Standardize measurements with z-scores

Transform numeric columns separately to prepare measurements for a subsequent analysis.

Guides · Worksheets and data tools · 4 min read

Example: drying batches

A drying study records wet batch mass, inlet temperature, drying time and electricity use for 48 batches. Transform each measurement using this sample’s values.

Download the drying-batch measurements (CSV)

This is the same example used in Help. The CSV contains the measurements to import. The four numeric columns use kg, °C, minutes and kWh; batch_id keeps track of the batch.

1. Create the analysis

In the sidebar, open Data utilities, choose Standardize & Normalize, and name the analysis. Select New blank worksheet and Create analysis.

2. Import the data

On Worksheet, choose Import. Select the downloaded file or paste its contents. Set the delimiter to Comma, use Decimal dot, and check First row contains column names. Preview the import, then choose Import into worksheet.

3. Select the input columns

On Inputs, open the column picker for Variables to transform. Select wet_batch_mass_kg, inlet_temperature_c, drying_time_min and electricity_kwh, in that order. Use the up and down arrows to correct their order if needed.

Leave batch_id unselected; it identifies a batch, rather than a measurement.

4. Set the method and output names

In Method, choose Standardize (z-scores). Under Output names, enter the matching name for each source column.

Source columnOutput name
wet_batch_mass_kgwet_batch_mass_kg_zscore
inlet_temperature_cinlet_temperature_c_zscore
drying_time_mindrying_time_min_zscore
electricity_kwhelectricity_kwh_zscore

Check the destination worksheet and the note showing 4 new columns. The original columns are retained.

Standardize & Normalize: Inputs with the example’s assignments and settings
The four selected source columns, Standardize (z-scores) method and four output names on Inputs. View full-size image (opens in a new tab)

5. Transform

Choose Transform, then open Results. Open Worksheet to see the four new columns beside the originals. Each successful transform appends new columns; repeating it does not replace the earlier output.

6. Interpret results

  1. Read the source summary

    The summary describes the four original columns, each with 48 values and no missing readings. For mass, the average is 45.4906 kg, sample standard deviation is 7.00915 kg, and observed range is 32.57–66.24 kg.

  2. Understand the transformation

    Subtract each column’s own mean, then divide by its sample standard deviation. Zero means the source average; +1 means one sample standard deviation above it. The result has no original measurement unit.

  3. Read the first transformed batch

    For the first batch, mass is 50 kg. Subtract 45.4906 kg and divide by 7.00915 kg to get about +0.6434. This batch is about 0.64 sample standard deviations above the average mass. Each other column uses its own mean and sample SD.

  4. Choose the next analysis

    Z-scores let you compare how far measurements sit from their own averages, despite different original units. They do not turn the values into probabilities. Select the new columns explicitly for your next analysis. Scaling does not make the data normally distributed, remove dependence or establish acceptable process performance.

  5. Keep the saved operation in context

    All 48 rows remain in batch order and the originals are preserved. Results records the transformation as it ran. Later worksheet edits or Undo can change the worksheet without changing that saved result.

More details: read each result section

Complete result tables use six significant digits, as in Help.

Transformation summary

Source and Output column identify each original and new column. Valid values counts usable source readings; Missing counts missing readings. Source mean, Source SD, Source minimum and Source maximum describe the original column in its measurement unit. Subtract each column’s own mean, then divide by its sample standard deviation. Zero means the source average; +1 means one sample standard deviation above it. The result has no original measurement unit.

Calculated example output. Running a practice copy writes new columns to its independent worksheet.

Transformation summary · 4 rows
SourceOutput columnMethodValid valuesMissingSource meanSource SDSource minimumSource maximum
wet_batch_mass_kgwet_batch_mass_kg_zscoreStandardize (z-scores)48045.49067.0091532.5766.24
inlet_temperature_cinlet_temperature_c_zscoreStandardize (z-scores)48064.50833.2456757.170.4
drying_time_mindrying_time_min_zscoreStandardize (z-scores)48030.5944.5197823.0241.72
electricity_kwhelectricity_kwh_zscoreStandardize (z-scores)48017.12391.7496114.26522.814

Transformed values

Row 1 is the first imported batch. Each column contains its transformed measurements, with all 48 rows kept in collection order. For the first batch, mass is 50 kg. Subtract 45.4906 kg and divide by 7.00915 kg to get about +0.6434. This batch is about 0.64 sample standard deviations above the average mass.

Captured values in original row order. Exports retain full precision.

Transformed values · 48 rows
Rowwet_batch_mass_kg_zscoreinlet_temperature_c_zscoredrying_time_min_zscoreelectricity_kwh_zscore
10.6433550.3979660.6739360.326418
2-1.50526-1.32741-1.07172-1.08361
30.6918630.1206731.596550.415581
40.641929-1.881990.08319910.66135
5-0.4794620.983360.722611-0.579498
62.242690.3979662.461632.54291
7-0.435235-0.156619-0.396913-0.820123
8-1.05871-2.28253-1.38147-1.63402
92.960330.8601192.18953.25221
10-0.522264-1.050120.324361-0.694952
11-1.32407-0.495531-0.379213-1.41626
12-0.0828381-0.618772-0.372575-0.257141
130.0255915-1.66632-1.44342-1.00416
14-0.129919-0.27986-0.987649-0.292577
15-0.510850.95255-0.456650.0246364
160.379415-0.526342-0.2044250.733937
17-0.426674-0.341480.0278867-0.384598
180.1668351.6920.7004860.493884
19-0.6592270.8293090.0345242-0.500623
202.064350.5828271.209361.57813
21-0.1028121.26065-1.1204-0.268
22-1.62653-0.803634-1.67574-1.46027
230.03415180.6752581.032360.0274942
24-0.9659691.16822-1.30846-0.464044
25-0.8446991.47632-0.1823-0.617221
26-0.783351-0.310670.0610741-0.863561
27-1.11863-0.31067-0.4301-0.803548
280.7132640.983360.5389730.791093
29-0.517984-0.834444-1.32174-1.00588
30-0.104239-1.57389-0.646925-0.0793867
310.4536030.336345-0.3438130.215536
32-0.583612-0.988495-0.602675-0.262285
33-0.413834-0.495531-0.5827620.120658
34-0.4794620.829309-0.70445-0.086817
350.0270182-1.080930.6938480.173241
36-0.567918-0.957685-1.44342-0.664088
370.385122-0.4339110.6960610.196675
380.2795451.6920.1119620.336706
390.5334990.860119-0.368150.122372
400.82312-0.1874291.131920.171526
41-0.1342-0.372290.0831991-0.266857
421.566430.2439140.3885241.23405
431.761891.815240.8133231.9022
44-1.84339-0.896065-1.01862-1.42197
45-0.3838730.3363450.514636-0.091961
46-0.6635081.22984-0.828349-0.644655
470.93155-0.2490491.061121.09916
480.9429640.3979662.120911.24834

7. Create a report

Keep Transformation summary and all rows of Transformed values. Record the selected method, source columns and output names. The summary describes the original measurements; the values table contains the transformed output.

Choose Add to report from the completed run. Open Choose individual items and advanced options to select tables and charts, then choose Add to draft. Hidden items stay in the saved analysis.

Name the report and add the purpose of the study and your interpretation. Choose Save, review Preview, then use Export → Download HTML. The example below contains the full selected content, including results beyond one screen.

Complete native output for this Help example, including applicable tables, charts and run notes. Report numbers use the app’s displayed precision. Exported charts are static. On narrow screens, scroll wide charts and tables sideways.
View example report: Z-scores for drying batches

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