Reporting Quantitative Research Results: A Guide to Phrasing and Foundational Knowledge

When reporting the results from a quantitative research study, there are some general guidelines to follow. This blog post will address a few types of analyses and describe appropriate ways to describe the results.

APA Style: Basics

APA style dictates reporting the exact p value within the text of a manuscript (unless the p value is less than .001).
Generally, most statistics should be rounded to two decimal places.
Generally, percentages are displayed in parentheses with no decimal places, for example (38%).
Mean and Standard Deviation presented within parentheses, with M = mean and SD = standard deviation, for example (M = 22.43, SD = 2.77).
Statistical symbols should be italicized.

Correlation: Foundations

Correlation analysis allows the determination of the strength of the linear relationship between two variables. A correlation statistic may range from -1 to 1, with “0” indicating no relationship, and -1 or 1 indicating a perfect relationship (this means you could perfectly predict one variable if you knew the value of the other). The sign of the statistic indicates direction, that is a negative sign indicates that as one variable increases in value the other decreases. A positive sign indicates that as one variable increases so does the other.

Correlations can be measured with either the Pearson product-moment correlation coefficient (r) or the Spearman rho correlation coefficient (r_s). The Pearson procedure is a parametric procedure and thus is stronger than Spearman rho, however, r relies on a more stringent set of assumptions then rho and thus may not always fit the particular situation.

Correlation: Phrasing Results

Given: r = .815, df = 16, significance level (p value) = .02

A Pearson correlation coefficient was calculated examining the relationship between "x" and "y". A strong positive correlation was found (r(16) = .814, p = .02) indicating a significant linear relationship between the two variables. <then describe the relationship, i.e., "Older students tend to score higher.">

Given: r = .15, df = 22, significance level (p value) = .07

A Pearson correlation coefficient was calculated examining the relationship between "x" and "y". A weak correlation that was not significant was found (r(22) = .15, p > .05). <then describe the relationship, i.e., "Age is not significantly associated with scores.">

Means Comparison Testing

It is common in quantitative research studies to conduct a “means comparison” analysis. This indicates that a variable has been measured for two or more groups (or a single group being compared to the known value of a population), and the average (that’s the “mean”) has been calculated for each. Then, the means of the groups are compared to see if they are different enough to warrant making a claim of a statistical significant difference. Two common statistical procedures used for conducting this analysis are the “t test” and the ANOVA (Analysis of Variance) procedure. The t test is appropriate when working with two groups, and the ANOVA procedure is used when working with three or more groups.

Types of t Tests

Single sample t test: Compares the mean of a single sample to a known population parameter.
Independent samples t test: Compares the means of two samples. Each sample should be normally distributed and independent of each other.
Paired samples t test: Compares the means of two scores from related samples. For example, comparing a pretest and a posttest score for a group of subjects would require a paired samples t-test.

t Tests: Phrasing Results

Given: Comparing the means of two independent samples.

If results are significant:

An independent t test comparing the mean scores of <group 1> and <group 2> found a significant statistical difference between the means of the two groups (t(df) = ###, p < .05). The mean of the group 1 was significantly higher (M = ###, SD = ###) than the mean of group 2 (M = ###, SD = ###).

If results are not significant:

An independent t test was calculated comparing the mean score of <group 1> to the mean score of <group 2>. No significant difference was found (t(df) = ###, p > .05). The mean of <group 1> (M = ###, SD = ###) was not significantly different from the mean of <group 2> (M = ###, SD = ###).

Given: Comparing the means of two paired samples.

If results are significant:

A paired samples t test was calculated to compare the mean <variable name, e.g., "pretest"> score to the mean <variable name, e.g., "posttest"> score. The mean on the <variable name, e.g., "pretest"> was ### (SD = ###) and the mean on the <variable name, e.g., "posttest"> was ### (SD = ###). A significant <increase/decrease> from <variable name, e.g., "pretest"> to <variable name, e.g., "posttest"> was found (t(df) = ###, p < .05).

If results are not significant:

A paired samples t test was calculated to compare the mean <variable name, e.g., "pretest"> score to the mean <variable name, e.g., "posttest"> score. The mean on the <variable name, e.g., "pretest"> was ### (SD = ###) and the mean on the <variable name, e.g., "posttest"> was ### (SD = ###). No significant difference from <variable name, e.g., "pretest"> to <variable name, e.g., "posttest"> was found (t(df) = ###, p > .05).

By following these guidelines and examples, researchers can effectively report the results of their quantitative studies in a clear and standardized manner.