Research in Education II: Measurement Scales, Quantitative and Qualitative Data Analysis, and Qualitative Research Designs

The second half of Unit 6 covers how collected data is actually analysed: the four measurement scales, descriptive statistics, hypothesis testing and the named statistical techniques, qualitative analysis strategies, and the four qualitative research designs the syllabus lists in detail — grounded theory, narrative research, case study and ethnography — plus mixed methods. The paper asks which scale of measurement a variable is, which statistical test fits a described comparison, which type of error a described mistake is, and which qualitative design a described study follows; every entry carries its defining feature and its year or founder where one is named.

1. Measurement scales and descriptive data analysis

Stanley Stevens's four types of measurement scale
Scale	Property and example
Nominal	Categories with no inherent order — labels only (gender, subject stream, school type); only frequency counts and mode make sense
Ordinal	Categories with a meaningful order but unequal, unknown intervals between them (class rank, letter grades A/B/C); median and percentile make sense, but not meaningful arithmetic averaging
Interval	Equal intervals between points but no true zero (temperature in Celsius, most standardised achievement-test scores); addition and subtraction are meaningful, ratios are not (20°C is not 'twice as hot' as 10°C)
Ratio	Equal intervals with a true, meaningful zero (age, number of correct answers, time taken); all arithmetic operations including ratios are meaningful (a score of 40 is genuinely twice a score of 20)

Descriptive data analysis summarises what a data set shows without inferring beyond it. Measures of central tendency locate the 'typical' value: the mean (arithmetic average, most informative for interval/ratio data but distorted by extreme scores), the median (the middle value when ordered, robust to outliers, works for ordinal data too) and the mode (the most frequent value, the only measure of central tendency meaningful for nominal data). Measures of variability describe spread around that centre: the range (highest minus lowest, crude), the standard deviation and variance (how far scores typically fall from the mean, using every score), and fiduciary limits (confidence intervals — a range within which the true population value is expected to fall with a stated level of confidence, such as 95%). Graphical presentation — histograms, frequency polygons, bar charts, box plots — makes these patterns visible at a glance before any statistical test is run.

🧠 Identifying the scale from the variable

Ask two questions in order: does the order of categories mean anything (if no, nominal), and if yes, is there a true zero and are the intervals equal (if intervals are equal but zero is arbitrary, interval; if both equal intervals and a true zero, ratio; if order matters but intervals are not known to be equal, ordinal). 'Roll number' looks numeric but is nominal (an arbitrary label); 'first, second, third rank' is ordinal; 'IQ score' is conventionally treated as interval (no true zero IQ); 'number of items answered correctly' is ratio (zero means zero, and 20 correct really is twice 10 correct).

2. Testing of hypotheses, and inferential quantitative techniques

Hypothesis testing decides, from sample data, whether to reject the null hypothesis. Two kinds of error are possible: a Type I error rejects a true null hypothesis (concluding there IS an effect when there actually is not — a false positive), and a Type II error fails to reject a false null hypothesis (concluding there is NO effect when there actually is one — a false negative). The level of significance (commonly set at 0.05 or 0.01) is the researcher's chosen probability of committing a Type I error, fixed before the test is run; the power of a statistical test is its probability of correctly rejecting a false null hypothesis (avoiding a Type II error), which rises with larger sample size and a larger true effect size; effect size itself measures the magnitude of a difference or relationship, independent of sample size, and is reported alongside significance because a result can be statistically significant yet practically trivial when the sample is very large.

Parametric and non-parametric techniques
Technique	When used
Correlation (Pearson's r)	Measures the strength and direction of a linear relationship between two interval/ratio variables, from -1 to +1; correlation does not by itself establish causation
t-test	Compares the means of two groups (independent-samples t-test) or two conditions on the same group (paired/dependent-samples t-test) for a statistically significant difference; parametric
z-test	Compares a sample mean to a known population mean, or two large-sample means, when the population standard deviation is known or the sample is large; parametric
ANOVA (analysis of variance)	Compares means across three or more groups simultaneously without inflating Type I error the way multiple t-tests would; parametric
Chi-square test	Tests whether observed frequencies in categorical (nominal) data differ from expected frequencies — goodness-of-fit against an equal-probability hypothesis, or independence against a normal-probability/expected distribution; non-parametric
Mann-Whitney U test	The non-parametric alternative to the independent-samples t-test, comparing two independent groups when data are ordinal or the normality assumption is not met
Kruskal-Wallis H test	The non-parametric alternative to one-way ANOVA, comparing three or more independent groups when data are ordinal or non-normal
Rank correlation (Spearman's rho)	The non-parametric alternative to Pearson's r, measuring the strength of a monotonic (not necessarily linear) relationship between two ranked/ordinal variables

⚠️ Choose the test by the number of groups and the data's scale — not by memory alone

Two groups, interval/ratio data, parametric assumptions met → t-test. Three or more groups, same conditions → ANOVA. Two groups, ordinal data or normality violated → Mann-Whitney U (the non-parametric mirror of the t-test). Three or more groups, ordinal/non-normal → Kruskal-Wallis H (the non-parametric mirror of ANOVA). Categorical/nominal frequency data → chi-square. Strength of association between two continuous variables → Pearson's r; between two ranked/ordinal variables → Spearman's rho. Parametric techniques require assumptions (normal distribution, interval/ratio data, homogeneity of variance) that non-parametric techniques do not — which is exactly the condition named in the syllabus's own phrase 'conditions to be satisfied for using parametric techniques'.

3. Qualitative data analysis: reduction, induction and triangulation

Data reduction and classification — the researcher sifts a large mass of interview transcripts, field notes or documents down to manageable, meaningful units, coding them into categories and themes rather than analysing every word equally.
Analytical induction — the researcher develops a tentative explanation from an initial case, then tests and progressively revises it against each new case examined, until the explanation fits all cases studied — building theory upward from data rather than testing a theory decided in advance.
Constant comparison — a technique (central to grounded theory, below) in which each new piece of data is continuously compared against previously coded data and emerging categories, refining the categories throughout data collection rather than only at the end.
Triangulation — using more than one data source, method, investigator or theory to examine the same phenomenon, so that a finding confirmed across multiple independent angles is more trustworthy than one resting on a single source — the qualitative parallel to a quantitative study's concern with reliability.

💡 Quantitative and qualitative analysis as two different microscopes

Quantitative analysis is like a low-power microscope scanning a thousand slides quickly, counting how many show a particular pattern and testing whether that count could have arisen by chance (hypothesis testing) — it tells you HOW MANY and WHETHER a pattern is real across a large field, but not much about any single slide's texture. Qualitative analysis is a high-power microscope on far fewer slides, revealing depth, context and meaning a low-power scan would miss entirely — data reduction, analytical induction, constant comparison and triangulation are the disciplined ways of making sure that close look is trustworthy rather than merely one researcher's impression.

4. Qualitative research designs: grounded theory, narrative research, case study, ethnography and mixed methods

Four qualitative research designs
Design	Purpose and characteristic steps
Grounded theory (Barney Glaser and Anselm Strauss, 1967)	Generates a new theory directly from systematically collected and analysed data (rather than testing an existing theory), through simultaneous data collection and analysis, open coding, constant comparison, theoretical sampling (choosing the next case based on what theory so far needs) and theoretical saturation (stopping once new data adds nothing new to the emerging categories); strength is grounded, data-close theory; weakness is being time-intensive and hard to replicate exactly
Narrative research	Studies one or a few individuals' lived experience by eliciting and analysing the stories they tell about their lives, preserving chronology, voice and meaning-making rather than fragmenting the account into coded categories; steps typically include identifying a storyteller, collecting the story through extended interview, restorying it chronologically, and collaborating with the participant to validate the account; strength is rich, holistic, first-person meaning; weakness is limited generalisability from one or few cases
Case study	An in-depth, bounded examination of one case (a single school, classroom, teacher or programme) using multiple data sources (interviews, observation, documents) to understand it in its real-life context; types include intrinsic (the case itself is of interest), instrumental (the case illuminates a broader issue) and collective/multiple-case (several cases compared); steps include defining the case's boundaries, selecting data-collection methods, analysing within and (if multiple) across cases; strength is contextual depth; weakness is limited generalisability and researcher-subjectivity risk
Ethnography	Studies an intact cultural group (a classroom, a school, a community) over an extended period through sustained participant observation, seeking to describe and interpret shared patterns of behaviour, language and belief from an insider's perspective; underlying assumption is that meaning is best understood through prolonged immersion, not brief external measurement; steps include gaining access, extended fieldwork with participant observation and field notes, and writing a thick, interpretive ethnographic account; strength is deep cultural insight; weakness is time cost and risk of the researcher's own presence altering what is observed

Mixed-method designs deliberately combine quantitative and qualitative approaches within one study, on the premise that the two together answer a research question more fully than either alone. Triangulation designs collect both types of data around the same time and merge them to cross-validate findings (does the survey's numbers agree with the interviews' themes); explanatory sequential designs collect quantitative data first and use a qualitative follow-up to explain an unexpected quantitative result; exploratory sequential designs collect qualitative data first to identify variables or build an instrument, then test it quantitatively on a larger sample. Steps in any mixed-method study include deciding the priority and timing of each strand, collecting and analysing each, and integrating findings at the level of design, methods or interpretation; strength is a fuller, more validated picture than a single-method study; weakness is the greater time, expertise and resource cost of doing both well.

🧠 Which design the stem is describing

'A new theory built directly from coded interview data, sampling more cases until nothing new emerges' → grounded theory (Glaser and Strauss, 1967, theoretical saturation). 'One teacher's life story, told chronologically in her own words' → narrative research. 'A deep, multi-source study of one struggling school in its real context' → case study. 'A researcher lives inside a school community for a year to understand its unwritten norms' → ethnography. 'Survey data first, then interviews to explain a surprising survey finding' → explanatory sequential mixed methods.

Key takeaways

Stevens's four measurement scales — nominal (labels), ordinal (ranked, unequal intervals), interval (equal intervals, no true zero) and ratio (equal intervals, true zero) — decide which statistics are legitimate to compute.
Hypothesis testing risks Type I (false positive) and Type II (false negative) errors, controlled by the level of significance and a test's power; parametric tests (t-test, z-test, ANOVA, Pearson's r) assume normal, interval/ratio data, while non-parametric equivalents (Mann-Whitney U, Kruskal-Wallis H, Spearman's rho, chi-square) do not.
Qualitative analysis uses data reduction and classification, analytical induction, constant comparison and triangulation to make close interpretive reading trustworthy.
Four qualitative designs — grounded theory (Glaser and Strauss, 1967, theory from data), narrative research (one life story, chronological), case study (bounded, multi-source depth) and ethnography (extended immersion in a culture) — each answer a different kind of question; mixed-method designs (triangulation, explanatory sequential, exploratory sequential) deliberately combine quantitative and qualitative strands.

Practice questions (8)

Attempt each one before opening the answer. Every explanation names the tempting wrong option as well as the right one, because that is where marks are lost.

A variable such as 'letter grade' (A, B, C, D), where the order is meaningful but the intervals between grades are not known to be equal, is measured on which scale?
1. Nominal
2. Ordinal
3. Interval
4. Ratio
Show answer
Answer: B — Ordinal
Ordinal scales have meaningful order but unequal or unknown intervals. Nominal has no order at all; interval has equal intervals but no true zero; ratio has equal intervals and a true zero.
Rejecting a true null hypothesis — concluding an effect exists when it actually does not — is called:
1. Type I error
2. Type II error
3. Sampling error
4. Standard error
Show answer
Answer: A — Type I error
A Type I error is a false positive — rejecting a true null. A Type II error is a false negative, failing to reject a false null. Sampling error and standard error describe the natural variability of sample estimates, not this specific decision error.
To compare the means of three or more independent groups simultaneously, without inflating the risk of a Type I error the way repeated t-tests would, a researcher should use:
1. Pearson's correlation
2. ANOVA
3. Chi-square test
4. Mann-Whitney U test
Show answer
Answer: B — ANOVA
ANOVA compares three or more group means at once. Pearson's correlation measures relationship strength between two continuous variables, not group-mean comparison; chi-square tests categorical frequency data; Mann-Whitney U compares only two groups and is non-parametric.
When comparing two independent groups on data that are ordinal or where the assumption of normal distribution is not met, the appropriate non-parametric test is:
1. Independent-samples t-test
2. Mann-Whitney U test
3. Kruskal-Wallis H test
4. Pearson's r
Show answer
Answer: B — Mann-Whitney U test
Mann-Whitney U is the non-parametric alternative to the independent-samples t-test, for exactly two groups. Kruskal-Wallis H is its equivalent for three or more groups; Pearson's r measures correlation, not group comparison; the t-test itself is parametric and requires the assumptions this question says are not met.
Barney Glaser and Anselm Strauss's 1967 qualitative design, which generates a new theory directly from systematically collected data through constant comparison and theoretical sampling until saturation, is:
1. Narrative research
2. Case study
3. Grounded theory
4. Ethnography
Show answer
Answer: C — Grounded theory
Grounded theory (Glaser and Strauss, 1967) generates theory from data via constant comparison and theoretical sampling to saturation. Narrative research studies one life story; case study is a bounded, multi-source examination of one unit; ethnography is extended immersion in a cultural group.
A researcher lives within a school community for a year, engaging in sustained participant observation to describe its unwritten norms and shared meanings from an insider's perspective. This design is:
1. Ethnography
2. Narrative research
3. Grounded theory
4. Explanatory sequential mixed methods
Show answer
Answer: A — Ethnography
Ethnography studies an intact cultural group through extended immersion and participant observation. Narrative research focuses on one individual's story; grounded theory aims to generate a new explanatory theory rather than a cultural description; explanatory sequential mixed methods combines quantitative-first and qualitative-follow-up phases, unrelated here.
Using interview data, classroom observation and school documents together to cross-validate a single finding about one struggling school is an example of:
1. Analytical induction
2. Triangulation
3. Theoretical saturation
4. Chi-square testing
Show answer
Answer: B — Triangulation
Triangulation uses multiple data sources or methods to examine the same phenomenon and cross-validate a finding. Analytical induction progressively revises an explanation across cases; theoretical saturation is the stopping point in grounded theory sampling; chi-square testing is a quantitative technique for categorical data, unrelated to this qualitative cross-validation.
A study first collects a large-scale quantitative survey, then conducts follow-up interviews specifically to explain an unexpected pattern found in the survey results. This mixed-method design is:
1. Triangulation design
2. Explanatory sequential design
3. Exploratory sequential design
4. Grounded theory design
Show answer
Answer: B — Explanatory sequential design
Explanatory sequential design collects quantitative data first and uses qualitative follow-up to explain the results. Triangulation collects both types around the same time; exploratory sequential design collects qualitative data first to build an instrument, then tests it quantitatively; grounded theory is a purely qualitative design, not a mixed-method one.