Quantitative Research: Methods, Examples and How It Works
Quantitative research turns a research problem into variables that can be measured consistently and analyzed numerically. It is useful when a study needs to estimate how common something is, compare groups, examine relationships, track change, test a prediction, or evaluate whether an intervention is associated with an outcome. The numbers are not the point by themselves. The point is to use a design, sample, measures, and analysis that allow the numbers to answer the research question credibly.
Students often reduce quantitative work to “using statistics.” That skips most of the difficult decisions. Before analysis begins, the researcher must define the population, decide what will count as evidence, operationalize variables, choose a design, recruit or identify a sample, select measures, anticipate bias, and plan how the data will be interpreted. The broader research design guide explains how qualitative, quantitative, and mixed approaches differ; this article focuses on how the quantitative approach works in practice.
What Is Quantitative Research?
Quantitative research is a structured approach to inquiry that represents relevant characteristics, exposures, behaviors, outcomes, or other phenomena with numerical data and analyzes those data using statistical methods. The design may be descriptive, observational, experimental, or quasi-experimental. The data may come from surveys, tests, sensors, records, structured observations, experiments, or existing datasets.
CDC program-evaluation guidance describes quantitative methods as methods that rely on numerical data to draw conclusions and compare results. That definition is useful, but a sound quantitative study also requires alignment: the variables, sampling strategy, measurement process, and statistical analysis must all fit the question being asked.
| Core idea
Quantitative research is not simply “research with numbers.” It is research in which the question is translated into measurable variables and the design specifies how numerical evidence will be collected, compared, and interpreted. |
When Is Quantitative Research Appropriate?
A quantitative approach is usually a strong fit when the central question asks about amounts, frequencies, differences, associations, predictions, trends, or effects. It is especially useful when the researcher needs standardized information from many cases or wants to make a carefully justified inference from a sample to a wider population.
| Question purpose | Typical quantitative wording | Example |
| Describe | How many? How often? What proportion? What is the average? | What proportion of first-year students use campus tutoring at least once per semester? |
| Compare | Do two or more groups differ? | Do mean exam scores differ between students in two teaching formats? |
| Relate | Are variables associated? | Is weekly study time associated with course grade? |
| Predict | Which variables help predict an outcome? | Do attendance and prior GPA predict final course performance? |
| Evaluate effect | Does an intervention or exposure change an outcome? | Does a structured reminder intervention increase follow-up attendance compared with usual practice? |
If the study instead asks how people interpret an experience, why a process unfolds in a particular context, or how meaning is constructed, the completed EssayEco guide to qualitative research is usually the more appropriate starting point. A future mixed-methods cluster will explain how both forms of evidence can be integrated deliberately.
Quantitative Research vs. Qualitative Research
| Feature | Quantitative research | Qualitative research |
| Primary evidence | Numbers, counts, scores, measurements, categories coded for analysis. | Words, narratives, observations, documents, images, interactions, meanings. |
| Common aims | Estimate, compare, test, predict, model, measure change. | Explore, interpret, understand, describe context, develop concepts. |
| Sampling logic | Often probability-based when population inference is required; nonprobability samples are also used with limits. | Usually purposive or information-rich sampling rather than population estimation. |
| Data collection | Surveys, tests, experiments, structured observations, sensors, records, existing datasets. | Interviews, focus groups, open observation, documents, artifacts, field notes. |
| Analysis | Descriptive and inferential statistics, models, estimates, effect measures. | Coding, thematic analysis, content analysis, narrative analysis, interpretive comparison. |
| Typical output | Estimates, distributions, group differences, associations, model coefficients, uncertainty. | Themes, patterns of meaning, explanations, contextual interpretations, participant perspectives. |
The Building Blocks of Quantitative Research
Variables and Operational Definitions
A variable is a characteristic that can take different values across people, cases, settings, or time. The same broad concept can be measured in several ways, so the researcher needs an operational definition: a precise statement of how the concept will be represented in the study. “Academic engagement,” for example, might be operationalized as attendance rate, learning-platform activity, a validated engagement scale, or a combination of indicators. Each choice captures something slightly different.
| Concept | Possible operational definition | Why the choice matters |
| Stress | Score on a validated perceived-stress questionnaire. | Creates a standardized numeric measure but depends on the instrument and timeframe. |
| Medication adherence | Percentage of prescribed doses taken during a defined period. | Requires a reliable source such as records, electronic monitoring, or a defensible self-report measure. |
| Academic performance | Final course percentage or GPA. | Different indicators have different scales, timing, and comparability. |
| Exercise | Minutes of moderate-to-vigorous activity per week. | Self-report and device-based measurement can yield different estimates. |
Independent, Dependent, Predictor, and Outcome Variables
In experiments, the independent variable is the factor manipulated or assigned by the researcher, while the dependent variable is the measured outcome. In observational studies, terms such as exposure, predictor, explanatory variable, and outcome are often more accurate because the researcher did not assign the exposure. Avoid calling every predictor an “independent variable” if the design is observational and no manipulation occurred.
The completed EssayEco guide on the research hypothesis shows how measurable variables support directional, non-directional, null, and alternative hypotheses. Hypotheses are common in quantitative studies, but a purely descriptive quantitative study may not need one if its purpose is estimation rather than hypothesis testing.
Levels and Types of Measurement
Before choosing an analysis, identify what kind of data each variable produces. A categorical variable sorts cases into groups or labels; a quantitative variable records numerical magnitude. Some courses also distinguish nominal, ordinal, interval, and ratio measurement levels. The practical reason for classifying variables is that the scale and distribution of the data affect which summaries, graphs, and statistical procedures are appropriate.
Penn State statistics guidance emphasizes classifying variables before selecting descriptive and inferential procedures. A category code such as 1 = online and 2 = in-person is still categorical; the numbers are labels, not amounts.
Major Quantitative Research Designs
Quantitative research includes several design families. The design determines when variables are measured, whether an exposure or intervention is assigned, how groups are formed, and how strongly the study can support causal conclusions.
| Design | What it does | Typical use / caution |
| Descriptive study | Summarizes characteristics, frequencies, distributions, or trends. | Useful for “what is happening?” questions; does not by itself explain why patterns occur. |
| Cross-sectional study | Measures variables at one point or short period in time. | Efficient for prevalence and associations; temporal order is often unclear. |
| Correlational study | Examines the strength or direction of association between variables. | Useful for relationships and prediction; correlation alone does not establish causation. |
| Cohort study | Follows or reconstructs groups defined by exposure or other characteristics and compares outcomes. | Can establish temporal sequence more clearly than cross-sectional work; confounding may remain. |
| Case-control study | Starts with outcome status and looks backward for differences in prior exposures or characteristics. | Efficient for uncommon outcomes; vulnerable to selection and recall problems. |
| Randomized experiment | Researcher assigns an intervention and uses random allocation to conditions. | Strong design for causal effects when implemented well; may be infeasible or unethical for some questions. |
| Quasi-experiment | Evaluates an intervention without full random assignment, often using comparison groups, pre/post data, or time series. | Can support stronger causal reasoning than simple observation, but alternative explanations require careful control. |
STROBE focuses on transparent reporting of cohort, case-control, and cross-sectional observational studies. Its checklist asks researchers to define outcomes, exposures, predictors, confounders, measurement methods, study size, handling of quantitative variables, and statistical methods. STROBE is a reporting guideline, not a substitute for designing the study well.
OpenTextBC research-methods guidance distinguishes quasi-experiments from true experiments by noting that the independent variable may be manipulated but participants are not randomly assigned. That missing randomization leaves more room for confounding, so causal claims require extra caution.
Population, Sample, and Sampling
The population is the larger set of cases about which the study hopes to learn. The sample is the subset actually measured. A statistic describes the sample; a population parameter is the corresponding value for the population. Inferential statistics use sample data to estimate or test claims about population parameters, but the credibility of that inference depends heavily on how the sample was obtained and who actually responded.
Penn State Applied Research Methods explains this population-sample-statistic-parameter relationship and emphasizes that sampling is necessary because measuring an entire population is often impractical.
| Sampling approach | Basic idea | Main implication |
| Simple random sampling | Every eligible case has a known selection chance under the sampling procedure. | Supports population inference when the frame and response process are adequate. |
| Stratified sampling | Population is divided into meaningful strata, then sampled within each. | Can improve representation of important subgroups and precision. |
| Cluster / multistage sampling | Groups such as schools, clinics, or geographic areas are sampled, then cases within them. | Efficient for dispersed populations but analysis must account for clustering. |
| Convenience sampling | Uses cases easiest to access. | Fast and common in student projects, but limits generalizability and can introduce selection bias. |
| Purposive / quota nonprobability sampling | Selects cases to meet specified characteristics or quotas without probability selection. | Can ensure desired composition, but population error cannot be treated like a probability sample. |
| Generalization caution
A large convenience sample is not automatically representative. Sample size and sampling quality answer different questions: more observations can improve precision, but they do not erase systematic selection bias. |
Sample Size and Statistical Power
Sample-size planning should happen before data collection whenever the study will test hypotheses or estimate effects with a target level of precision. The required size depends on the design, expected variability, effect size or precision target, number of groups or predictors, desired confidence or power, and anticipated missing data or nonresponse.
Avoid universal rules such as “30 participants are enough for quantitative research.” A sample that is adequate for one descriptive estimate may be badly underpowered for a small between-group effect or a multivariable model. For formal hypothesis-testing studies, seek statistical guidance early rather than choosing the sample size after seeing the results.
Common Quantitative Data Collection Methods
1. Surveys and Questionnaires
Surveys collect standardized information from respondents so answers can be compared numerically. Items may measure demographics, knowledge, attitudes, behaviors, experiences, or outcomes. Good survey design depends on clear wording, appropriate response options, logical ordering, piloting, and consistent administration.
CDC questionnaire-design resources emphasize that survey questions should be evaluated systematically because misunderstanding, response error, nonresponse, and different interpretations across groups can damage comparability. A questionnaire is a measurement instrument, not merely a list of questions.
2. Tests, Scales, and Standardized Instruments
Quantitative studies often use established scales or tests to measure constructs such as depression, self-efficacy, satisfaction, knowledge, or cognitive performance. Before using an instrument, check what it measures, how scores are calculated, whether permission or licensing is required, and what evidence exists for reliability and validity in a population and context similar to yours.
3. Structured Observation and Counts
Observation can be quantitative when the researcher uses predefined categories, counts, durations, or ratings. Examples include counting safety-protocol violations, timing waiting periods, recording how often a behavior occurs, or scoring performance with a structured rubric. The observation rules must be specific enough that different observers can apply them consistently.
4. Experiments and Instrumented Measurements
Experiments produce data under controlled or partly controlled conditions. Measurements may come from laboratory instruments, devices, software logs, physiological monitors, performance tasks, or other systems. Calibration, standardized procedures, blinding where appropriate, and consistent timing can matter as much as the later statistical test.
5. Existing Records and Secondary Data
Administrative records, electronic health records, government datasets, institutional data, financial records, learning-platform logs, and prior surveys can support quantitative analysis without collecting new observations directly. The completed guide to primary vs secondary research explains this distinction in more detail. Before using an existing dataset, verify how variables were defined, why the data were collected, who is missing, how quality was checked, and whether access and privacy rules permit the intended analysis.
How to Conduct Quantitative Research Step by Step
Step 1: Define the Problem and Question
Start with a focused problem and a question that can be answered with measurable evidence. Identify whether the aim is to describe, compare, relate, predict, or estimate an effect.
Step 2: Review Relevant Literature and Theory
Use existing scholarship to refine definitions, justify variables, identify established measures, anticipate confounders, and avoid repeating weak designs. Use the existing EssayEco literature-review guide rather than creating a duplicate Research & Methodology page.
Step 3: Specify the Variables and Hypotheses
State the main outcome, exposure or predictor variables, comparison groups, and any prespecified hypotheses. Define expected direction only when theory or prior evidence justifies it.
Step 4: Choose the Quantitative Design
Select descriptive, cross-sectional, cohort, case-control, experimental, quasi-experimental, or another defensible design based on the question, timing, ethics, available access, and causal claim you need to support.
Step 5: Define the Population and Sampling Plan
State who or what is eligible, how cases will be identified, how the sample will be selected, and why that sampling method fits the intended inference.
Step 6: Operationalize and Measure Each Variable
Specify exactly how each construct becomes a value. Choose established measures where appropriate and document scoring, units, categories, cut points, timing, and data sources.
Step 7: Plan Ethics, Privacy, and Data Management
Address consent or lawful data access, confidentiality, secure storage, identifiers, retention, permissions, and institutional review requirements before collection begins.
Step 8: Pilot the Procedures or Instrument
Test survey wording, data-entry forms, measurement timing, recruitment, randomization procedures, observation rules, and data exports on a small scale when feasible.
Step 9: Collect Data Consistently
Use the same procedures across cases unless the protocol explicitly requires variation. Record deviations, missingness, refusals, attrition, and technical problems rather than hiding them.
Step 10: Clean and Describe the Data
Check ranges, coding, duplicates, impossible values, missing data, group sizes, distributions, and outliers. Produce descriptive summaries before attempting complex inference.
Step 11: Conduct the Prespecified Analysis
Choose statistical procedures that fit the question, design, variable types, sampling structure, assumptions, and level of measurement. Report estimates and uncertainty, not only whether a p-value crosses a threshold.
Step 12: Interpret Within the Design Limits
Return to the question. Separate association from causation, statistical from practical importance, sample findings from population claims, and observed results from speculation. State limitations honestly.
Descriptive Statistics: What the Data Look Like
Descriptive statistics summarize the observations you actually collected. They may include counts, percentages, means, medians, ranges, standard deviations, quartiles, rates, and graphs. The appropriate summary depends on the variable type and distribution. A mean can be misleading for a heavily skewed variable, while a percentage is more interpretable than a mean for many categorical outcomes.
Penn State describes descriptive statistics as operations that summarize the data in front of the researcher rather than making claims about a wider population. Descriptive analysis should usually precede inferential analysis because it reveals coding errors, extreme values, sparse groups, and unexpected distributions.
| Data situation | Useful descriptive tools | What they show |
| Categorical variable | Counts, percentages, bar charts, contingency tables. | How observations are distributed across categories. |
| Approximately symmetric quantitative variable | Mean, standard deviation, histogram. | Center, spread, and distribution shape. |
| Skewed quantitative variable | Median, interquartile range, boxplot, histogram. | Typical value and spread without excessive influence from extremes. |
| Two quantitative variables | Scatterplot, correlation, fitted line summaries. | Pattern, direction, strength, and possible nonlinearity in association. |
| Repeated measurements over time | Line plots, change scores, repeated summaries. | Trends and within-case or group change across time. |
Inferential Statistics: Learning Beyond the Sample
Inferential statistics use sample data to estimate population quantities or test hypotheses under stated assumptions. Confidence intervals quantify uncertainty around estimates. Hypothesis tests evaluate how compatible the observed data are with a null model. Regression and related models can estimate associations while accounting for additional variables.
Penn State Applied Statistics distinguishes descriptive statistics from inference: descriptive procedures summarize a sample, while inferential procedures use sample statistics to learn about unknown population parameters.
| Do not choose a test by name first
Start with the research question, study design, outcome variable, predictor structure, sampling method, repeated measurements, and assumptions. The correct analysis follows from those features; it should not be chosen because a test is familiar or produces a desired p-value. |
| Research situation | Common analysis family (illustrative) | Question being answered |
| Estimate one mean or proportion | Confidence interval; one-sample inference. | What population value is plausible given the sample? |
| Compare two groups | Difference in means/proportions; t-based or categorical methods where appropriate. | How large is the group difference, and how uncertain is it? |
| Compare several groups | ANOVA/general linear models or categorical alternatives. | Do outcomes differ across multiple groups or conditions? |
| Relate two quantitative variables | Correlation or regression. | How are the variables associated, and what is the estimated relationship? |
| Predict an outcome using several variables | Multiple linear/logistic or other regression models. | How do predictors jointly relate to or predict the outcome? |
| Analyze repeated or clustered data | Paired/repeated-measures, multilevel, GEE, or other dependence-aware models. | How should non-independent observations be modeled? |
This table is intentionally high level. Statistical method selection can become technical quickly, and specialized analysis should be checked against course guidance or a statistician when the project involves complex sampling, repeated measures, missing data, many predictors, nonstandard outcomes, or causal modeling.
Reliability and Validity in Quantitative Research
A study can be statistically sophisticated and still fail if its measures are weak. Reliability concerns consistency: would the measurement behave similarly under comparable conditions? Validity concerns whether the evidence supports interpreting the measure as representing the intended construct for the intended purpose and context. Reliability is important, but a consistently wrong measure is not valid simply because it is reproducible.
PubMed summary on measurement, reliability, and validity describes reliability as consistency across repeated measurement and validity as measuring what is intended. More recent measurement work also stresses that validity depends on purpose and context rather than being a permanent property of an instrument in every population.
| Quality issue | Question to ask | Example risk |
| Reliability | Are scores or observations sufficiently consistent? | Two observers classify the same behavior very differently. |
| Construct validity | Does the measure represent the intended concept? | Using number of logins as the sole measure of meaningful engagement. |
| Content validity | Does the measure adequately cover the relevant domain? | A knowledge test samples only one small part of the curriculum. |
| Criterion-related evidence | Does the measure correspond appropriately with a relevant external criterion? | A screening tool performs poorly against a suitable reference assessment. |
| Measurement invariance / comparability | Does the measure function similarly across groups or contexts being compared? | Different groups interpret the same survey item differently. |
Bias, Confounding, Missing Data, and Error
Quantitative results are shaped by more than random sampling variation. Selection bias can arise when the included sample differs systematically from the target population. Information or measurement bias can arise when variables are recorded inaccurately or differently across groups. Confounding occurs when a third factor is related to both an exposure and an outcome and creates or distorts an observed association. Missing data can also bias results if absence is related to variables in the study.
Good design tries to prevent these problems before analysis. Clear eligibility criteria, appropriate comparison groups, randomization where ethical and feasible, standardized measurement, blinding where relevant, high follow-up, prespecified analyses, and careful data management can reduce threats to validity. Statistical adjustment can help with measured confounders, but it cannot magically repair every design problem or account for variables that were never measured.
Correlation, Prediction, and Causation
A correlation shows that two variables vary together; it does not by itself show that one causes the other. Reverse direction, confounding, selection effects, measurement artifacts, and chance can all produce associations. Prediction is also not the same as explanation: a variable can improve prediction without being a causal mechanism.
Causal claims require design and assumptions that justify them. Randomized experiments are powerful because random allocation can make groups comparable on average with respect to both measured and unmeasured pre-intervention factors. Well-designed quasi-experiments and observational studies can also contribute to causal reasoning, but they require stronger assumptions and careful handling of alternative explanations.
Worked Quantitative Research Examples
| Field | Research question | Possible design and evidence |
| Education | Is attendance associated with final course performance among first-year students? | Observational correlational design using attendance records and final scores; regression may estimate the association while accounting for prespecified covariates. |
| Nursing | Does a discharge reminder intervention improve 30-day follow-up attendance? | Randomized or quasi-experimental comparison of reminder vs. usual-practice groups with follow-up attendance as the outcome. |
| Business | What factors predict repeat purchase among customers in an online store? | Analysis of transaction and customer data using a defined prediction model; outcome may be repeat purchase within a fixed period. |
| Psychology | Do mean stress scores differ between students who work more than 20 hours weekly and those who do not? | Cross-sectional group comparison using a defined stress measure; causal language should be avoided. |
| Public health | What proportion of adults in a target community meets a physical-activity guideline? | Probability survey if population estimation is the goal, with weighting/design considerations when applicable. |
| Operations | Did waiting time change after a scheduling policy was introduced? | Interrupted time-series or controlled before-after design if randomization is unavailable and sufficient time points exist. |
Advantages of Quantitative Research
- Standardized measurement can make comparisons across people, groups, settings, or time more transparent.
- Probability sampling can support population estimates when the sampling frame, response, and analysis are appropriate.
- Experiments and strong quasi-experiments can evaluate effects more directly than purely descriptive designs.
- Statistical models can estimate effect sizes, associations, predictions, and uncertainty.
- Large structured datasets can reveal patterns that would be difficult to detect case by case.
- Prespecified variables and procedures can make replication and auditing easier when reporting is complete.
Limitations of Quantitative Research
- Numerical indicators can oversimplify complex experiences or contexts when operational definitions are weak.
- Poor sampling can produce precise estimates for the wrong population.
- Measurement error and construct mismatch can undermine conclusions even with sophisticated analysis.
- Observational associations may be confounded and should not automatically be interpreted as causal.
- Statistical significance can be mistaken for practical, clinical, educational, or policy importance.
- Large datasets can encourage data dredging or selective reporting if questions and analyses are not disciplined.
- Missing data, attrition, nonresponse, and protocol deviations can bias results if ignored.
Common Quantitative Research Mistakes
| Mistake | Why it weakens the study | Better approach |
| Choosing the test before defining the question | The analysis may not match the design or variable structure. | Start with the question, design, outcome, predictors, and sampling structure. |
| Using a convenience sample but generalizing to everyone | Selection mechanism may differ systematically from the target population. | Limit the claim or use a defensible probability design when population inference is required. |
| Treating coded categories as numerical quantities | Codes such as 1 and 2 may be labels, not magnitudes. | Classify variables correctly before summarizing or modeling them. |
| Reporting only p-values | A threshold does not show the magnitude or uncertainty of an effect. | Report effect estimates and confidence intervals where appropriate. |
| Calling correlation causation | Association does not eliminate reverse direction or confounding. | Match causal wording to the design and assumptions. |
| Ignoring missing data or attrition | Missingness can change the composition of the analyzed sample. | Report the extent, pattern, handling method, and sensitivity where relevant. |
| Using an unvalidated measure without justification | Scores may not represent the intended construct. | Use suitable measures and explain evidence for reliability/validity in context. |
| Hiding data cleaning decisions | Undocumented exclusions and recoding reduce transparency. | Prespecify where possible and document all material decisions. |
Quantitative Research Checklist Before Submission
| Check | Question to ask |
| Alignment | Does the quantitative design directly answer the research question and objectives? |
| Variables | Are outcomes, exposures/predictors, group variables, confounders, and operational definitions clear? |
| Population | Is the target population defined, and is the sample appropriate for the intended claim? |
| Sampling | Is the sampling method described honestly, including nonresponse or recruitment limits? |
| Measurement | Are instruments, units, scoring, timing, reliability, validity, and permissions addressed? |
| Design | Is the study described accurately as descriptive, observational, experimental, quasi-experimental, or another design? |
| Ethics | Are consent/access, privacy, secure data handling, and institutional review requirements addressed? |
| Data quality | Are missing data, outliers, coding, duplicates, protocol deviations, and attrition documented? |
| Analysis | Do the descriptive and inferential methods fit the variables, design, sampling structure, and assumptions? |
| Reporting | Are estimates, uncertainty, group sizes, missingness, and key limitations reported clearly? |
| Claims | Are causal, predictive, and generalization claims no stronger than the design permits? |
| Transparency | Could another informed reader understand what was planned, done, analyzed, and changed? |
Frequently Asked Questions
Does quantitative research always require a hypothesis?
No. A descriptive quantitative study may aim to estimate a prevalence, mean, rate, or distribution without testing a predictive hypothesis. Hypotheses are especially useful when the study is designed to test expected differences, relationships, or effects.
Is a survey always quantitative?
No. Surveys can contain closed-ended items that produce structured quantitative data, open-ended items that require qualitative analysis, or both. The method should be classified by the evidence and analysis actually used, not by the word “survey” alone.
How many participants do I need for quantitative research?
There is no universal number. Required sample size depends on the design, effect or precision target, variability, desired statistical power or confidence, number of groups or predictors, sampling structure, and expected missingness. Use a design-specific calculation or seek statistical guidance.
What is the difference between descriptive and inferential statistics?
Descriptive statistics summarize the observed sample. Inferential statistics use sample information, under assumptions, to estimate or test claims about a wider population or data-generating process.
Can quantitative research prove causation?
Some designs can support strong causal conclusions, especially well-conducted randomized experiments, but no method produces causation merely because the data are numerical. Causal interpretation depends on design, implementation, assumptions, bias control, measurement, and analysis.
Is statistical significance the same as importance?
No. A small effect can be statistically detectable in a very large sample, while an important effect may be estimated imprecisely in a small study. Interpret the magnitude, uncertainty, context, and practical meaning rather than relying on a p-value alone.
Final Takeaway
Good quantitative research begins long before a statistical test. It starts by turning a focused question into measurable variables, selecting a design that can support the intended claim, obtaining an appropriate sample, collecting data consistently, and choosing analyses that match the structure of the evidence.
The strongest studies make the chain of reasoning visible. Readers should be able to see how the problem led to the question, how the question led to the variables and design, how the design shaped sampling and measurement, and how the analysis supports – but does not exceed – the conclusions. When that alignment is clear, quantitative results become evidence rather than just numbers
