Descriptive and Inferential Statistics
The division that decides what your numbers are allowed to claim, given here in two lines on a slide with no headings and a bare web address for a source. This page prints the vocabulary in full, together with an audit of which of its terms the week defines and which it only uses.
The two branches, as the source distinguishes them
This is the distinction that governs what a set of numbers is entitled to claim: whether you are describing the cases in front of you, or reaching past them to a population you did not observe. The supplied material makes the distinction in two table rows and does not return to it.
The first of those is broken as printed, and the break is not trivial - it changes how many things descriptive statistics is said to do.
Reading one
- Describes the distribution of, or the relationship among, variables.
- Two functions: distributions, and relationships.
- Requires reading a missing "or" into the line.
Reading two
- Describes the distribution of a relationship.
- One function, and an unclear one.
- Takes the line as printed, at the cost of sense.
The eight-term table in full
The two branches are rows one and two of an eight-row table on a single slide. The other six rows are the week's definitional vocabulary for quantitative work, and they are worth having in one place because the deck never repeats them.
THE EIGHT TERMS, QUOTED VERBATIM AND IN THE ORDER GIVEN
| Term | Definition as given | Note |
|---|---|---|
| Descriptive statistics | "Describes distribution of relationship among variables" | Grammatically broken; two readings |
| Inferential statistics | "Used to estimate how likely it is that a statistical result based on data from a random sample is representative" | No inferential procedure is named anywhere in the week |
| Central tendency | "Most common value for variables measured at a nominal level" | This is the table's definition of the mode - see the central tendency page |
| Base number | "Total number of cases in the distribution" | Defined and never used again in the deck |
| Frequency distribution | "Numerical display of the number of cases corresponding to each value or group of values of a variable" | No frequency distribution is shown anywhere in the week |
| Mean | "The weighted average calculated by totalling the value of all the cases and dividing by the total number" | Label and procedure describe different statistics |
| Median | "The point that divides the distribution in half" | No procedure given |
| Mode | "Most popular value" | Same quantity as the central tendency row |
The table carries no column headings in the source and no number, formula, symbol or worked figure appears anywhere in it. Its stated source is a publisher's companion website for a fourth-edition social research text, cited as a bare address with no author, year or title. The three averages are treated in full at Measures of Central Tendency.
What inference is said to be, and the sampling problem underneath it
The inferential definition is the more serviceable of the two: estimating how likely it is that a result from a random sample is representative. It is also the definition that quietly imports a requirement the subject has already told the reader they probably cannot meet.
The one thing the week says about statistical significance
That is the deck's only definition of statistical significance and the only inferential idea it explains outside the eight-term table. It appears as item four on the second of two slides listing issues in data analysis, alongside fifteen items that carry no explanation at all.
Sixteen issues in data analysis, presented as sixteen labels
Two consecutive slides carry eight items each. There is no lead-in sentence, no framing, no instruction, no numbering and no stated count. As a prompt list it is genuinely useful; as teaching material it is a list of headings for a chapter nobody wrote.
THE SIXTEEN ITEMS, QUOTED VERBATIM AND IN ORDER
| First slide | Second slide |
|---|---|
| Having the necessary skills to analyse | Manner of presenting data |
| Concurrently selecting data collection methods and appropriate analysis | Environmental/contextual issues that may compromise the data |
| Drawing unbiased inference | Data recording method |
| Inappropriate subgroup analysis | Statistically significant - unlikely to have happened by chance |
| Following acceptable norms for disciplines | Breaking up of text material by words, clauses, sentences when analysing qualitative data |
| Determining relationships in the sample | Training for people conducting analyses |
| Clearly defined and objective measures | Reliability and Validity |
| Providing honest and accurate analysis | Depth of data analysis |
Fifteen of the sixteen are bare labels with no definition, explanation or elaboration anywhere in the deck. The exception is the nine-word gloss in the fourth row of the second column.
One item repays more attention than its length suggests. "Concurrently selecting data collection methods and appropriate analysis" is the only design principle in the week that links collection to analysis, and it is the closest thing in the supplied material to an answer to the question the previous week's notes pose and never answer: how will the data be analysed and presented in order to address the key questions? It is one fragment in a list of sixteen. The sequence it belongs to is at The Data Collection and Analysis Sequence.
The vocabulary audit: defined, used undefined, absent
Because the week is the subject's only quantitative content, it is worth knowing exactly how far its vocabulary reaches. The audit below is assembled from the deck as a whole rather than from any one slide.
Named and given a definition
- The eight terms in the table above.
- Data management, screening and cleaning, coding keys, data coding, outlier.
- Statistically significant, effective digits, skewed.
- Univariable, bivariable, multivariable.
- Distribution, bell shaped curve, parameter, variation and variability.
- Twenty-two terms in all, several of them defined two ways.
Used and never defined
- Standard deviation - used four times on one slide.
- Spread - declared a key feature of a distribution, twice.
- Location, shape.
- Statistical assumptions - invoked twice, none named.
- Multivariate technique, internal consistence, messy data.
- Histogram, scatter diagram, line graph, trends, clusters, ratios.
- At least twenty-one terms in all.
The week's own objectives include assessing categorising, coding and analysing. The audit of the supplied material records that the deck performs no analysis and describes no analytical procedure: no statistic is computed anywhere in the week, on any data, at any point. Two of the three objectives are recorded as undelivered and the third as partially delivered - see What This Material Does Not Teach.
Using the distinction without overreaching
The branch you are in decides the verbs you are allowed. Descriptive work says what these cases show; inferential work says what that implies about cases you did not observe, with an explicit statement of how confident you are and why.
What each branch permits, on the material's own definitions
What to carry forward
- The definition of descriptive statistics is broken as printed and admits two readings. Quote it as it stands or use a definition you can cite properly.
- Inference is defined in terms of a random sample the previous week has already said you probably cannot obtain, and no inferential procedure is named anywhere in the week.
- The whole of the week's statement on significance is that a statistically significant result is unlikely to have happened by chance. No level, no test, no threshold.
- Sixteen analysis issues are listed and fifteen are bare labels. Use them as a prompt list; do not cite them as coverage.
- Twenty-two terms defined, at least twenty-one used without definition, and no measure of dispersion anywhere. Know which side of that line your own vocabulary sits on.
Frequently asked questions
What is the difference between descriptive and inferential statistics here?
The supplied table says descriptive statistics "Describes distribution of relationship among variables" - a line that is broken as printed and admits two readings - and that inferential statistics is "Used to estimate how likely it is that a statistical result based on data from a random sample is representative". The working difference is between describing the cases you have and estimating what they imply about cases you do not have, and the material states no procedure for the second.
Which statistical tests does this material teach?
None. No test, no confidence interval, no estimation method and no sampling distribution is named anywhere in the week. It defines inferential statistics and never says how inference is performed, which is why any test you use must be cited to a text outside this material.
What makes a result statistically significant?
The supplied material says only that it is "unlikely to have happened by chance", in nine words inside a list of unexplained issues. No significance level, probability value, alpha or null hypothesis appears anywhere in the week, so the threshold and the test have to come from elsewhere and be cited there.
Can I make inferential claims from a convenience sample?
The material defines inference in terms of a random sample and does not address the convenience case, even though the previous week states that random selection is often not possible and offers no alternative. The defensible course is to describe your cases, state plainly how the sample was obtained, and let the reader judge how far the findings travel.
Are the sixteen issues in data analysis worth using?
As a prompt list, yes - they name real risks, from analyst skill to subgroup analysis to depth of analysis. As teaching, no: fifteen of the sixteen are bare labels with no explanation anywhere in the deck, one of them is a definition rather than an issue, and one concerns qualitative rather than quantitative analysis.
Where is the standard deviation defined in this material?
Nowhere. It is used four times on the slide that states the 68-95-99.7 rule and is defined on no slide - it is not among the five key terms, not among the eight terms in this table, and not on the slide that declares spread one of three key features of a distribution. No measure of dispersion of any kind is defined in the week.
References and source attribution
- Veal, A. J. 2005, Business Research Methods: A Managerial Approach, Longman - the one work with complete bibliographic data cited in the supplied quantitative week.
- Bryman, A. 2016, Social Research Methods, 5th ed., Oxford University Press, Oxford - cited elsewhere in the supplied source; a place to obtain the inferential procedures this week does not supply.
- O'Leary, Z. 2017, The Essential Guide to Doing Your Research Project, 3rd ed., Sage Publications, London.
- Naoum, S. G. 2013, Dissertation Research & Writing for Construction Students, 3rd ed., Routledge.
- The supplied teaching source: the quantitative analysis and presentation slide deck, slides 11, 12 and 13, read with the whole deck's vocabulary. The eight-term table is attributed on the slide to a publisher's companion website for a fourth-edition social research text, cited as a bare address with no author, year or title. The week's study notes are listed in the upload manifest and are not present in the supplied files.
Suggested questions for Ask KEVOS
- Which descriptive statistics should I report for a forty-response project delivery survey?
- Give me cited definitions of descriptive and inferential statistics to use instead of the broken one.
- How should I word findings from a convenience sample so I am not claiming more than I can?
- Explain what a statistical test would need from my data, given this material names none.
- Turn the sixteen analysis issues into a review checklist for my results chapter.