PR 3 | Reporting Statistics and Common Statistical Tests in APA Format

Writing the Full Word for Numbers

• for numbers under 10

• a number that appears at the start of the sentence

Writing the Exact Numeral for Numbers

• Exact numbers before units of measurement or time

• Mathematical equations

• Percentages and percentiles

• Ratios, decimals, and uncommon fractions

• Scores and points on scales (e.g., 7-point scale)

• Exact amounts of money

Reporting Approximate Figures

• spell numbers under 10

• spell the names of units of measurement

Decimal Places and Leading Zeroes

• use two or three decimal places

• only use leading zeroes for values that can exceed zero

Using N vs n

• N is for the total number of elements in a sample

• n is for the number of elements in each subgroup for the full sample

Which Abbreviations to Define in Reporting Figures

• Abbreviations that do not represent statistics: ANOVA, CI, CFA

• Non-standard abbreviations that appear in tables and figures, even if they are already defined in the text.

Which Abbreviations to Not Define in Reporting Figures

• Statistical symbols or abbreviations: M, SD, F, t, df, p, N, n, OR

• Greek letters: α, β, χ²

Capitalization, Italicization, and Hyphenation

• Statistical terms for tests and values (e.g. t-test, z-test, an p-value) always begin with a lowercase, italicized letter

• Never begin a sentence with lowercase statistical abbreviations.

• Only hyphenate terms if they modify a word.

• Pluralize statistical symbols by adding a non-italicized “s” with no apostrophe.

• Italicize letters when they are statistical symbols or algebraic variables.

What should you not italicize?

• greek letters

• subscripts for statistical symbols

• trigonometric terms

• vectors/matrices (boldface instead)

• Names of effects or variables only when they appear with multiplication sign

When to Use Parentheses in Reporting Figures

Use when reporting

• degrees of freedom

• statistical values when they aren’t already in parentheses

When to Not Use Parentheses in Reporting Figures

Use when reporting

• Confidence interval limits

• Statistics in a text that’s already enclosed within parentheses

Other Guidelines for Reporting Figures

• Always use or include metric units for all measurements

• Only use the words “percent” or “percentage” when numbers aren’t used, or when a percentage appears at the start of a sentence.

• Use symbols for statistical terms when directly referring to a numerical quantity or operator.

• Use words for statistical terms in the main text.

Descriptive Statistics

these statistics summarize and organize characteristics of a data set

Reporting Descriptive Statistics

• Categorical variables can be reported using proportions.

• Quantitative data can be reported using means and standard deviations.

• For a large set of numbers, a table is the most effective presentation format.

• Include sample sizes (overall and for each group) as well as appropriate measures of central tendency and variability for the outcomes in your results section.

Reporting Means and Standard Deviations

• Can be presented in the main text and/or in parentheses.

• Report data in parentheses like this: (M = 111.1 cm, SD = 12.1)

• Don’t need to repeat the units of measurement for statistics relating to the same data.

• Report means and standard deviations for data measured on integer scales to one decimal.

• Report other means, standard deviations, correlations, proportions, and inferential statistics to two decimals.

Inferential Statistics

Makes inferences about the broader population using the sample data

p-value

a posteriori probability that the result that you obtained, or one more extreme, occurred by chance

Alpha Level

the a priori criterion for the probability of falsely rejecting your null hypothesis

Reporting p-values

You may either use the alpha level (e.g. F(1, 16) = 44, p < .05) or report the exact value (e.g. F(1, 16) = 44, p = .03)

Reporting Correlations

Include the following:

• the degrees of freedom in parentheses

• the r value (the correlation coefficient)

• the p value

Example: r(25) = .12, p < .001 or (r = .12, p = .001)

Reporting a Significant Correlation

• Round the p-value to three decimal places.

• Round the value for r to two decimal places.

• Drop the leading 0 for the p-value and r (e.g. use .77, not 0.77)

• The degrees of freedom (df) is calculated as N – 2.

Format for Reporting a Significant Correlation

“A Pearson correlation coefficient was computed to assess the linear relationship between [variable 1] and [variable 2].

“There was a [negative or positive] correlation between the two variables, r(df) = [r value], p = [p-value].”

Reporting Regressions

Include the following:

• the R² value (the coefficient of determination)

• the degrees of freedom in parentheses

• the F-value (the F statistic)

• the p-value

Example: R² = .30, F(1, 25) = .12, p < .001

Reporting t tests

Include the following:

• the degrees of freedom in parentheses

• the t-value (the t statistic)

• the p-value

Example: t(25) = .12, p < .001

Reporting Analysis of Variance (ANOVA)

Include the following:

• the degrees of freedom in parentheses

• the F value (the F statistic)

• the p value

Example: F(1, 25) = .12, p < .001

Reporting a Chi-squared Test

Include the following:

• the degrees of freedom in parentheses

• the chi-square value (the chi-square test statistic)

• the p value

Example: X²(25) = .12, p < .001

Format for Reporting a Chi-squared Test

“A Chi-Square Test of Independence was performed to assess the relationship between [variable 1] and [variable 2].

“There [was or was not] a significant relationship between the two variables, X²(df, N) = [X² value], p = [p-value].”