What descriptive statistics should a dissertation report?

Direct answer: Descriptive statistics are numbers, tables and charts that summarise a sample without drawing conclusions about a wider population. Kaliyadan and Kulkarni (2019) describe them as giving a summary of the sample studied without inferences based on probability theory. The mean, the standard deviation and a frequency table are typical examples.

Curtin University Library (n.d.) draws the same line from the student side: descriptive statistics summarise and describe the variables in a sample, as opposed to drawing conclusions about the larger population the sample came from, which is the job of inferential statistics. Curtin University Library (n.d.) illustrates the categorical case with a sample of 80 people: 91.3% were single or married, 7 people chose the option other, and the relative frequency of married people was 0.36. Each of those statements is descriptive, because it reports the sample and claims nothing beyond it. The practical consequence is simple. A descriptive figure is a fact about your data set, so it needs no p value and no confidence claim, but it does need to be accurate, complete and labelled with the sample size it rests on.

Descriptive statistics can describe one variable at a time (univariate analysis) or the relationship between two or more variables, for example through a scatter plot (Kaliyadan & Kulkarni, 2019) or a cross-tabulation of two categorical variables (Curtin University Library, n.d.). In a dissertation, the univariate summaries usually come first, and the bivariate ones appear where they help the reader understand the variables before the main tests.

Direct answer: Many teaching guides group descriptive statistics into measures of frequency, central tendency, dispersion and position. Mishra et al. (2019) name frequency, central tendency and dispersion as the three major types, and list quartiles and percentiles within dispersion. Many courses split those position measures out, which gives the four types students are usually taught.

Mishra et al. (2019), six authors writing in the Annals of Cardiac Anaesthesia, list the contents of each group in detail. Frequency covers counts and percentages, central tendency covers the mean, median and mode, and dispersion covers the variance, standard deviation, standard error, quartiles, interquartile range, percentiles, range and coefficient of variation. They also add a rule that decides which group you use for which variable: frequencies are usually used for categorical data, while the other measures are used for quantitative data. Counts and percentages are easiest to present with a frequency distribution table.

The table is a guide to choice, not a list to fill in for every variable. A variable such as programme of study needs only counts and percentages, while a continuous outcome needs a measure of centre together with a measure of spread. If you are unsure which centre to quote for a variable, mean, median and mode: choosing the right measure explains the choice.

Direct answer: Report the sample size, the characteristics of the participants, and the descriptive summary of every variable used in your main analyses, including any subgroups you compare. The APA reporting standards ask for the number of cases, means, standard deviations and the extent of missing data, so a reader can check the analysis.

The Journal Article Reporting Standards for quantitative research, published in 2018 in American Psychologist by a six-member task force of the APA Publications and Communications Board (Appelbaum et al., 2018), are the most detailed published checklist, and they can serve as a benchmark outside psychology too. For the results, they ask for a description of each primary and secondary outcome for the total sample and for each subgroup, giving the number of cases, the cell means, the standard deviations and other measures that characterise the data (Appelbaum et al., 2018). The same table of standards asks you to report the frequency or percentages of missing data and the major demographic characteristics of the sample, such as age and sex.

In a dissertation this usually translates into four pieces of writing:

• Sample description: the final n, how many cases were excluded and why, and a demographic table in counts and percentages.
• Variable summaries: a mean and standard deviation (or median and interquartile range) for every continuous variable in the analysis, with the n behind each figure.
• Subgroup summaries: the same figures for each group you compare, so the reader can see the size and direction of the difference before reading the test.
• Data screening: missing data, outliers and the shape of each distribution, because these decide which inferential test is appropriate.

A common gap is reporting a test result, such as a t statistic, for a comparison whose group means and standard deviations appear nowhere in the chapter. The descriptive figures are what make that test result interpretable, so they belong in the same chapter and preferably in the same table.

Direct answer: Report the mean and standard deviation when a continuous variable is roughly symmetrical, and the median and interquartile range when it is skewed or has outliers. Mishra et al. (2019) note that the mean is affected by extreme values while the median is not, which is the main reason for the switch.

The choice should follow from your data screening rather than from habit. A histogram or box plot shows the shape of each distribution (Curtin University Library, n.d.), and if one long tail pulls the mean away from where most cases sit, the median gives the reader a more honest picture of the typical value. Income, time on task and counts of events are frequent examples of skewed variables in student projects.

The choice of summary also links to the choice of test. Students often move to a non-parametric test for a skewed variable and then describe the result purely as a difference in medians, but that reading needs care. Hart (2001) warns: "Whereas a t test is a test of population means, the Mann-Whitney test is commonly regarded as a test of population medians. This is not strictly true, and treating it as such can lead to inadequate analysis of data" (p. 391). Reporting the median and interquartile range for each group, alongside the test, lets the reader see differences in spread as well as in the typical value.

Direct answer: A descriptive statistics table lists each variable in rows and the summary measures in columns, usually n, M and SD, with a note giving the total sample size. APA Style keeps a set of sample tables, including a demographic table in counts and percentages and a table of descriptive statistics and correlations.

The American Psychological Association (n.d.) recommends using a standard table format where possible, because readers know where to look for the information, and it offers 8 sample tables. Its sample demographic table reports each characteristic as n and % for every condition and for the full sample, and its correlation table places n, M and SD for each variable before the correlation columns. The APA demographic example describes N = 150 participants, n = 50 in each of three conditions, with 68 women (45%) and 82 men (55%) in the full sample, and puts the mean age of 39.5 years (SD = 10.1) in the table note. Its correlation example reports n, M and SD for 7 variables, with sample sizes from 694 to 3,697, which shows that n can differ between variables. A minimal version for a dissertation might look like this, with illustrative figures only:

Note. N = 212. Four participants did not report weekly study hours. Figures are invented for illustration.

Mishra et al. (2019) show what a full set of descriptive output for one variable looks like in practice. For mean arterial pressure in 15 patients they report a mean of 97.47 with a standard deviation of 11.01, a median of 95, quartiles of 88 and 107, an interquartile range of 19 and a range of 82 to 116. Nobody needs every one of these figures in a results chapter, so the skill lies in choosing the two or three that answer the reader's question. The same paper reports the standard error (2.84), the mode (116) and the coefficient of variation (11.3%) for that variable, and for the categorical variable sex it gives 8 males (53.3%) and 7 females (46.7%) out of 15, which is exactly the counts-and-percentages format a demographic table uses.

Direct answer: Descriptive statistics summarise the sample you have, while inferential statistics use that sample to draw conclusions about a population, with a stated level of uncertainty. Kaliyadan and Kulkarni (2019) draw this line explicitly. A mean is descriptive, while a t test comparing two means and reporting statistical significance is inferential.

Writing in the Indian Dermatology Online Journal in 2019, Kaliyadan and Kulkarni make the point that even when the primary aim of a study is inferential, descriptive statistics are still used to give a general summary. In a dissertation the two therefore work in sequence. The descriptive section tells the reader who took part and what the variables look like, and the inferential section tests the hypotheses. If the descriptive figures are missing, a marker cannot judge whether a significant result is large enough to matter.

Direct answer: No. ANOVA is an inferential test that compares the means of two or more groups (usually three or more, since two groups are often compared with a t test) and reports whether the differences are statistically significant. The group means and standard deviations that ANOVA compares are descriptive statistics, and they should be reported alongside the test.

The confusion is understandable, because ANOVA output in most software prints a descriptive table before the test table. Report that descriptive table, either in your text or as a table with n, M and SD for each group, and then report the F test as part of your inferential results. The same logic applies to a t test, a chi-square test and a correlation: each has descriptive figures underneath it that the reader needs to see.

Direct answer: In SPSS, use Analyze, then Descriptive Statistics, then Frequencies for categorical variables or Descriptives for continuous ones. Mishra et al. (2019) give this route, and the Frequencies dialogue can also produce quartiles, percentiles and a histogram for checking the shape of a distribution.

For group comparisons, the Explore option under the same menu reports the mean, median, standard deviation and interquartile range for each group and draws box plots, which makes it the fastest way to check outliers before choosing a test. Whichever software you use, copy the figures into a properly formatted table rather than pasting raw output, and round consistently.

Most students can produce descriptive statistics themselves once they know which figures their design needs, and building that skill is worth the effort. Help is useful when the data are messy, when you are unsure whether a variable should be summarised with a mean or a median, or when your supervisor has asked for a results chapter that matches a reporting standard. MAAS has supported students since 2015 with a network of more than 100 experts. Through SPSS, R and Python help in your discipline, a MAAS expert works with you on your own data, explains the output and reviews how you report it, so you can defend each figure in your viva or marking. Our guide to thesis statistics help explains which kinds of support a university normally allows and which parts of the analysis must stay your own.