Quiz 16 — Statistical Tests & Research Approaches

Statements 1 and 4 are correct. H₀, the hypothesis of no difference or no relationship, is the one actually tested; the research hypothesis H₁ is supported only indirectly, when H₀ is rejected (IGNOU MPC-006 Block 1 Unit 3, §3.6). The level of significance α is the Type I risk the researcher agrees to accept, and it is fixed before the data are seen, so that the data cannot choose their own criterion. Statement 2 is wrong: failing to reject H₀ means only that the evidence was not strong enough; it does not prove H₀ true, which is why careful texts say 'retained' or 'not rejected' rather than 'accepted'. Statement 3 is wrong: the p-value is the probability of a result at least as extreme as the one obtained, calculated on the assumption that H₀ is true; it is not the probability that H₀ is true. (b) keeps only one of the two correct statements. (c) and (d) let in statement 2 or 3, or both, the two misreadings of a significance test that examiners plant most often.

These are four of Creswell's five approaches to qualitative inquiry (Qualitative Inquiry and Research Design; IGNOU MES-016 Block 2 Unit 8, §8.6). Narrative research studies an individual through the stories of his life; the 1998 edition called it 'biography' (A-3). Phenomenology seeks the essence of the lived experience of a phenomenon among people who have lived it, the researcher bracketing (epoché) his own preconceptions (B-4). Grounded theory generates a theory from the data by constant comparison and theoretical sampling until the categories are saturated (C-1). Ethnography describes and interprets a culture-sharing group through prolonged fieldwork and participant observation (D-2). The fifth approach, the case study, is the in-depth study of a bounded system such as a pupil, a programme or a school. (b) swaps narrative research and phenomenology. (c) swaps phenomenology and ethnography. (d) swaps grounded theory and ethnography.

Statement-I is incorrect and Statement-II is correct. The central limit theorem says that for large random samples the sample means are normally distributed about μ, with a standard deviation equal to the standard error, whatever the shape of the parent population; that independence from the population's shape is the point of the theorem (IGNOU eGyanKosh Unit 2, §2.3.1; Garrett). The figure N > 30 often quoted with it is a convention for 'large enough', not part of the theorem. Statement-II is the definition of the standard error: the standard deviation of the means of repeated equal-size random samples, SE = σ/√N, which is why quadrupling N halves it. (a) and (b) accept Statement-I, which reverses the theorem: if the population is normal the means are normal at every N, but the theorem's claim is that they approach normality even when it is not. (c) accepts Statement-I and rejects Statement-II, the exact reverse of the position.