What Is Descriptive Statistics? How to Read SPSS Output

What is descriptive statistics

You open your SPSS file, run Frequencies or Descriptives, and see columns for Mean, Std. Deviation, Minimum, and Maximum. These numbers do not test your hypotheses or tell you whether an independent variable affects a dependent variable. They describe the data you have: where the data are concentrated, how widely they vary, and the range covered by the observed values.

Descriptive statistics are a group of methods used to summarize a dataset through measures such as frequency, percentage, Mean, Median, Mode, Standard Deviation, Variance, Minimum, and Maximum. For categorical variables such as gender or age group, you usually examine Frequency and Percent. For quantitative variables or scale scores, you usually examine Mean, Standard Deviation, Minimum, and Maximum.

If the observations of a variable are called (x_1, x_2, ..., x_n), Mean is calculated by dividing the sum of the values by the number of observations:

[ Mean = \frac{x_1 + x_2 + ... + x_n}{n} ]

Standard Deviation shows how far the observations tend to be from the Mean. The larger the standard deviation, the more widely the data are spread around the average. This describes your sample data. It does not establish that one variable affects another.

In quantitative research, you can also read the articles under the Statistics topic when you need to distinguish descriptive statistics from hypothesis tests, regression, or factor analysis.

Why descriptive statistics matters in quantitative research

Descriptive statistics usually appears at the beginning of the results chapter because it shows you what the actual dataset looks like before you run further analyses. If your questionnaire uses a 5-point Likert scale, the Mean of a variable can show whether respondents tend toward disagreement, neutrality, or agreement. Mean is still only the average response. It does not automatically prove that the scale is reliable or that a hypothesis is supported.

For demographic information, Frequency and Percent help you describe the research sample. For example, you can report how many respondents belong to each gender, age group, or income category. When reporting the results, include both the count and the percentage. Reporting only the percentage makes it difficult for the reader to check the actual sample size.

For observed variables, Mean and Standard Deviation help you identify items with noticeably different response patterns. A variable with a much lower Mean than the others may reflect wording that respondents found difficult to understand, content that does not fit the context, or another aspect of the construct. This is a signal to check the data, not sufficient evidence for deleting the item.

Minimum and Maximum help you check whether the data fall within the range specified in the questionnaire. If the questionnaire uses a Likert scale from 1 to 5 but the output shows a Minimum of 0 or a Maximum of 7, go back and check the coding, data entry, and missing values. If you see a few values that are very different from the rest, check the outliers before deciding how to handle them.

Descriptive statistics also helps you present the sample before running Cronbach's Alpha, EFA, regression, or a PLS-SEM model. SPSS can calculate many statistics, but your thesis should keep the measures that serve the research question and help the reader understand the data.

What level of descriptive statistics is acceptable

This is where many students look for a single number that will let them declare the result acceptable or unacceptable. Descriptive statistics does not have a universal cutoff such as Mean above 3 or Standard Deviation below 1. A Mean reflects responses in a specific context. A Mean of 2.8 may be reasonable if respondents rate an attribute poorly, while a Mean of 4.2 does not automatically prove that the scale has good reliability.

Evaluate the results through three questions: do the values fall within the range of the scale, is the data affected by incorrect coding or unusual missing values, and do the statistics fit the purpose of describing the variable. Scale quality tests use their own criteria. For example, Cronbach's Alpha from 0.7 upward is generally accepted according to (Nunnally, 1978), while Corrected Item-Total Correlation from 0.3 upward is used according to (Nunnally and Bernstein, 1994). These two cutoffs are not cutoffs for descriptive statistics.

The table below provides a practical interpretation, not an acceptance table for every research topic. Sources are included in the rows that contain specific methodological criteria.

In your thesis, do not write that “Mean is acceptable” simply because you see an average value. A more accurate sentence states that the variable's data fall within the measurement range, gives the average level, describes the dispersion, and then moves to the appropriate test for evaluating the scale or hypothesis.

How to read descriptive statistics in the output

There are two common ways to run this analysis in SPSS. If you need Mean, Standard Deviation, Minimum, and Maximum for several variables, open Analyze > Descriptive Statistics > Descriptives. Move the variables you need into Variable(s), click Options, select Mean, Standard deviation, Minimum, and Maximum, then click Continue and OK.

If you need Median, Mode, Percentiles, or charts as well, use Analyze > Descriptive Statistics > Frequencies. Move the variable into Variable(s) and select Statistics to mark the measures you want to calculate. You can select Charts if you need a chart, but do not put every chart in your thesis simply because SPSS generated it.

Illustrative output

The table below is illustrative output, constructed to resemble an SPSS Descriptive Statistics table. It is not the result of a real study and must not be copied into Chapter 4 of your thesis.

The Variable column contains the variable name in the file. It does not have to be the full wording of the statement in the questionnaire. N is the number of valid observations that SPSS used for that variable. If one variable has a lower N than the others, it may contain missing values, or you may have filtered the data before running the analysis.

A Minimum of 1 and a Maximum of 5 fit the 5-point Likert scale in this example. If every respondent selects the same level, Minimum and Maximum will be equal. This situation deserves attention because the variable may have little ability to distinguish between observations, but you still need to check the context before making a decision.

A Mean of 3,62 for DV1 means that the average response across 185 observations is 3,62. A Std. Deviation of 0,781 indicates a certain amount of dispersion around the Mean. Do not turn this number into a causal conclusion, and do not compare the Mean of two variables if their content, scale, or coding differs.

If you run Frequencies, the output may also show a Statistics table and a Frequency table. For gender, read Frequency as the number of people in each group and Percent as the percentage. Check the total number of valid observations, the number of missing values, and the value labels in Variable View before writing the results.

What to do when descriptive statistics looks unacceptable

Because descriptive statistics has no single acceptance cutoff, your response should begin with the type of abnormality you see. Do not immediately delete variables with a low Mean or high Standard Deviation. That can remove important content from the results and change the sample in a way that is difficult to explain.

Step 1: Check the coding and variable type

Open Variable View and compare Type, Values, and Missing with your data codebook. Confirm that Likert variables are entered as numbers, reverse-coded values have been recoded, and no text characters are mixed into a numeric column. If you created a composite variable, check whether the averaging formula includes the correct observed variables.

Step 2: Check missing values and unusual observations

Compare N across variables, review the Frequencies table, and check for values outside the questionnaire range. A response row with too many blank cells or the same option selected throughout the questionnaire should be reviewed against the criteria you set in advance. Any decision to remove an observation needs a reason. Record the row number, the exclusion condition, and the sample size before and after processing.

Step 3: Recheck the variable before deleting it

If a variable has a noticeably different Mean, reread its wording and check its correlation, scale reliability, or EFA against the research model. If Corrected Item-Total Correlation is below 0.3, you may consider the item according to (Nunnally and Bernstein, 1994), but the final decision must also account for the theoretical basis and the effect on the scale.

Step 4: Run the analysis again and save each version

Save the original data file, the cleaned file, and the syntax or output from each run. EFA, Cronbach's Alpha, and regression often require you to return to the data after finding an error. If an item has to be removed, record the reason instead of submitting only the final results table.

If Mean or Standard Deviation looks unusual because of a few extreme responses, this is the point to check outliers. If the issue concerns how you model a moderating variable, read about moderating, because descriptive statistics cannot replace an interaction test.

Descriptive statistics versus inferential statistics

Descriptive statistics answers the question, “What does my sample data look like?” Inferential statistics answers questions such as, “Is there enough statistical evidence for the observed relationship?” or “Does the sample result support the research hypothesis?” T-test, ANOVA, correlation, regression, and p-value tests belong to the inferential group, even though they are often presented next to descriptive tables.

For example, a Mean of 3,70 for purchase intention only describes the average level in the sample. The regression coefficient helps you evaluate the direction and level of the relationship between an independent variable and purchase intention, while the p-value or confidence interval supports your conclusion about the test. A high Mean cannot be used to claim that a factor has a strong effect.

Descriptive statistics is also different from reliability testing. Cronbach's Alpha evaluates the internal consistency of a group of observed variables, while Mean describes the average response to each variable. If you are preparing a scale, first distinguish clearly what a scale is before combining variables into a representative score.

Another common mistake is using descriptive statistics to conclude that a variable is a moderator or mediator. A moderator changes the strength or direction of a relationship, while a mediator explains the transmission mechanism. A Mean and Standard Deviation table cannot test either role. You can read more about moderator and mediator to choose the correct analysis.

Common mistakes

Reporting only Mean and leaving out N. The reader needs to know how many observations were used to calculate the Mean. If the valid count differs across variables, explain the reason for the missing values.

Calling Standard Deviation an error. Standard Deviation describes the dispersion of observations. It is not Standard Error and it is not the confidence interval for Mean.

Concluding that a scale is acceptable because Mean is high. A high Mean only indicates a high response tendency in the sample. The reliability and validity of the scale need to be evaluated through the relevant analyses.

Calculating a composite Mean without checking the scale first. If DV1 through DV4 measure the same construct, define how they will be combined according to the research design and the scale test results. Do not average variables only because their names share the same prefix.

Copying the SPSS table unchanged into the thesis. The output may contain many decimal places, unused rows, and variable names that are difficult to read. Select the necessary statistics, rename the variables in the table according to the conventions in Chapter 3, and keep the original output file for comparison.

How to write this in your thesis: “The descriptive statistics results show that the observed variables of the [scale name] scale have Mean values ranging from [lowest value] to [highest value], while Standard Deviation ranges from [lowest value] to [highest value]. The Minimum and Maximum values fall within the [measurement range], indicating that the data were coded consistently with the scale used.” Replace every placeholder with the actual values in your output.

Frequently asked questions

What is descriptive statistics in SPSS?

It is a group of SPSS commands used to summarize data through Frequency, Percent, Mean, Median, Mode, Standard Deviation, Minimum, and Maximum. The two commonly used paths are Analyze > Descriptive Statistics > Descriptives and Analyze > Descriptive Statistics > Frequencies.

What Mean is acceptable in descriptive statistics?

Mean has no universal acceptance cutoff. Read Mean in relation to the scale range, the content of the variable, and the research objective. A high or low Mean does not replace tests of reliability, scale validity, or hypotheses.

Does descriptive statistics require a p-value?

A basic descriptive statistics table does not require a p-value. p-value appears in inferential tests or models such as t-test, ANOVA, correlation, and regression. Do not add p-value to a table simply to make it look more complete.

Why is N missing in the Descriptives table?

N may be lower because of missing values, an active data filter, or a calculation based on variables with different numbers of valid observations. Check Data > Select Cases, the Missing column in Variable View, and the Frequencies table for that variable.

What Standard Deviation is acceptable?

There is no mandatory Standard Deviation for every scale. Read it together with Mean, the measurement range, and the response distribution. If Standard Deviation equals 0, every observation has the same value, so check the data and whether the variable can distinguish between observations.

Do I need to run descriptive statistics before Cronbach's Alpha?

You should check the data and describe the sample before running subsequent analyses. However, the order of presentation in the thesis can follow your research method, as long as you clearly explain the data, missing-value treatment, scale tests, and model.

Open your SPSS file now, run Analyze > Descriptive Statistics > Descriptives, compare N, Minimum, Maximum, Mean, and Std. Deviation with your data codebook, and save the output before moving to the tests. If you need to run the analysis on your own .sav or .csv file, use M4 analysis by DoThesis.