Appendix L — SPSS Tutorial: Percentiles and Z-Scores

Computing and interpreting percentiles, percentile ranks, and standard scores

NoteLearning Objectives

By the end of this tutorial, you will be able to:

  • Compute percentiles and percentile ranks using SPSS Frequencies procedure
  • Calculate z-scores manually and using SPSS Descriptives
  • Create standardized variables (z-scores) for further analysis
  • Interpret SPSS output for percentile and z-score calculations
  • Export and report percentile and standard score results in APA format

L.1 Overview

This tutorial demonstrates how to use SPSS to compute percentiles, percentile ranks, and z-scores for individual observations and entire datasets. These transformations are essential for:

  • Comparing individual performance to group norms
  • Creating standardized scores for cross-scale comparisons
  • Identifying outliers systematically
  • Building composite performance profiles

We will use fitness testing data to illustrate realistic Movement Science applications.

L.2 Dataset for this tutorial

We will use the Core Dataset (core_session.csv) filtered to the pre-training time point (N = 60). Download it here: core_session.csv

For this tutorial, we will analyze two continuous variables:

  • sprint_20m_s — 20-meter sprint time in seconds (lower is better)
  • vo2_mlkgmin — Aerobic capacity (VO₂max) in mL·kg⁻¹·min⁻¹ (higher is better)

Open the dataset in SPSS, then filter to pre-training only:

  1. Data → Select Cases → If condition is satisfied
  2. Enter: time = 'pre'
  3. Click Continue → OK

L.3 Part 1: Computing percentiles using Frequencies

L.3.1 Procedure

The Frequencies procedure provides percentile values for any variable.

  1. Analyze → Descriptive Statistics → Frequencies
  2. Move the variable(s) of interest (e.g., sprint_20m_s) to the Variable(s) box
  3. Click Statistics button
  4. Under Percentile Values:
    • Select Quartiles for 25th, 50th, 75th percentiles
    • Or select Cut points for X equal groups (e.g., 10 for deciles)
    • Or manually enter specific percentiles in Percentiles box
  5. Continue → OK

L.3.2 Example: Computing quartiles for sprint times

Request:

FREQUENCIES VARIABLES=sprint_20m_s
  /STATISTICS=QUARTILES
  /ORDER=ANALYSIS.

L.3.3 Interpreting the output

The output includes a Percentiles table:

Percentile Value
25 3.54
50 (Median) 3.80
75 4.03

Interpretation: * 25% of participants had sprint times ≤ 3.54 s (Q₁) * 50% had times ≤ 3.80 s (Median) * 75% had times ≤ 4.03 s (Q₃) * The IQR = 4.03 − 3.54 = 0.48 s (middle 50% of participants span 0.48 s)

TipAPA Reporting Example

Sprint times ranged from 2.90 to 4.45 seconds, with a median of 3.80 s (IQR = 0.48 s). The 25th and 75th percentiles were 3.54 and 4.03 seconds, respectively.

L.4 Part 2: Computing percentile ranks for individual scores

SPSS does not directly compute percentile ranks for individual values, but you can estimate them using the cumulative percentage column in the Frequencies output.

L.4.1 Procedure

  1. Analyze → Descriptive Statistics → Frequencies
  2. Move the variable to Variable(s) box
  3. Ensure Display frequency tables is checked
  4. OK

L.4.2 Reading the cumulative percent column

For a continuous variable like sprint_20m_s, the Frequencies table lists each unique value with its cumulative percent. A participant with a sprint time of 3.60 s falls at approximately the 30th percentile — meaning 30% of the sample had times at or below 3.60 s.

NoteNote on directionality

For “lower is better” measures (sprint time, reaction time), a lower value ranks higher in performance despite a higher cumulative percentage. For “higher is better” measures (VO₂max, strength), the cumulative percentage directly represents the performance ranking.

L.5 Part 3: Computing z-scores using Descriptives

L.5.1 Procedure: Viewing z-scores in output

  1. Analyze → Descriptive Statistics → Descriptives
  2. Move variable(s) to Variable(s) box
  3. Click Options button
  4. Ensure Mean and Std. deviation are selected
  5. Continue → OK
  6. Use the formula: z = (X − Mean) / SD

L.5.2 Procedure: Creating standardized variables

To create new z-score variables in your dataset:

  1. Analyze → Descriptive Statistics → Descriptives
  2. Move variable(s) to Variable(s) box
  3. ✓ Check Save standardized values as variables
  4. OK

SPSS creates new variables with the prefix Z (e.g., sprint_20m_s → Zsprint_20m_s).

L.5.3 Example: Computing z-scores for sprint times

Descriptive Statistics (pre-training, N = 60):

Variable N Mean Std. Deviation
sprint_20m_s 60 3.79 0.354

For an athlete with sprint_20m_s = 2.90 s (fastest in sample):

\[ z = \frac{2.90 - 3.79}{0.354} = \frac{-0.89}{0.354} = -2.51 \]

Interpretation: This athlete is 2.51 standard deviations faster than the mean (the most negative z-score = best sprint performance).

For an athlete with sprint_20m_s = 4.45 s (slowest in sample):

\[ z = \frac{4.45 - 3.79}{0.354} = \frac{+0.66}{0.354} = +1.87 \]

Interpretation: This athlete is 1.87 standard deviations slower than the mean.

L.5.4 Viewing saved z-scores

After creating standardized variables, you can view them in Data View:

ID sprint_20m_s Zsprint_20m_s
P_fast 2.90 −2.51
P_avg 3.79 0.00
P_slow 4.45 +1.87

L.6 Part 4: Cross-scale comparisons using z-scores

To compare performance across different tests (e.g., sprint time vs. VO₂max), standardize all variables and compare z-scores.

L.6.1 Procedure

  1. Standardize each variable using Descriptives with Save standardized values
  2. View z-scores for each participant across tests
  3. Create composite scores if needed using Transform → Compute Variable

L.6.2 Example: Dual-component fitness profile for Participant P001

Group Statistics (pre-training, N = 60):

Variable Mean SD
sprint_20m_s 3.79 0.354
vo2_mlkgmin 41.34 6.82

Participant P001’s raw scores:

sprint_20m_s vo2_mlkgmin
3.44 s 40.8 mL·kg⁻¹·min⁻¹

Computed Z-Scores:

ID ZSprint ZVO2
P001 −0.98 −0.08

Interpretation: Participant P001 shows: * Sprint performance slightly above average (z = −0.98; lower sprint time = faster) * Aerobic capacity essentially at the group mean (z = −0.08)

L.6.3 Creating composite scores

To create an average z-score across multiple tests:

  1. Transform → Compute Variable
  2. Target Variable: Z_Composite
  3. Numeric Expression: (-1 * Zsprint_20m_s + Zvo2_mlkgmin) / 2
    • Note: Sprint z-score is multiplied by −1 to make “higher = better” for all components
  4. OK
WarningImportant: Directionality

When creating composite z-scores, ensure all variables are oriented the same way (higher = better or lower = better). For sprint times, multiply z-scores by −1 to flip the direction before averaging.

L.7 Part 5: Identifying outliers using z-scores

L.7.1 Procedure

  1. Create standardized variables (see Part 3)
  2. Transform → Compute Variable
  3. Create a flag variable for extreme values:
    • Target Variable: Outlier_Sprint
    • Numeric Expression: ABS(ZSprint20m) > 3
  4. OK

This creates a flag (0 = not outlier, 1 = outlier) for values with |z| > 3.

L.7.2 Alternative: Visual inspection

  1. Graphs → Legacy Dialogs → Scatter/Dot → Simple Scatter
  2. Y-Axis: Standardized variable (e.g., ZSprint20m)
  3. X-Axis: ID or sequence variable
  4. OK

Add a reference line at z = ±3 to identify extreme values: - Double-click the chart - Options → Y-axis reference line - Add lines at +3 and −3

L.8 Part 6: Percentiles by group (e.g., age, sex)

To compute percentiles separately for males and females:

  1. Data → Split File
  2. Select Organize output by groups
  3. Move grouping variable (e.g., Sex) to Groups Based on box
  4. OK
  5. Run Frequencies procedure as in Part 1
  6. Data → Split File → Reset when done

Output: SPSS produces separate percentile tables for each group, allowing age- and sex-specific norm comparisons.

L.9 Part 7: Exporting results

L.9.1 Exporting percentile and z-score tables

  1. Right-click on the output table
  2. Export
  3. Choose format (Excel, Word, PDF)
  4. Export

L.9.2 Copying tables to manuscripts

  1. Right-click on table → Copy
  2. Paste into Word document
  3. Format as APA table:
    • Remove gridlines
    • Add horizontal lines (top, below header, bottom)
    • Ensure decimal alignment
TipAPA Table Example

Table 1

Descriptive Statistics and Quartiles for Fitness Variables at Pre-Training (N = 60)

Variable M SD Q1 Mdn Q3 Min Max
Sprint Time (s) 3.79 0.35 3.54 3.80 4.03 2.90 4.45
VO₂max (mL·kg⁻¹·min⁻¹) 41.34 6.82 36.03 41.55 45.82 26.90 56.50

Note. M = mean; SD = standard deviation; Q1 = 25th percentile; Mdn = median; Q3 = 75th percentile. Negative z-scores for Sprint indicate faster times (better performance).

L.10 Practice exercises

Use the Core Dataset (core_session.csv, pre-training, N = 60) to complete these tasks:

  1. Compute quartiles for vo2_mlkgmin and interpret the results.
  2. Determine the percentile rank for a participant with sprint_20m_s = 3.60 s (hint: approximately the 30th percentile).
  3. Create z-score variables for sprint_20m_s and vo2_mlkgmin using Descriptives → Save standardized values.
  4. Identify participants with z-scores > +2 or < −2 on either test (potential outliers).
  5. Create a composite fitness score by averaging z-scores across both tests (adjust Sprint direction first by multiplying by −1).
  6. Compare percentiles by group: Split the file by group (training vs. control) and compute quartiles for sprint_20m_s.

L.11 Common mistakes and troubleshooting

Problem Solution
Z-scores not appearing in dataset Ensure “Save standardized values” is checked
Percentiles seem wrong Check for outliers or data entry errors
Composite z-scores favor one test Ensure all tests are on the same directionality
Percentile rank doesn’t match z-score Remember: connection only holds if distribution is normal
Output tables are split unexpectedly Reset Split File: Data → Split File → Reset

L.12 Summary

This tutorial covered:

  • Computing percentiles using the Frequencies procedure
  • Estimating percentile ranks from cumulative frequency tables
  • Creating z-score variables using Descriptives
  • Comparing performance across different scales using z-scores
  • Creating composite scores and identifying outliers
  • Generating age- and sex-specific norms using Split File
TipNext steps

Practice these procedures with your own data. Remember: * Use percentiles for skewed data or ordinal scales * Use z-scores for symmetric data and cross-scale comparisons * Always visualize distributions before interpreting standardized scores * Report both raw scores and standardized scores for complete interpretation

L.13 Additional resources

  • SPSS Help: Frequencies Procedure
  • SPSS Help: Descriptives Procedure
  • SPSS Help: Split File
  • Textbook Chapter 6: Percentiles and Standard Scores