Research and statistics on the NCE: the numbers you need and the ones you do not.
Scales of measurement, the normal curve, which test to use when, and threats to validity. Nothing more than that is asked.
By Dr. Andrew Wichterman · September 15, 2026 · 7 min read
The research and program evaluation area frightens people out of proportion to its difficulty. The NCE does not ask you to compute anything beyond reading a normal curve. It asks you to recognize designs, name the right statistic, and spot a threat to validity. That is a vocabulary task, and vocabulary can be learned.
Scales of measurement
Nominal (categories), ordinal (ranks), interval (equal intervals, no true zero, like IQ or temperature), ratio (true zero, like height or count). The scale determines the statistic: nominal data take a chi-square; interval and ratio data can take a t-test or ANOVA.
The normal curve, once and for all
About 68 percent of scores fall within one standard deviation of the mean, 95 percent within two, and 99.7 percent within three. A z-score is the number of standard deviations from the mean. T-scores have a mean of 50 and standard deviation of 10. Deviation IQ has a mean of 100 and standard deviation of 15. Stanines run 1 to 9 with a mean of 5. A percentile is the percent of scores at or below. In a positively skewed distribution the tail points right and the mean is pulled above the median; negatively skewed is the reverse. Mode is the peak.
Which test
- Two groups, interval data: t-test (independent or paired).
- Three or more groups: ANOVA. Two independent variables: factorial ANOVA. A covariate to control: ANCOVA. Several dependent variables: MANOVA.
- Relationship between two variables: correlation (Pearson r for interval; Spearman for ranks). Correlation is not causation, and r ranges from -1 to +1.
- Predicting one variable from others: regression.
- Frequencies or categories: chi-square.
- Nonparametric alternatives exist when assumptions fail: Mann-Whitney, Wilcoxon, Kruskal-Wallis.
Hypotheses and errors
The null hypothesis says there is no difference. A Type I error rejects a true null (a false positive); alpha, usually .05, is its probability. A Type II error fails to reject a false null; beta. Power is 1 minus beta, and it rises with sample size and effect size. Statistical significance is not the same as practical significance; effect size addresses the latter.
Designs and validity
True experiments randomly assign participants; quasi-experiments do not. Internal validity asks whether the treatment caused the effect; threats include history, maturation, testing, instrumentation, regression to the mean, selection, mortality (attrition) and the Hawthorne effect. External validity asks whether the results generalize. Single-subject designs use notation like ABAB. Qualitative research uses terms like trustworthiness, triangulation and saturation instead of reliability and validity.
Program evaluation
Formative evaluation happens during a program to improve it; summative evaluation judges it at the end. Needs assessment comes before either. Know that evaluation-based accountability is expected of counselors, and that this is where the exam connects research to practice.
Practice this. The flashcards and practice tests on this site are sorted by content area, so you can drill this one until it holds.
No calculation, only recognition. Make the vocabulary automatic and this becomes one of the easier areas on the exam.