What Is SD? How to Read Standard Deviation in SPSS

What Is SD

You open the SPSS output and see the Descriptive Statistics table with the columns N, Minimum, Maximum, Mean, and Std. Deviation. The Std. Deviation column is SD, short for Standard Deviation. SD shows how far the observed values are dispersed from the Mean.

When SD is small, the responses or data values are generally concentrated around the Mean. When SD is large, the data are more widely dispersed. SD does not independently tell you whether a variable is good or bad, and it does not by itself show whether a research hypothesis is supported.

Technically, SD is the square root of the variance. For a sample with n observations, the formula is usually written as follows:

SD = √[Σ(xᵢ - x̄)² / (n - 1)]

Here, xᵢ is each observed value, x̄ is the sample Mean, and n is the number of observations. The denominator n - 1 is used when calculating the standard deviation of a sample in research. When you run descriptive statistics in SPSS, the software calculates this value from the valid values of the variable.

For example, if a variable has a Mean of 3.80 and an SD of 0.45 on a 5-point Likert scale, the responses are relatively concentrated around 3.80. If the Mean is still 3.80 but the SD is 1.20, the differences between respondents are much larger.

SD may also appear as Std. Deviation in SPSS, Standard deviation in Excel, or SD in thesis results tables. When reading a source or output, identify this column correctly before interpreting it.

The Meaning of SD in Quantitative Research

In quantitative research, SD helps you describe data dispersion before moving to analyses such as regression, EFA, CFA, or PLS-SEM. It is part of descriptive statistics and is commonly reported with frequencies, percentages, Mean, Minimum, and Maximum. You can also read the posts under the Statistics topic to place SD within the broader analysis process.

For demographic variables, SD can give you a sense of the dispersion of age, income, or years of experience. For Likert variables, SD reflects how differently respondents agree with the statements. Two variables can have the same Mean and very different SD values, so looking only at the Mean is not enough.

SD can also point to an issue that needs further checking. An SD of 0 means that all valid values of the variable are identical. A very small SD may appear when respondents select almost the same option. A large SD may reflect dispersed opinions, different respondent groups, or outliers in the data. If you suspect unusual values, check the post about outliers as well.

SD is not an automatic item-deletion criterion in every situation. Do not see a large SD and delete the item immediately. Your decision should also consider the scale, distribution, frequency table, item content, and analysis objective. If you are confusing SD with a measurement concept, read what is a scale to distinguish a scale, an item, and a statistical index.

In a report, SD usually helps answer three questions: around which average level are the data located, how dispersed are they, and is there an unusual pattern that needs checking? It is descriptive information, not a causal conclusion.

What SD Is Acceptable

There is no single SD threshold that applies to every variable, scale, and research topic. SD depends on the measurement range, coding, data distribution, and respondents. Therefore, the question of what standard deviation is acceptable must be answered in context rather than by applying one mechanical number.

For a 5-point Likert scale, SD generally ranges from 0 to a theoretical maximum that depends on how the response options are distributed. An SD of about 0.4 and an SD of about 1.1 can both be reasonable in different situations. Look at the Mean, Minimum, Maximum, and frequency table together.

The table below summarizes a practical way to read SD. These descriptions guide data interpretation and are not mandatory pass thresholds for a test. The cited sources support the related checking principles, because there is no source in the approved list for one general SD threshold across all Likert scales.

Some descriptive statistics guides may give an empirical SD range for a particular type of scale. Use that range only when your supervisor or the research method for your topic explicitly requires it. Do not turn a descriptive convention into a universal pass criterion.

SD does not have an acceptance threshold equivalent to Cronbach's Alpha at 0.7 or KMO at 0.5. Those thresholds belong to different indicators. If someone asks what SD is acceptable, the careful answer is that you need to consider the scale and analysis purpose, then check the data rather than compare it with one isolated number.

How to Read SD in the Output

You can run SD in SPSS through Analyze > Descriptive Statistics > Descriptives. Move the variables you want to inspect into Variable(s), click Options, select Mean, Std. deviation, Minimum, and Maximum, then click Continue and OK. If you want a detailed frequency view, use Analyze > Descriptive Statistics > Frequencies.

The table below is illustrative output, not the result of a real study. The table name and column names follow the way SPSS commonly displays them in the output.

In the CL1 row, the Mean is 3,84 and Std. Deviation is 0,72. This shows that the responses for CL1 tend to be around 3,84 and have a certain amount of dispersion. You could report that CL1 has a Mean of 3,84, an SD of 0,72, and 214 valid observations.

HL1 has a lower Mean than CL1 and a higher SD. Respondents therefore gave it a lower average rating and showed greater differences in their responses. You should not conclude that HL1 is a poor-quality variable simply because its SD is 1,08. Check the frequencies, item content, and subsequent testing steps as well.

If N differs between variables, check the missing values. SPSS may calculate each variable using its own number of valid observations, while another analysis may use Valid N (listwise), which retains only rows with complete data for all variables. Record this difference when reporting the sample size.

You should also open Analyze > Descriptive Statistics > Frequencies to see how often levels 1, 2, 3, 4, and 5 were selected. SD is only a summary number. Two data sets can have the same Mean and SD while having different distribution shapes.

What to Do When SD Is Not Acceptable

Because SD has no universal acceptance threshold, start by identifying what concerns you. If SD equals 0 or is close to 0, check the coding and original data first. You may have entered the same value in the entire column, reversed a code incorrectly, or selected the wrong variable in the SPSS dialog box.

Check the Measurement Range and Coding

Confirm that the variable uses the correct scale. A Likert variable from 1 to 5 should not suddenly contain 0, 6, or 99 unless those codes have been defined. Open Variable View, check Values, Missing, and Measure, then inspect Frequencies for unfamiliar codes.

If an item is reverse-coded, create the recoded variable before calculating the scale score. Incorrect reverse coding can distort the interpretation of the Mean and SD and can also affect Reliability Analysis and EFA.

Check for Unusual Data

Review the Minimum, Maximum, frequency table, and chart. For a continuous variable, you can check a boxplot to identify extreme points. An outlier is not automatically an error. Compare it with the questionnaire response or with the data-cleaning rules stated in your research method.

If the data are valid and represent a group with genuinely different views, retaining the observation may be more reasonable than deleting it. If you find a data-entry error, correct it using the original data and keep a record of the change.

Check Questionnaire Quality

A very small SD across many items may indicate that respondents selected the same level for almost the entire questionnaire. Check completion time, repeated response patterns, and the completion rate. You need a cleaning rule stated in advance rather than a rule created after seeing an unattractive result.

A large SD for one item may also reflect unclear wording or different interpretations of the construct. Once data collection is complete, do not rewrite the item simply to reduce the SD. If an item needs to be removed, base that decision on theory, measurement quality, and discussion with your supervisor.

Rerun the Descriptive Statistics With a Documented Basis

After each valid change, run Analyze > Descriptive Statistics > Descriptives again and save the output by version. Do not keep only the final table if you removed rows or corrected codes. The committee may ask why the sample size changed, and you need to explain it.

If the issue involves a moderator or mediator, SD is not the indicator for deciding that role. You can also read about moderator, moderating, or mediator to distinguish these concepts from descriptive statistics.

Distinguishing SD from Mean and SE

Mean is the average value and describes the center of the data. SD describes how the observations are dispersed around the Mean. These two indicators often appear together in a descriptive table, but they answer different questions.

Standard Error, usually written as SE or Std. Error, reflects the uncertainty of an estimate such as the Mean. SE usually decreases as sample size increases, while SD describes the dispersion of the observations themselves. Do not use SE instead of SD when reporting how dispersed respondents' answers are.

Variance is the squared SD. Therefore, if SD is 0,72, the variance is approximately 0,5184. In a thesis, SD is easier to interpret because it remains in the same units as the variable, while variance uses squared units.

Range is the spread of the data, calculated as Maximum minus Minimum. Range uses only the two boundary values, while SD uses all observations. Two data sets can have the same range and different SD values if the values between the boundaries are distributed differently.

SD is also different from Cronbach's Alpha. SD describes how dispersed one variable or score is, while Alpha evaluates the internal consistency of the items in the same scale. You can have a reasonable SD but a low Alpha, or an acceptable Alpha while one item still has a distribution that needs checking.

Common Mistakes

The first mistake is writing that “SD above 0,5” is a mandatory criterion. This number is not a general threshold in the cited criteria for SD. Describe SD in relation to the scale and distribution, and cite the criteria that genuinely apply.

The second mistake is reporting only the Mean and leaving out SD. In quantitative research, readers need to know both the center and the dispersion. A descriptive statistics table should include at least N, Mean, and SD when these indicators are suitable for the variable.

The third mistake is calling Std. Error the standard deviation. In the output, look at the exact column name. Std. Deviation is SD, while Std. Error is the standard error.

The fourth mistake is deleting an item simply because its SD is large. Before deciding, check coding, missing values, outliers, item content, and the results of related analyses. Every data deletion needs a reason and a written record.

The fifth mistake is comparing the SD of variables with different measurement ranges without standardizing the interpretation. The SD of age measured in years cannot be read in the same way as the SD of agreement measured from 1 to 5.

You should also not use SD to conclude whether a hypothesis has an effect. Hypothesis conclusions must rely on the relevant model and test, such as a regression coefficient, p-value, confidence interval, or path coefficient in PLS-SEM.

Frequently asked questions

What standard deviation is acceptable?

There is no single SD value that is considered acceptable for every study. Examine SD in relation to the measurement range, Mean, frequencies, sample size, and analysis objective. For a Likert scale, describe the dispersion and check the data instead of deleting an item using a self-imposed threshold.

Does an SD of 0 mean the data are wrong?

An SD of 0 means that the valid values are identical. This may be genuine data, but you should usually recheck the coding, calculation formula, and data column. If a variable has no variation, it generally provides little information for analyses that require differences between observations.

Is a smaller SD always better?

A small SD only shows that the responses are concentrated around the Mean. It does not prove that the scale is good or that the data are high quality. If every respondent selected the same level because the item was predictable, because of the collection process, or because of data filtering, a small SD may hide a problem rather than indicate quality.

Should I delete an item with a large SD?

There is not enough evidence to delete it. Check the scale, frequencies, outliers, coding, and the Reliability Analysis or EFA results. If the item remains theoretically appropriate and the data are valid, a large SD may simply reflect genuine differences between respondents.

Which column contains SD in SPSS?

In the Descriptive Statistics table, read the Std. Deviation column. Do not confuse it with Std. Error. If the table has no SD column, go to Analyze > Descriptive Statistics > Descriptives, select Options, and check Std. deviation before running it again.

How to write this in your thesis

Report the table name, the number of valid observations, the Mean, and the SD, then explain the observed dispersion without turning it into a hypothesis conclusion. Use wording such as: “[Variable] had a Mean of [value] and an SD of [value] based on [N] valid observations.”

Open your SPSS file, check Std. Deviation together with N, Mean, Minimum, Maximum, and the frequency table, then document how you handled every unusual value before running the next analysis. If you need to run the statistics on your own .sav or .csv file, M4 analysis by DoThesis supports this step.