What Is Numerical Data in Quantitative Research
What Is Numerical Data
Numerical data is data represented by numbers so that a computer can store it, sort it, and perform calculations. In quantitative research, numerical data commonly appears as age, income, number of purchases, mean scores, or agreement levels on a Likert scale. You can view these observations in a .sav file, a .csv file, or SPSS's Data View.
For example, when a respondent selects an agreement level of 4, SPSS stores the value 4 in the data cell. When 120 respondents complete the same item, that column becomes a numerical variable with 120 values. The software can calculate the mean, standard deviation, correlation, or include the variable in a regression model.
You need to distinguish numerical data from a variable that has simply been coded with digits. Gender may be entered as 1 = Male and 2 = Female, but the codes 1 and 2 are only category labels. Calculating the mean of this variable does not produce a meaningful real-world interpretation. Genuine numerical data must support calculations that match the way the variable was measured.
In a quantitative study, numerical data commonly comes from a questionnaire, transaction records, or a measurement system. If you are designing a questionnaire, the scale selection should be accompanied by a coding rule from the beginning. You can also read what a scale is to distinguish the scale from the data entered after the survey.
Why Numerical Data Matters in Quantitative Research
Numerical data determines which analyses you can run and how far your conclusions can go. A directly collected age variable with values of 23, 31, and 42 has different properties from an age-group variable coded as 1 = under 25, 2 = from 25 to 34, and 3 = 35 or older. Both look like numerical columns in SPSS, but you read and analyze them differently.
For continuous or approximately continuous numerical data, you can describe the variable using Mean, Standard Deviation, Minimum, and Maximum. These values help you detect whether a variable was entered incorrectly. For example, a variable measuring years of work experience with a Maximum of 250 in a sample of workers may contain an entry error where 25 was intended, even though the software accepts 250.
Numerical data is also the input for statistical testing. Item scores can be used to run Cronbach's Alpha, EFA, linear regression, or a PLS-SEM model. When you check a correlation, the software uses the distances and variation between values. If you enter text, use the wrong code, or mix measurement units, the results can be distorted even though the output tables still appear normally.
You should distinguish three layers of information in the file:
- The actual value is the number stored in the cell, such as 4 or 25.
- The value label explains a numerical code, such as 1 = Male and 2 = Female.
- The measure type tells SPSS how to handle the variable, including Nominal, Ordinal, or Scale.
In Variable View, the Type column shows whether the data is stored as Numeric or String. The Values column contains labels for category codes. The Measure column shows Nominal, Ordinal, or Scale. Check these three columns before running an analysis, because a variable entered as Numeric can still be categorical in substance.
If your model includes a mediator or moderator, numerical data also affects how you create new variables and test interactions. You can read more about mediators, moderators, and moderating to avoid confusing the roles of variables in your model.
How Much Numerical Data Is Acceptable
There is no single threshold that applies to every numerical dataset. A value is valid when it matches the variable definition, measurement unit, permitted range in the questionnaire, and research design. Check validity first, then apply statistical thresholds to the scale or model.
The table below brings together criteria you will commonly encounter. Apply each row only to the step named in that row. Do not use a Cronbach's Alpha threshold to claim that raw data is clean.
| Check | Reference level | Interpretation | Source |
|---|---|---|---|
| Cronbach's Alpha | 0.7 or above | Reliability is generally considered acceptable | (Nunnally, 1978) |
| Cronbach's Alpha for an exploratory scale | 0.6 or above | May be acceptable in an exploratory context | (Hair et al., 2010) |
| Corrected Item-Total Correlation | 0.3 or above | The item correlates appropriately with the total scale | (Nunnally and Bernstein, 1994) |
| KMO | 0.5 or above | The data meets the minimum level for considering EFA | (Kaiser, 1974) |
| Bartlett's Test | Sig. below 0.05 | The correlation matrix differs from an identity matrix at the selected significance level | (Kaiser, 1974) |
| Factor loading | 0.5 or above | A factor-loading level commonly used when assessing an item | (Hair et al., 2010) |
| Total Variance Explained | 50% or above | A reference level for explained variance in factor analysis | (Hair et al., 2010) |
| 5 to 10 observations per item | According to the sample design | A reference rule when planning questionnaire sample size | (Hair et al., 2010) |
The thresholds in the table do not replace reading the data context. For example, a high Alpha can occur when items are too similar, but that does not prove that the questionnaire measures the intended construct. Similarly, an acceptable KMO does not mean that every variable is clean or that the theoretical model is correct.
If your study uses SmartPLS, you will encounter other criteria such as outer loading, CR, AVE, HTMT, VIF, R², and Q². Do not use the CFI, TLI, or RMSEA criteria of CB-SEM to assess a PLS-SEM model. Numerical data is the input, while the assessment criteria must follow the method you selected.
How to Read Numerical Data in the Output
In SPSS, you can start with descriptive statistics. Open Analyze > Descriptive Statistics > Frequencies if you want to check frequencies and unusual values for each variable. For numerical variables where you need the Mean and Standard Deviation, go to Analyze > Descriptive Statistics > Descriptives, move the variable to Variable(s), and select the statistics you need.
The example below is illustrative output, not the result of a real study. The column names are kept in the form SPSS commonly displays so that you can compare them with the file currently open.
Descriptive Statistics, illustrative output
| N | Minimum | Maximum | Mean | Std. Deviation |
|---|---|---|---|---|
| 186 | 1.00 | 5.00 | 3.72 | 0.81 |
If this is an HL1 variable measured on a Likert scale from 1 to 5, a Minimum of 1 and a Maximum of 5 fall within the designed range. A Mean of 3.72 describes the average response level in the illustrative sample, while a Std. Deviation of 0.81 describes the spread around the mean. You cannot conclude that a hypothesis is supported from these two numbers alone.
When you run Frequencies, you may see a table like this:
Frequencies, illustrative output
| HL1 | Frequency | Percent | Valid Percent | Cumulative Percent |
|---|---|---|---|---|
| 1 | 8 | 4.3 | 4.3 | 4.3 |
| 2 | 17 | 9.1 | 9.1 | 13.4 |
| 3 | 39 | 21.0 | 21.0 | 34.4 |
| 4 | 74 | 39.8 | 39.8 | 74.2 |
| 5 | 48 | 25.8 | 25.8 | 100.0 |
| Total | 186 | 100.0 | 100.0 | 100.0 |
Frequency is the number of observations at each level. Percent is calculated using all rows, while Valid Percent excludes missing values before calculating the percentage. When there is no missing data, these two columns are equal. Cumulative Percent is the running total percentage, which is often useful when examining an ordinal variable.
If you want to check numerical data outside the permitted range, go to Analyze > Descriptive Statistics > Frequencies, select Statistics, and then inspect Minimum and Maximum. A Likert variable from 1 to 5 with a value of 0 or 6 needs to be checked in Data View. You can also use Data > Sort Cases to move the smallest or largest values to the top.
When numerical data contains many items, do not look only at each column separately. Check the variable codes, variable labels, number of valid rows, and missing values. A response row in which every item has the same value may indicate a fixed response pattern, but you need to review the response time and the cleaning rules you defined in advance as well.
What to Do When Numerical Data Is Not Acceptable
Work from the clearest errors to the issues that require methodological judgment. Record every change in a file or log, including the observation ID, affected variable, reason for the decision, and result after processing. Deleting data without a record makes it difficult to explain your decisions when your supervisor asks.
Check the Variable Definition and Coding
Open the original questionnaire and compare it with Variable View. If valid responses range from 1 to 5 but the file contains 7, determine whether this is an entry error, a code for no response, or an option that was not included in your documentation. Do not automatically change 7 to 5 because the two values may have different meanings.
For a reverse-worded item, recode it before calculating the scale score. In SPSS, use Transform > Recode into Different Variables to create a new variable and keep the original variable as a reference copy. Overwriting the original variable increases the risk that you will be unable to recover the initial coding.
Check Missing Data
Use Analyze > Descriptive Statistics > Frequencies to see the number of missing values for each variable. If a respondent left large parts of the questionnaire blank, apply the exclusion rule specified in your methods section. If only a few values are missing, the appropriate treatment depends on the variable type, missing proportion, and your supervisor's requirements.
Do not fill large numbers of missing values with the mean simply to increase the number of valid rows. This can reduce data variation and affect correlations. If you use a missing-data replacement method, state which variables were treated, which rule was used, and why the method was appropriate.
Check for Outliers
An outlier is an observation that differs substantially from the rest of the data. You can use a boxplot, histogram, or standardized scores to detect initial warning signs. However, a different value is not automatically an error. It may accurately represent a respondent with unusual income, age, or purchase frequency.
Read outliers to distinguish data-entry errors from valid extreme observations. Delete an outlier only when you have clear grounds, such as a value outside what is practically possible or a violation of the sampling conditions. If you remove one, preserve the original file and state the criterion in your thesis.
Rerun the Analysis After Each Change
After correcting coding, removing a row, or creating a new variable, rerun the relevant analysis step. If Cronbach's Alpha changes, save the output from both the earlier and later runs. EFA rarely looks clean on the first run, but item removal should be based on factor loading, cross-loading, theoretical grounds, and discussion with your supervisor, rather than only on the desire to make the results table look better.
Distinguishing Numerical Data from Categorical Data
Numerical data, quantitative data, and Scale variables are often used interchangeably. Quantitative data emphasizes that values can be measured and analyzed numerically. Categorical data uses numbers to label groups. In SPSS, both can appear in a Numeric column, so looking only at the storage type is not enough.
| Example variable | Values in the file | Nature | Appropriate descriptive analysis |
|---|---|---|---|
| Age | 18, 22, 35 | Quantitative | Mean, standard deviation, Min, Max |
| Number of purchases per month | 0, 1, 4 | Discrete quantitative | Mean, median, frequency |
| Agreement level | 1 to 5 | Ordinal, often treated as approximately continuous in many studies | Frequency, Mean according to the research design |
| Gender | 1 = Male, 2 = Female | Nominal categorical | Frequency, Percent |
| Income group | 1, 2, 3, 4 | Ordinal categorical | Frequency, Percent, median when appropriate |
| Respondent ID | 1001, 1002, 1003 | Identifier | Do not calculate the mean |
A common mistake is to treat the respondent ID as an explanatory variable. ID = 1001 does not mean that the person has a higher level of an attribute than someone with ID = 1000. Similarly, the codes 1 and 2 for gender do not create a numerical distance of one unit.
Another mistake is assuming that all Likert data is the same. A single item from 1 to 5 clearly has an ordinal nature. When several items measure the same construct, their reliability is assessed and they are combined into a score, the next analytical step needs to be explained in the methods section.
Common Errors
Entering Numbers but Setting the Wrong Measure
If an age variable is set to Nominal, some procedures may treat it as a categorical variable. If gender is set to Scale, SPSS can still run a regression, but the result does not automatically become meaningful. Set Measure according to the nature of the variable and the model. Do not select Scale for every numerical column.
Using a Missing Code as a Real Value
Some questionnaires use 99 or 999 for a non-response. If you forget to declare it as missing, SPSS will include 999 in the Mean and distort the Maximum. In Variable View, check the Missing column and compare it with the questionnaire's coding rules.
Concluding That the Data Is Good Because the Mean Is Within Range
A Mean of 3.5 on a scale from 1 to 5 does not prove that the data contains no errors. You still need to check missing values, extreme values, distributions, duplicate responses, and coding consistency. A clean dataset results from a checking process, not from a single number.
Deleting Rows to Reach a Sample Threshold
Deleting data only to make Alpha, KMO, or a p-value meet a desired level increases the risk of bias. Statistical thresholds should support methodological decisions, not become a target for adjusting the data. Record the number of observations before and after processing, and explain the exclusion criterion in the methods chapter.
Frequently asked questions
What is numerical data, and is it the same as quantitative data?
Numerical data is data stored or represented as numbers. In research, most quantitative data is numerical, but a numerical column can still contain only category codes, such as gender or respondent ID. Check the nature of the variable before selecting a calculation.
What should Measure be set to for numerical data in SPSS?
SPSS has three common choices: Nominal, Ordinal, and Scale. Nominal is used for groups without an order, Ordinal is used for ordered groups, and Scale is used for variables treated as quantitative data according to the research design. This setting describes how the variable is analyzed. It does not turn a categorical code into quantitative data.
How much numerical data is acceptable?
There is no general threshold for every numerical dataset. Check the permitted range in the questionnaire, missing values, entry errors, and the nature of the variable. Thresholds such as Alpha of 0.7, Corrected Item-Total Correlation of 0.3, or factor loading of 0.5 apply to specific analytical steps, with the corresponding sources shown in the criteria table.
What should I do when numerical data is missing?
First determine whether the missing value reflects a blank response, an entry error, or a code such as 99. Then check the missing proportion by variable and by row, apply the rule stated in your methods section, and preserve the original dataset. Do not automatically replace every blank cell with the Mean without considering the variable type and the extent of missingness.
Does numerical data need to be checked for outliers?
Yes, especially for age, income, number of purchases, and continuous variables. You can begin with Minimum, Maximum, a boxplot, and a histogram. An outlier may be an error or a valid case, so the decision to remove it must be based on evidence and recorded.
Can I use numerical data to run Cronbach's Alpha and EFA?
Yes, when the numerical values are scores for items designed to measure the same construct and they have been coded correctly. Check reverse-worded items, missing values, and score ranges before running the analysis. Then read Reliability Statistics, Item-Total Statistics, KMO and Bartlett's Test, and Rotated Component Matrix in the correct analytical order.
How to write this in your thesis
Open your data file now, check Type, Values, Missing, and Measure in Variable View, then run Frequencies to review Minimum, Maximum, and the number of missing cells before continuing with the analysis. If you need to run the complete .sav or .csv dataset in SPSS and SmartPLS, you can use M4 analysis by DoThesis.