Service overview
Research planning, literature synthesis, methodology, proposals and feasibility work. This service is part of that division and is scoped individually around what you need to learn, decide or publish.
Meta-analysis combines results from several studies into a single quantitative summary and examines why the studies differ. When the studies address the same question with comparable measures, pooling increases precision and can reveal patterns that no single study could show. When they do not, pooling can produce a confident-looking number that means nothing.
Engineering evidence makes this judgement difficult. Tests may follow different standards, specimens may differ in size or preparation, simulations may use different models and outcomes may be reported as means without variances. Responsible meta-analysis in engineering therefore begins with a frank assessment of comparability and treats the statistical machinery as a tool for exploring variation, not just averaging it.
If you plan to publish the outcome, see manuscript & publication support, for example computational & simulation manuscripts or original research article writing.
What this service covers
Problems this service can address
- Primary studies that report results in incompatible forms or units
- Unclear whether pooling is statistically and physically justified
- Publication bias and small-study effects that distort a pooled estimate
Methods and analytical approaches
- Effect-sise selection and unit harmonisation
- Fixed- and random-effects pooling
- Heterogeneity assessment (Q, I-squared, meta-regression)
- Publication-bias diagnostics such as funnel-plot inspection
Applications
- Comparing performance of material treatments across studies
- Pooling experimental results on a technology
- Evidence summaries for design guidance
Relevant engineering disciplines
Scope, inputs and deliverables
Scope of work
- Review of your objectives, constraints and the evidence already available
- Selection of methods suited to the question and the data
- Analysis or synthesis with documented, repeatable steps
- Written outputs you can reuse in a thesis, proposal or report
- Feasibility check on: a defined research question and eligibility criteria
Typical inputs required from you
- A defined research question and eligibility criteria
- The set of candidate studies or a systematic search output
- Preferred effect measure, if any
Deliverables
- Extraction dataset with documented harmonisation rules
- Pooled estimates, forest and funnel plots
- Methods and results write-up suitable for reporting
Highly specialised requests are first checked for feasibility from this information. Please do not send confidential data through the public form; describe it first and agree secure transfer afterwards.
Project workflow and method
- 01Enquiry and requirement assessment
- 02Technical scoping and proposal
- 03Execution
- 04Quality review and delivery, with an agreed round of revisions
Read the full project workflow.
In depth: how the work is done
Deciding whether to pool at all
The first decision is whether the studies are similar enough in design, conditions and outcome definitions for a combined estimate to be meaningful. We examine the question, the range of test conditions and the physical rationale for expecting a common effect. If the studies measure related but different things, a structured narrative synthesis or subgroup analysis is often more honest. Documenting why pooling was or was not appropriate is part of the deliverable, because reviewers rightly challenge this choice.
Effect measures and harmonisation
Common effect measures include standardised mean differences, ratios of means or response ratios, correlation coefficients and, for proportions, log odds ratios. Engineering outcomes with natural units often suit ratio-of-means measures because they express relative change. Where studies report in different units or on different scales, conversion rules are defined and recorded. Missing variances are handled with documented approximations or sensitivity analyses, and the effect of each assumption on the result is checked.
Pooling models and heterogeneity
A fixed-effect model assumes one true effect; a random-effects model assumes a distribution of true effects across studies and is usually more appropriate when conditions differ. Heterogeneity is quantified using Cochran's Q and I-squared and explored with subgroup analysis or meta-regression on moderators such as temperature, specimen size or material class. Prediction intervals are reported alongside confidence intervals because they show the range of effects a new study might observe.
Bias, sensitivity and robustness
Small studies with large effects can be over-represented because null results are less likely to be published. Funnel plots and formal tests give indications but have limited power with few studies, so conclusions are worded with care. Leave-one-out analysis, alternative models and exclusion of low-quality studies test whether the result depends on a few influential inputs. Results that survive these checks are reported with confidence; results that do not are reported as fragile.
Reporting transparently and reproducibly
The extraction dataset, the harmonisation rules and the analysis script form the evidence trail. Reviewers and readers should be able to see which numbers came from which study and how each was transformed. We recommend sharing the dataset as a supplementary file and describing every conversion in plain language. Transparent reporting lets others challenge or update the analysis, which is the strongest sign that a quantitative synthesis was done carefully rather than assembled to reach a preferred conclusion.
Quality control and good practice
Quality-control approach
- Search, selection or analysis steps are documented so another researcher can repeat them.
- Assumptions, exclusions and limitations are stated rather than implied.
- Numbers in text, tables and figures are cross-checked for consistency.
- Conclusions are limited to what the evidence supports.
Common pitfalls this service helps avoid
- Pooling incomparable test conditions. Combining studies with different standards, scales or environments can create an average that describes no real situation.
- Treating I-squared as a verdict. A high heterogeneity statistic signals variation to explain, not an automatic reason to abandon the analysis.
- Ignoring dependent measurements. Multiple outcomes from the same specimen or study should not be treated as independent data points.
- Over-reading publication-bias plots. Funnel asymmetry can arise from true heterogeneity as well as bias, and tests are unreliable with few studies.
What good reporting looks like
A complete meta-analysis report gives the eligibility criteria, the search and selection process, the effect measure and its justification, the extraction rules including how missing data were handled, the model used, a forest plot, heterogeneity statistics with exploration, sensitivity analyses and a discussion of bias and applicability. It states what the pooled result means in engineering terms and where it should not be applied. It does not claim causation beyond what study designs allow, and it makes the extraction dataset available so others can check the numbers.
An illustrative scenario
Hypothetical example written for explanation. It is not a client case, a result or a testimonial.
Suppose several laboratories have reported the effect of a surface treatment on fatigue life of similar alloys. After extraction, the analyst finds that some report mean cycles to failure with standard deviations, while others report only medians. Ratios of means are chosen as the effect measure and conversion rules are documented. A random-effects model gives a pooled ratio with a wide prediction interval, and meta-regression shows that stress amplitude explains part of the heterogeneity. The report therefore recommends design guidance only for the stress range actually tested.
Questions to settle before you begin
- Do the candidate studies measure the same outcome under comparable conditions?
- Which effect measure expresses the result in engineering terms?
- How will I treat studies with missing variances?
- Which moderators could explain differences between studies?
- What will I conclude if heterogeneity is very high?
Key terms
- Effect size
- A standardised measure of the magnitude of a difference or relationship.
- Heterogeneity
- Variation in true effects between studies beyond chance.
- Random-effects model
- A pooling model that allows the underlying effect to vary between studies.
- Forest plot
- A figure showing each study's estimate and the pooled estimate.
- Prediction interval
- The range in which the effect of a new study is expected to fall.
Working together on Research & Academic Consulting projects
Research and academic consulting engagements usually begin with a short conversation and a written summary of the question, the existing evidence and the intended outcome, such as a thesis chapter, a proposal or a journal article. We ask for what you already have, however rough: notes, drafts, data tables and the instructions of the committee or funder. Review is iterative and focuses on reasoning rather than wording, so you should expect questions that challenge assumptions. Authorship, scientific claims and institutional compliance remain yours. Deliverables are written so that you can reuse them directly in your own documents and defend them when asked how a decision was reached.
Frequently asked questions
Can any set of engineering studies be meta-analysed?
No. If outcomes, conditions or measures are too dissimilar, pooling can mislead. In that case we advise a structured narrative synthesis instead and explain why.
How many studies do I need for a meta-analysis?
There is no universal minimum. Two studies can technically be combined, but estimates of heterogeneity and bias are unreliable with few studies, so conclusions must be modest.
Can I combine experimental and simulation studies?
Usually they should be analysed separately because their sources of error differ. A comparison between the two groups can itself be informative if designed carefully.
What software is used?
Analyses can be done with standard statistical environments that support meta-analysis. The choice is guided by the models required and what you need to reproduce the work.
Is a meta-analysis always better than a systematic review alone?
No. If studies are not comparable, a well-conducted systematic review without pooling is the more defensible product.
How is this service scoped and priced?
After your enquiry we review what you need, ask for missing information and send a written scope and quotation. Price depends on complexity, deliverables and timeline. See the project workflow.