Appendix X — SPSS Tutorial: Clinical Measures

This tutorial walks through the clinical statistics covered in Section 20.1–Section 20.9 using SPSS and the core_session.sav dataset. Each section maps directly to the corresponding chapter section.

TipBefore you start

Open core_session.sav in SPSS. You will also need a wide-format version of the data for some analyses (one row per participant, with separate columns for pre- and post-test scores). See the Data Restructuring note in the Wilcoxon SPSS tutorial (Appendix: SPSS Tutorial: Nonparametric Tests) for instructions on pivoting from long to wide format.

Key variables used in this tutorial:

Variable Description
function_0_100 Self-reported functional ability (0–100)
strength_kg Post-test muscular strength (kg)
group 1 = Control, 2 = Training
time 1 = Pre, 2 = Mid, 3 = Post

X.1 Part A: Calculating MCID and Classifying Responders

The MCID is not computed directly in SPSS — it is derived from descriptive statistics and then applied as a classification rule.

Step 1: Compute the baseline standard deviation

Analyze → Descriptive Statistics → Explore…

  • Move function_0_100 to the Dependent List.
  • Move group to the Factor List to get group-specific statistics.
  • Under Statistics, ensure Descriptives is checked.
  • Click OK.

Record Std. Deviation for the pre-test observations. Filter to pre-test first:

Data → Select Cases → If condition is satisfied → enter time = 1 → Continue → OK

Re-run the Explore procedure. Record SD_pre for the full sample (or by group, depending on your research question).

Distribution-based MCID = 0.5 × SD_pre. For function_0_100 in the core_session dataset, SD_pre = 12.2, so MCID = 6.1 points.

Step 2: Compute individual change scores

You need pre- and post-test scores in separate columns (wide format). Using:

Transform → Compute Variable…

Create a new variable:

change_function = function_post - function_pre

Step 3: Classify responders

Transform → Recode into Different Variables…

  • Input: change_function
  • Output: responder (new variable)
  • Click Old and New Values…:
    • Range: lowest through 6.09 → New Value: 0 (non-responder)
    • Range: 6.1 through highest → New Value: 1 (responder)
  • Click Continue → OK

Step 4: Compute responder rates by group

Analyze → Descriptive Statistics → Crosstabs…

  • Row: responder
  • Column: group
  • Click Cells…, check Row and Column percentages → Continue → OK

The output will show the number and percentage of responders and non-responders in each group. For the core_session training group: 12/25 = 48%; control group: 10/30 = 33%.

X.2 Part B: Number Needed to Treat (NNT)

SPSS does not compute NNT directly, but the required quantities come from the crosstabulation above.

Step 1: Record event rates from the crosstabulation

From the Crosstabs output (Part A, Step 4):

  • EER = proportion of responders in the training group
  • CER = proportion of responders in the control group

Step 2: Compute ARR and NNT

Transform → Compute Variable…

Create the following computed variables (entering the numeric values from the output):

ARR = EER - CER
NNT = 1 / ARR

Alternatively, use the Statistical Calculators appendix to enter EER and CER and obtain ARR, NNT, RR, and RRR with 95% CIs in one step.

For the core_session dataset: EER = .480, CER = .333, ARR = .147, NNT ≈ 7, RR = 1.44, RRR = 44%.

Step 3: Confidence interval for ARR

The 95% CI for ARR uses the standard error of the difference between two proportions:

\[SE_{ARR} = \sqrt{\frac{EER(1-EER)}{n_{tr}} + \frac{CER(1-CER)}{n_{ctrl}}}\]

\[CI_{ARR} = ARR \pm 1.96 \times SE_{ARR}\]

Compute in SPSS via:

Transform → Compute Variable…

SE_ARR = SQRT((EER*(1-EER)/n_tr) + (CER*(1-CER)/n_ctrl))
CI_low  = ARR - 1.96 * SE_ARR
CI_high = ARR + 1.96 * SE_ARR
NNT_low  = 1 / CI_high
NNT_high = 1 / CI_low

Replace EER, CER, n_tr, n_ctrl with the numeric values from your output. For the core_session data: ARR = .147, 95% CI [−.042, .336], NNT 95% CI [3.0, ∞]. The CI crosses zero, confirming the modest and uncertain treatment advantage at this sample size.

NoteWhen the NNT confidence interval spans infinity

If the 95% CI for ARR includes zero, the reciprocal CI for NNT will include ∞ (and possibly negative values, which are interpreted as Number Needed to Harm). This is not an error — it reflects genuine uncertainty about the direction of the treatment effect. Report “NNT = 6.8, 95% CI [3.0, ∞]” and note that the result did not reach statistical significance for the responder comparison (even though the group ANCOVA was significant, because the responder analysis is lower-powered).

X.3 Part C: Sensitivity, Specificity, PPV, NPV, and Likelihood Ratios

Step 1: Create a binary classifier variable

Using post-test strength as the classifier, first filter to post-test data (time = 3), then create a binary test variable:

Transform → Recode into Different Variables…

  • Input: strength_kg
  • Output: test_positive
  • Old and New Values:
    • Range: lowest through 79.79 → New Value: 0 (test negative)
    • Range: 79.8 through highest → New Value: 1 (test positive)

Step 2: Cross-tabulate against the true condition

The “true condition” is group membership (group): training = condition present (1), control = condition absent (0).

Analyze → Descriptive Statistics → Crosstabs…

  • Row: test_positive
  • Column: group
  • Click Statistics…, check Chi-square and Risk → Continue
  • Click Cells…, check Observed counts and Row percentages → Continue → OK

Step 3: Read the output

From the Crosstabulation table, identify:

Cell Count
test_positive = 1, group = Training TP
test_positive = 1, group = Control FP
test_positive = 0, group = Training FN
test_positive = 0, group = Control TN

The Risk Estimate table from SPSS reports Odds Ratio and Risk Ratios — these are not sensitivity/specificity directly. Compute sensitivity and specificity manually:

Transform → Compute Variable…

Sensitivity = TP / (TP + FN)
Specificity = TN / (TN + FP)
PPV         = TP / (TP + FP)
NPV         = TN / (TN + FN)
PLR         = Sensitivity / (1 - Specificity)
NLR         = (1 - Sensitivity) / Specificity

Replace TP, FP, FN, TN with the numeric counts from your crosstabulation table.

For the core_session post-test strength example (cut = 79.8 kg): TP = 20, FP = 10, FN = 10, TN = 20. Sensitivity = .667, Specificity = .667, PPV = .667, NPV = .667, +LR = 2.00, −LR = 0.50.

TipUsing SPSS ROC output for sensitivity and specificity

If you run a ROC analysis (Part D below), SPSS will produce a coordinate points table listing sensitivity and 1 − specificity at every possible threshold. You can use this table to find the cut-point that maximises sensitivity + specificity (Youden’s Index) rather than specifying the cut-point in advance.

X.4 Part D: ROC Curves and AUC

SPSS has a dedicated ROC curve procedure.

Step 1: Filter to post-test data

Data → Select Cases → If condition is satisfied → enter time = 3 → Continue → OK

Step 2: Open the ROC dialog

Analyze → Classify → ROC Curve…

Step 3: Assign variables

  • Test Variable: strength_kg (the continuous classifier)
  • State Variable: group (the binary true condition)
  • Value of State Variable: 2 (the code for the training group — the “positive” condition)

Step 4: Request output

Under Display, check: - ✅ ROC Curve - ✅ With diagonal reference line - ✅ Standard error and confidence interval (for AUC) - ✅ Coordinate points of the ROC Curve (for cut-point selection)

Click OK.

Step 5: Read the output

Area Under the Curve table — records:

Output value What to report
Area AUC (range 0–1)
Std. Error Standard error of AUC
Asymptotic Sig. p-value (H₀: AUC = 0.50)
Asymptotic 95% CI: Lower/Upper 95% CI for AUC

For the core_session strength example: AUC = .683, p = .008, 95% CI [.55, .81].

Coordinates of the Curve table — lists sensitivity and 1 − specificity at every threshold. To identify the optimal cut-point (maximising Youden’s Index = sensitivity + specificity − 1):

Transform → Compute Variable…

After saving the coordinate table as a dataset, compute:

Youden = Sensitivity + (1 - OneMinusSpecificity) - 1

The row with the highest Youden value is the optimal cut-point. For the strength example, this occurs near 79.8 kg.

NoteAUC and the Mann-Whitney connection

AUC is mathematically equivalent to the Mann-Whitney U statistic divided by (n₁ × n₂). Specifically:

\[AUC = \frac{U}{n_{positive} \times n_{negative}}\]

This means you can verify the AUC from SPSS by running a Mann-Whitney U test (Appendix: SPSS Tutorial Nonparametric Tests, Part C) on the continuous test variable with group as the grouping variable and dividing U by the product of the two group sizes.

X.5 Troubleshooting

The ROC Curve dialog is grayed out. The ROC Curve procedure requires the Advanced Statistics module. If it is unavailable, use the Mann-Whitney U approach to compute AUC manually (see the callout note in Part D above), or use the Statistical Calculators appendix.

The Risk Estimates table shows Odds Ratio, not Sensitivity/Specificity. SPSS’s Crosstabs Risk Estimates reports relative risk and odds ratios, not diagnostic accuracy statistics. Compute sensitivity, specificity, PPV, NPV, and LRs manually from the cell counts using the Compute Variable formulas in Part C.

NNT confidence interval is very wide or includes negative values. This is expected when the ARR is small and/or the sample size is modest. It means the study does not provide precise enough evidence to pin down how effective the intervention is in terms of responder rates. Report the result transparently and note the uncertainty.

The MCID threshold does not match published values for my outcome measure. The distribution-based MCID (0.5 × SD) is an approximation. If published anchor-based MCIDs exist for your specific outcome measure and population, use those values instead. Always cite the source.

X.6 Practice Exercises

  1. MCID and responders. Using core_session.sav, compute the distribution-based MCID for pain_0_10 (0.5 × SD at pre-test). Classify participants in the training group as responders or non-responders based on this threshold (pain decrease ≥ MCID). What proportion of the training group achieved a clinically meaningful pain reduction?

  2. NNT. Using your responder classifications from Exercise 1, compute the responder rates for both groups, then calculate ARR, NNT, and RR. Interpret the NNT in plain language for a clinician.

  3. Sensitivity and specificity. Using vo2_mlkgmin at post-test as a classifier (cut-point = sample median), test how well it discriminates training from control group participants. Compute sensitivity, specificity, PPV, NPV, +LR, and −LR. Is VO₂max a better or worse classifier than post-test strength?

  4. ROC curve. Run a ROC analysis on function_0_100 at post-test to discriminate training from control group participants. Report the AUC, 95% CI, and p-value. Identify the optimal cut-point from the Coordinates of the Curve table. How does the AUC for functional ability compare to the AUC for strength (.683)?