lee, 2009),” it would be a bit more forgiving due to the 1912 date.  However, if Lee could find the original source for his 2009 work, why can’t you?  A literature review is a demonstration of tenacity and willingness to go the extra mile for your research study. You are trying to prove that these topics are beneficial to the entire field, should be studied now, and are worthy of consuming the next 12-18 months of your life.

3.  Organize your proposal! Try using a Table of Contents and section headings.  You will have to write a Table of Contents eventually, so you may find it to be easier to start it at the beginning.  It is perfectly okay for you to use headings in your paper, per APA requirements.  Using headings will allow you to see where there are large gaps in your work and to ensure each variable is discussed.

4.  Begin using APA format to cite your references correctly in the body of your literature review immediately.  It is VERY time consuming to try to include these citations after you have finished writing.  When you finish a proposal draft, you will be itching to send it immediately to your Chair, not sit down with your APA manual to determine correct reference format.  Instead, keep your APA manual beside your computer and cite your reference correctly the first time.  Once you correctly type a few of these, you will get the hang of it and can continue without difficulty.

5.  Proofread! Let me say that again – PROOFREAD!  Please do not send your proposal to your Chair for review without proofreading your paper.  Yes, you will miss some small mistakes because you are very close to the work, and you have undoubtedly read your literature review 15 times already.  However, your Chair should not find sentences repeated twice in a row, words in the middle of a sentence that do not belong there, or spelling errors.  If you are concerned, visit the Writing Center on campus for their assistance.  The less your Chair has to edit means the faster she can read your proposal and the more progress you make in a shorter amount of time.

-To set off nonrestrictive clauses: Nonrestrictive clauses are extra information in a sentence.  If removed, the sentence would still make sense.

Incorrect:       His mother who was a great musician taught him to play piano.

Correct:          His mother, who was a great musician, taught him to play piano.

-Between coordinate adjectives: Coordinate adjectives are descriptors that you can reorder while maintaining their meaning. In such cases, a comma should separate these adjectives.

Incorrect:       The silly exuberant clown entertained the crowd.

Correct:          The silly, exuberant clown entertained the crowd.

Quick tip: When you edit dissertations and are unsure whether to place a comma between adjectives, try mentally replacing the comma with and—if it makes sense, you should likely include the comma.

-Between an author’s name and the year inside parenthetical citations:

Incorrect:       (Brown 2013).

Correct:          (Brown, 2013).

-After using et al. in parenthetical citations: When editing dissertations, this is an often-overlooked placement for a comma, but when you think about it, this rule follows logically from the one just covered.

Incorrect:       (Smith et al. 2013).

Correct:          (Smith et al., 2013).

This rule applies when editing a dissertation but only for citations. Standard rules apply to et al. when writing out a sentence.

Incorrect:       Smith et al. (2013), noted multiple instances of this phenomenon.

Correct:          Smith et al. (2013) noted multiple instances of this phenomenon.

Correct:          According to Smith et al. (2013), multiple instances of this phenomenon occurred.

Now let’s use a real-world example.  Say we need to know how many psychologists in North America favor nature over nurture as the explanation for individual behavioral differences (a popular debate and not a bad idea for a survey).  We can’t survey everyone, so we use a sample population representative of the whole population and survey that sample. Mostly opinion polls are a common and useful way to gather data. 

We survey a random sample of 300 psychologists, and we find that naturists represent 55% of the sample population, with nurturists trailing at 45%.  That’s great, but we did not survey every psychologist in North America, so the number we didn’t survey are going to represent our margin of error as some range of possible correct percentages either side of the real percentage.  If our margin of error is 6%, naturists may actually be somewhere between 49% and 61% (55 +- 6) and nurturists may be somewhere between 39% and 51% (45 +- 6).  As you can see, the poll winner can swing either way, depending on our margin of error.

The key is the ratio between our sample size and the full population.  With a population of 100,000 and a sample size of 300, the margin of error is approximately 6% at a 95% confidence level. To achieve greater accuracy, such as a 3% margin of error, surveying at least 1,000 participants (preferably 1,500) is recommended. Notably, for populations of 10,000 or more, a sample size of 1,000 often provides comparable accuracy to much larger samples (American Association for Public Opinion Research, 2007).

References

American Association for Public Opinion Research. (2007). Margin of sampling error. Available at http://www.aapor.org/

Nolan, S. A., & Heinzen, T. E. (2011). Essentials of statistics for the behavioral sciences. New York: Worth Publishers.  View

Weisstein, E. W. (2013). Error. Available at http://mathworld.wolfram.com/Error.html

Equating Non-Equivalent Groups:

Another, though controversial, use of ANCOVA is to correct for initial group differences that exists on the dependent variable.  Using this method, the researcher adjusts means on the dependent variable in an effort to correct for individual differences.  This allows the researcher to adjust the means on the dependent variable to what they would have been should all of the participants scored equally on the covariate.  Researchers commonly use this approach in non-experimental situations when they have not implemented random assignment. However, differences may have also have been due to other variables not measured or included as covariates.

• Adjustment of Means of Multiple Dependent Variables: This application is similar to the ones outlined above, but when the researcher is measuring multiple dependent variables, such as a Multivariate ANOVA (MANOVA).  This application typically occurs when the researcher wants to assess the contribution of the various dependent variables by removing their effects from the analyses.  This procedure is called a stepdown analysis.

The researcher can go about interpreting main effects and interactions as they typically would.  The difference is that researchers first estimate the regression of the covariate on the dependent variable before partitioning the variance in scores into between-group and within-group. differences.; however, the error term is adjusted from the regression line derived from the covariate on the DV vs. running through the means in ANOVA designs.

References:

Tabachnick, B., & Fidell, L. (2013). Using multivariate statistics (6th ed.)Upper Saddle

River, NJ: Pearson.

So what have we done and where are we going?  What we’ve done is honed several hundred web pages to assist students with quantitative and qualitative research methods, we’ve developed a dissertation template to show students the necessary bones of the research, data analysis plan templates, sample size write-ups, and the big news… the results chapter software application, Intellectus Statistics.

This online application takes the legwork out of purchasing and conducting analyses in SPSS, figuring out what statistics and assumptions are relevant, interpreting the analyses, and writing the results in APA 6^th edition.  (Click here for a free trial)

Close Guess.  The margin of error is not just a good guess.  The margin of error is a close guess about the confidence interval at a certain level of probability.  Your confidence interval is a range of possible values, typically some deviation from the mean; for example, if your guess is within 2% above or below the mean that would be a margin of error of 2%.  Let’s say your mean is 42, then your confidence interval would be from 40 (42 – 2) to 44 (42 + 2).  However, you also need to convey the likelihood of this interval over a number of trials, which is usually aimed at 95% of the time. This 95% is your level of confidence.

Explicit Guess.  Now that we know our margin of error is a confidence interval at some level of probability, how do we express it? Your margin of error is a plus-or-minus value above and below the ideal, and a percentage figure.  APA style has a nice succinct format to express it.  Using our example, a margin of error of 2% at a confidence level of 95% would be written: M = 42, 95% CI . Typically we would list the standard deviation as well, but for our purposes we will just list our guess as the mean (average) of our sample population (42), the confidence level as a percent (95%), and the margin of error we are allowing (+-2%), where the first figure in brackets (40) is the lower limit of our interval, and the second figure in brackets (44) is the upper limit.  For more specifics if you are using the APA format, please see chapter 4 “The Mechanics of Style” in the APA style manual (American Psychological Association, 2010).

Summary.  What is the margin of error in statistics?  It’s about guesses, confidence, and probability, and it’s about good guesses, close guesses, and explicit guesses.  Margin of error allows us to feel confident a certain percentage of the time, within a range above or below the ideal guess, represented by a margin we believe is least in error.

References

American Psychological Association. (2010). Publication manual of the American Psychological Association (6th ed., Kindle version). Washington, DC: Author.

Nolan, S. A., & Heinzen, T. E. (2011). Essentials of statistics for the behavioral sciences. New York: Worth Publishers.