Currently the two forms of DLT predominating are blockchain and directed acyclic graphs (DAGs). While quite distinct from one another, in theory the two technologies are intended to serve similar purposes, or were developed to address the same goals. In practice, blockchain and DAGs may have optimal use-cases that differ in nature from one another, or be better equipped to serve different goals – the nuance of which to be determined on a case by case basis.

Bitcoin is the first known example of blockchain, however blockchain goes well beyond the realms of bitcoin and cryptocurrency use cases. One of the earliest and currently predominating DAG DLT platforms is IOTA which has proved itself in a plethora of use cases that go well beyond what blockchain could currently achieve, particularly within the realm of the internet of things (IOT). Infact Iota has been operating an industry data marketplace since 2017 which makes it possible to store, sell via micro-tansactions and access data streams via web browser. For the purposes of this article we will focus on DLT applications in general and include use-cases in which blockchain or DAGs can be employed interchangeably. Before we begin, what is Distributed Ledger  technology?

DLT can address the problem of duplicate records in study data or patient records, make longitudinal data collection more consistent and reliable across multiple life cycles. Many disparate stakeholders, from doctor to insurer or researcher, can share in the same patient data source while maintaining patient privacy and improving data security. Patients can retain access to the data and decide with whom to share it with, which clinical studies to participate in and when to give or withdraw consent.

DLT, such as blockchain or DAGs, can improve collaboration by making the sharing of technical knowledge easier and centralising data or medical records, in the sense that they are located on the same platform as every other transaction taking place. This results in easier shared access by key stakeholders, shortening of negotiation cycles due to improved coordination and making established clinical research processes more consistent and replicable.

From a statisticians perspective, DLT should result in data of higher integrity which yields statistical analysis of greater accuracy and produces research with more reliable results that can be better replicated and validated in future research. Clinical studies will be streamlined due to the removal of much bureaucracy and therefore more time and cost effective to implement as a whole. This is particularly important in a micro-environment with many moving parts and disparate stakeholders such as the clinical trials landscape.

​
References and further reading:

From Clinical Trials to Highly Trustable Clinical Trials: Blockchain in Clinical Trials, a Game Changer for Improving Transparency?
https://www.frontiersin.org/articles/10.3389/fbloc.2019.00023/full#h4

Clinical Trials of Blockchain
https://www.phusewiki.org/docs/Frankfut%20Connect%202018/TT/Papers/TT18-1-paper-clinical-trials-on-blockhain-v10-19339.pdf

Blockchain technology for improving clinical research quality
https://trialsjournal.biomedcentral.com/articles/10.1186/s13063-017-2035-z

Blockchain to Blockchains in Life Sciences and Health Care
https://www2.deloitte.com/content/dam/Deloitte/us/Documents/life-sciences-health-care/us-lshc-tech-trends2-blockchain.pdf

Introduction
 
The misinterpretation of statistics or even the “mis”-analysis of data can occur for a variety of reasons and to a variety of ends. This article will focus on one such phenomenon contributing to the drawing of faulty conclusion from data – Simpson’s Paradox.

At times a situation arises where the outcomes of a clinical research study depict the inverse of expected (or essentially correct) outcomes. Depending upon the statistical approach, this could affect means, proportions or relational trends among other statistics.
Some examples of this occurrence are a negative difference when a positive difference was anticipated, a positive trend when a negative one would have been more intuitive – or vice versa. Another example commonly pertains to the cross tabulation of proportions, where condition A is proportionally greater over all, yet when stratified by a third variable, condition B is greater in all cases . All of these examples can be said to be instances of Simpson’s paradox. Essentially Simpson’s paradox represents the possibility of supporting opposing hypotheses – with the same data. Simpson’s paradox can be said to occur due to the effects of confounding, where a confounding variable is characterised by being related to both the independent variable and the outcome variable, and unevenly distributed across levels of the independent variable. Simpson’s paradox can also occur without confounding in the context of non-collapsability. For more information on the nuances of confounding versus non-collapsability in the context of Simpson’s paradox, see here.

 In a sense, Simpson’s paradox is merely an apparent paradox, and can be more accurately described as a form of bias. This bias most often results from a lack of insight into how an unknown lurking variable, so to speak, is impacting upon the relationship between two variables of interest. Simpson’s paradox highlights the fact that taking data at face value and utilising it to inform clinical decision making can often be highly misleading. The chances of Simpson’s paradox (or bias) impacting the statistical analysis can be greatly reduced in many cases by a careful approach that has been informed by proper knowledge of the subject matter. This highlights the benefit of close collaboration between researcher and statistician in informing an optimal statistical methodology that can be adapted on a per case basis.

The following three part series explores hypothetical clinical research scenarios in which Simpson’s paradox can manifest.

​Scenario and Example

A nutritionist would like to investigate the relationships between diet and negative health outcomes. As higher weight has been previously associated with negative health outcomes, the research sets out to investigate the extent to which increased caloric intake contributes to weight gain. In researching the relationship between calorie intake and weight gain for a particular dietary regime, the nutritionist uncovers a rather unanticipated negative trend. As caloric intake increases the weight of participants appears to go down. The nutritionist therefore starts recommending higher calorie intake as a way to dramatically lose weight. Weight does appear to go down with calorie intake, however if we stratify the data by different age groupings, a positive trend between weight and calorie intake emerges for each age group. While overall elderly have the lowest calorie intake, they also have the highest weight, and teens have the highest calorie intake but the lowest weight, this accounts for the negative trend but does not give an honest picture of the impact of calories on weight. In order to gain an accurate picture of the relationship between weight and calorie intake we have to know which variable to group or stratify the data by, and in this case it’s age. Once the data is stratified by five separate age categories a positive trend between calories and weight emerges in each of the 5 categories. In general, the answer to which variable to stratify by or control for isn’t typically this obvious and in most cases and requires some theoretical background and a thorough examination of the available data including associated variables for which the information is at hand.
​
​
Remedy
​
In the above example, age shows a negative relationship to the independent variable, calories, but a positive relationship to the dependent variable, weight. It is for this reason that a bit of data exploration and assumption checking before any hypothesis testing is so essential. Even with these practices in place it is possible to overlook the source of confounding and caution is always encouraged.
 
Randomisation and Stratification:
In the context of a randomised controlled trial (RTC), the data should be randomly assigned to treatment groups as well as stratified by any pertinent demographic and other factors so that these are evenly distributed across treatment arms (levels of the independent variable). This approach can help to minimise, although not eliminate the chances of bias occurring in any such statistical context, predictive modelling or otherwise.

Linear Structural Equation Modelling:
 If the data at hand is not randomised but observational, a different approach should be taken to detect causal effects in light of potential confounding or non-collapsability. One such approach is linear structural equation modelling where each variable is generated as a linear function of it’s parents, using a directed acyclic graph (DAG) with weighted edges. This is a more sophisticated and ideal approach to simply adjusting for x number of variables, which is needed in the absence of a randomisation protocol.

Heirachical regression:
This example illustrated an apparent negative trend of the overall data masking a positive trend In each individual subgroup, in practice, the reverse can also occur.
In order to avoid drawing misguided conclusion from the data the correct statistical approach must be entertained, a hierarchical regression controlling for a number of potential confounding factors could avoid drawing wrong conclusion due to Simpson’s paradox.

Article: Sarah Seppelt Baker

Reference:
The Simpson’s paradox unraveled, Hernan, M, Clayton, D, Keiding, N., International Journal of Epidemiology, 2011.

​
When we take a closer look, the picture changes. It turns out the clinical trial team forgot to take into account the patients stage of disease progression at the commencement of treatment. The table below shown that drug A was allocated to far more patients with stage II cancer (79.2%) and drug B was allocated to far more patients with stage IV cancer (79.8%). 

​
The chi-square statistic for the difference in remission rates between treatment groups for patients with stage IV disease progression at treatment outset is 13.3473. The p-value is .000259. The result is significant at p < .05.
​

Unfortunately the analysis of tabulated data is no less prone to bias in results akin to Simpson’s Paradox than continuous data. Given that stage II cancer is easier to treat than stage IV, this has given drug A an unfair advantage and has naturally lead to a higher remission rate overall for drug A. When the treatment groups are divided by disease progression categories and reanalysed, we can see that remission rates are higher for drug B in both stage II and stage IV baseline disease progression. The resulting chi squared statistics are wildly different to the first and statistically significant in the opposite direction to the first analysis.  In causal terms, stage of disease progression affects difficulty of treatment and likelihood of remission. Patients at a more advanced stage of disease, ie stage IV, will be harder to treat than patients at stage II. In order for a fair comparison between two treatments, patients stage of disease progression needs to be taken into account. In addition to this some drugs may be more efficacious at one stage or the other, independent of the overall probabilities of achieving remission at either stage. 

Remedy

Randomisation and Stratification:
​Of course in this scenario, stage of disease progression is not the only variable that needs to be accounted for in order to insure against biased results. Demographic variables such as age, sex socio-economic status and geographic location are some examples of variables that should be controlled for in any similar analysis. As with the scenario in part 1, this can be achieved is through stratified random allocation of patients to treatment groups at the outset of the study. Using a randomised controlled trial design where subjects are randomly allocated to each treatment group as well as stratified by pertinent demographic and diagnostic variables will reduce the chances of inaccurate study results occurring due to bias.

Further examples of Simpson’s Paradox in 2 x 2 tables

Simpson’s paradox in case control and cohort studies

Case control and cohort studies also involve analyses which rely on the 2×2 table. The calculation of their corresponding measures of association the odds ratio and relative risk, respectively, is unsurprisingly not immune to the effect of bias and in much the same way as the chi square example above. This time, a reversed odds ratio or relative risk in the opposite direction can occur if the pertinent bias has not been accounted and controlled for.

Simpson’s paradox in meta-analysis of case control studies

Following on from the example above, this form of bias can pose further problems in the context of meta-analysis. When combining results from numerous case control studies the confounders in question may or may not have been identified or controlled for consistently across all studies and some studies will likely have identified different confounders to the same variable of interest. The odds ratios produced by the different studies can therefore be incompatible and lead to erroneous conclusions. Meta-analysis can therefore fall prey to ecological fallacy as a result of systematic bias, where the odds ratio for the combined studies is in the opposite direction to the odds ratios of the separate studies. Imbalance in treatment arm size has also been found to act as a confounder in the context of meta-analysis of randomised controlled trials. Other methodological differences between studies may also be at play, such as differences in follow-up times between studies or a very low proportion of observed events occurring in some studies, potentially due to a shorted follow-up time.

That’s not to say that meta-analysis cannot be performed on these studies, inter-study variation is of-course more common than not, as with all other analytical contexts it is necessary to proceed with a high level of caution and attention to detail. On the whole an approach of simply pooling study results is not reliable, the use of more sophisticated meta-analytic techniques, such as random effects models or Bayesian random effects models that use a Markov chain algorithm for estimating the posterior distributions, are required to mitigate inherent limitations of the meta-analytic approach. Random-effects models assume the presence of study-specific variance which is a latent variable to be partitioned. Bayesian random-effects models can come in parametric, non-parametric or semi-parametric varieties, referring to the shape of the distributions of study-specific effects.
​​
For more information on Simpson’s paradox in meta-analysis, see here.

https://bmcmedresmethodol.biomedcentral.com/articles/10.1186/1471-2288-8-34

For more information on how to minimise bias in meta-analysis, see here.

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3868184/

https://onlinelibrary.wiley.com/doi/abs/10.1002/sim.4780110202

​

Simpson’s Paradox & Cox Proportional Hazard Models
​

​Scenario and example
 
A 2017 paper describes a scenario whereby the death rate due to tuberculosis was lower in Richmond than New York for both African-Americans and for Caucasian-Americans, yet lower in New York than Richmond when the two ethnic groups were combined.
For more details on this example as well as the mathematics behind it see here.
For more examples of Simpson’s paradox in Cox regression see here.

Site specific bias

Factors contributing to bias in survival models can be different to those in more straightforward contexts. Many clinical and epidemiological studies include data from multiple sites. More often than not there is heterogeneity across sites. This heterogeneity can come is various forms and can result in within and between–site clustering, or correlation, of observations on site specific variables. This clustering, if not controlled for, can lead to Simpson’s paradox in the form of hazard rate reversal, across some or all of time T, and has been found to be a common explanation of the phenomenon in this context. Site clustering can occur on the patient level, for example, due to site specific selection procedures for the recruitment of patients (lead by the principal investigators individual to each site), or differences in site specific treatment protocols. Site specific differences can occur intra or internationally and in the international case can be due, for example, to differences in national treatment guidelines or differences in drug availability between countries. Resource availability can also differ between sites whether intra or internationally. In any time to event analysis involving multiple sites (such as the Cox regression model) a site-level effect should be taken into account and controlled for in order to avoid bias-related inferential errors.
 

​
Remedy
 

Cox regression Model including site as a fixed covariate:
Site should be included as a covariate in order to account for site specific dependence of observations.

Cox regression Model treating site as a stratification variable:
In cases where one or more covariates violate the Proportional Hazards (PH) assumption as indicated by a lack of independence of scaled Schonefeld residuals to time, stratification may be more appropriate. Another option in this case is to add a time-varying covariate to the model. The choice made in this regard will depend on the sampling nuances of each particular study.

Cox shared frailty model:
In specific conditions the Cox shared frailty model may be more appropriate. This approach involves treating subjects from the same site as having the same frailty and requires that each subjects is not clustered across more than one level two unit. While it is not appropriate for multi-membership multi-level data, it can be useful for more straight forward scenarios.

In tailoring the approach to the specifics of the data, appropriate model adjustments should produce hazard ratios that more accurately estimate the true risk.

​

With any postulated statistical model it is imperative to assess and validate the model fit before concluding in favour of the integrity of the model and interpreting results. The acceptable way to do this across all structural equation models is the chi squared (χ²) statistic.

A statistically significant χ² statistic is indicative of the following:

• A systematically miss-specified model with the degree of misspecification a function of the χ² value.
• The set of parameters specified in the model do not adequately fit the data and thus that the parameter estimates of the model are inaccurate. As χ² operates on the same statistical principles as the parameter estimation, it follows that in order to trust the parameter estimates of the model we must also trust the χ², or vice versa.

•  As a consequence there is a need for an investigation of where these misspecification have occurred and a potential readjustment of the model to improve its accuracy.

While one or more incorrect hypotheses may have caused the model misspecification, the misspecification could equally have resulted from other causes. It is important to thus investigate the causes of a significant model fit test ​. In order to properly do this the following should be evaluated:

• Heterogeneity:
•  Does the causal model vary between sub groups of subjects?
• Are there any intervening within subject variables?

• Independence:
• Are the observations truly independent?

• Latent variable models involve two key assumptions: that all manifest variables are independent after controlling for any latent variables and, an individual’s position on a manifest variable is the result of that individual’s position on the corresponding latent variable (3).

• Multivariate normality:
• Is the multivariate normality assumption satisfied?

​
The study:

A 2015 meta-analysis of 75 latent variable studies drawn from 11 psychology journals has highlighted a tendency in clinical researchers to ignore the χ² exact fit statistic when reporting and interpreting the results of the statistical analysis of latent variable models (4).
97% of papers reported at least one appropriate model, despite the fact that 80% of these did not pass the criteria for model fit and the χ² exact fit statistic was ignored. Only 2% of overall studies concluded that the model doesn’t fit at all and one of these interpreted a model anyway (4).
Reasons for ignoring the model fit statistic: overly sensitive to sample size, penalises models when number of variables is high, general objection to the logic of exact fit hypothesis. Overall broach consensus of preference for Approximate fit indices (AFI).
AFI are instead applied in these papers to justify the models. This typically leads to questionable conclusions. In all just 41% of studies reported χ² model fit results. 40% of the studies that failed to report a p value for the reported χ² value did report a degrees of freedom. When this degrees of freedom was used to cross check the unreported p values, all non-reported p values were in fact significant.
The model fit function was usually generated through maximum likelihood methods, however 43% of studies failed to report which fit function was used.
A further tendency to accept the approximate fit hypothesis when in fact there was no or little evidence of approximate fit. This lack of thorough model examination empirical evidence of questionable validity. 30% of studies showed custom selection of more lax cut-off criteria for the approximate fit statistics than was conventionally acceptable, while 53% failed to report on cut-off criteria at all.
Assumption testing for univariate normality was assessed in only 24% of studies (4).
Further explanation of  χ² and model fit:

The larger the data set the more that increasingly trivial discrepancies are detected as a source of model misspecification. This does not mean that trivial discrepancies become more important to the model fit calculation, it means that the level of certainty with which these discrepancies can be considered important has increased. In other words, the statistical power has increased. Model misspecification can be the result of both theoretically relevant and irrelevant/peripheral causal factors which both need to be equally addressed. A significant model fit statistic indicating model misspecification is not trivial just because the causes of the misspecification are trivial. It is instead the case that trivial causes are having a significant effect and thus there is a significant need for them to be addressed. The χ² model fit test is the most sensitive way to detect misspecification in latent variable models and should be adhered to above other methods even when sample size is high. In the structural equation modelling context of multiple hypotheses, a rejection of model fit does not result in the necessary rejection of each of the models hypotheses (4).
Problems with AFI:

The AFI statistic does provide a conceptually heterogeneous set of fit indices for each hypothesis, however none of these indices are accompanied by a critical value or significance level and all except one arise from unknown distributions. The fit indices are a function of χ² but unlike the χ²  fit statistic they do not have a verified statistical basis nor do they present a statistically rigorous test of model fit. Despite this satisfactory AFI values across hypotheses are being used to justify the invalidity of a significant χ² test.
Mote Carlo simulations of AFI concluded that it is not possible to determine universal cut off criteria in any forms of model tested.  Using AFI, the probability of correctly rejecting a mis-specified model decreased with increasing sample size. This is the inverse of the  statistic. Another problem with AFI compared to χ²  is that the more severe the model misspecification or correlated errors, the more unpredictable the AFI become. Again this is the inverse of what happens with the χ²  statistic (4).
The take away:

Based on the meta-analysis the following best practice principles are recommended in addition to adequate attention to the statistical assumptions of heterogeneity, independence and multivariate normality outlined above:

1. Pay attention to distributional assumptions.
2. Have a theoretical justification for your model.
3. Avoid post hoc model modifications such as dropping indicators, allowing cross-loadings and correlated error terms.
4. Avoid confirmation bias.
5. Use an adequate estimation method.
6. Recognise the existence of equivalence models.
7. Justify causal inferences.
8. Use clear reporting that is not selective.

Image:  

​Michael Eid, Tanja Kutscher,  Stability of Happiness, 2014 Chapter 13 – Statistical Models for Analyzing Stability and Change in Happiness
​https://www.sciencedirect.com/science/article/pii/B9780124114784000138

​References:
(1). Latent Variables in Psychology and the Social Sciences
https://www.annualreviews.org/doi/full/10.1146/annurev.psych.53.100901.135239#f1

(2) Structural equation modelling and its application to network analysis in functional brain imaging
https://onlinelibrary.wiley.com/doi/abs/10.1002/hbm.460020104

(3) Chapter 7: Assumptions in Structural Equation modelling
https://psycnet.apa.org/record/2012-16551-007

(4) A cautionary note on testing latent variable models
https://www.frontiersin.org/articles/10.3389/fpsyg.2015.01715/full

“…. half of current published peer-reviewed clinical research papers … contain at least one statistical error… When just surgical related papers were analysed, 78% were found to contain statistical errors.”

Peer reviewed published research is the go to source for clinicians and researchers to advance their knowledge on the topic at hand. It also currently the most reliable way available to do this. The rate of change in standard care and exponential development and implementation of innovative treatments and styles of patient involvement makes keeping up with the latest research paramount. (1)

Unfortunately, almost half of current published peer-reviewed clinical research papers have been shown to contain at least one statistical error, likely resulting in incorrect research conclusions being drawn from the results. When just surgical related papers were analysed, 78% were found to contain statistical errors due to incorrect application of statistical methods. (1)

Compared to 20 years ago all forms of medical research require the application of increasingly complex methodology, acquire increasingly varied forms of data, and require increasingly sophisticated approaches to statistical analysis. Subsequently the meta-analyses required to synthesise these clinical studies are increasingly advanced. Analytical techniques that would have previously sufficed and are still widely taught are now no longer sufficient to address these changes. (1)

The number of peer reviewed clinical research publications has increased over the past 12 years. Parallel to this, the statistical analyses contained in these papers are increasingly complex, as is the sophistication with which they are applied. For example, t tests and descriptive statistics were the go to statistical methodology for many highly regarded articles published in the 1970’s and 80’s. To rely on those techniques today would be insufficient, both in terms of being scientifically satisfying and in, in all likelihood, in meeting the current peer-review standards. (1)

Despite this, some concerning research has noted that these basic parametric techniques are actually currently still being misunderstood and misapplied reasonably frequently in contemporary research. They are also being increasingly relied upon (in line with the increase in research output) when in fact more sophisticated and modern analytic techniques would be better equipped and more robust in answering given research questions. (1)

Another contributing factor to statistical errors is of course ethical in nature. An recent online survey consulting biostatisticians in America revealed that inappropriate requests to change or delete data to support a hypothesis were common, as was the desire to mould the interpretation of statistical results of to fit in with expectations and established hypotheses, rather than interpreting results impartially. Ignoring violations of statistical assumptions that would deem to chosen statistical test inappropriate, and not reporting missing data that would bias results were other non-ethical requests that were reported. (2)

The use of incorrect statistical methodology and tests leads to incorrect conclusions being widely published in peer reviewed journals. Due to the reliance of clinical practitioners and researchers on these conclusions, to inform clinical practice and research directions respectively, the end result is a stunting of knowledge and a proliferation of unhelpful practices which can harm patients. (1)

Often these errors are a result of clinicians performing statistical analyses themselves without first consulting a biostatistician to design the study, assess the data and perform any analyses in an appropriately nuanced manner. Another problem can arise when researchers rely on the statistical techniques of a previously published peer-reviewed paper on the same topic. It is often not immediately apparent whether a statistician has been consulted on this established paper. Thus it is not necessarily certain whether the established paper has taken the best approach to begin with. This typically does not stop it becoming a benchmark for future comparable studies or deliberate replications. Further to this it can very often be the case that the statistical methods used have since been improved upon and other more advanced or more robust methods are now available. It can also be the case that small differences in the study design or collected data between the established study and the present study mean that the techniques used in the established study are not the most optimal techniques to address the statistical needs of present study, even if the research question is the same or very similar.

Another common scenario which can lead to the implementation of non-ideal statistical practices is under-budgeting for biostatisticians on research grant applications. Often biostatisticians are on multiple grants, each with a fairly low amount of funding allocated to the statistical component due to tight or under budgeting. This limits the statistician’s ability to focus substantially on a specific area and make a more meaningful contribution in that domain. A lack of focus prevents them from becoming a expert at this particular niche and engage in innovation.This in turn can limit the quality of the science as well as the career development of the statistician.

In order to reform and improve the state and quality of clinical and other research today, institutions and individuals must assign more value to the role of statisticians in all stages of the research process. Two ways to do this are increased budgeting for and in turn increased collaboration with statistical professionals.

​
References:

(1) https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6106004/

​(2) https://annals.org/aim/article-abstract/2706170/researcher-requests-inappropriate-analysis-reporting-u-s-survey-consulting-biostatisticians

For the purposes of Transforming Skewed Data, the degree of skewness of a skewed distribution can be classified as moderate, high or extreme. Depending upon the degree of skewness and whether the direction of skewness is positive or negative, a different approach to transformation is often required. As a short-cut, uni-modal distributions can be roughly classified into the following transformation categories:

​​Starting with a more conservative option, the square root transformation, a major improvement in the distribution is achieved already. The extreme observations contained in the right tail are now more visible. The right tail has been pulled in considerably and a left tail has been introduced. The kurtosis of the distribution has reduced by more than two thirds.

Some thing to note is that in this case the log transformation has caused data that was previously greater than zero to now be located on both sides of the number line. ​Depending upon the context, data containing zero may become problematic when interpreting or calculating the confidence intervals of un-back-transformed data.  As  log(1)=0,  any data containing values <=1 can be made >0 by adding a constant to the original data so that the minimum raw value becomes >1 . Reporting un-back-transformed data can be fraught at the best of times so back-transformation of transformed data is recommended. Further information on back-transformation can be found here. 
​
Adding a constant to data is not without it’s impact on the transformation. As the below example illustrates the effectiveness of the log transformation on the above sales data is effectively diminished in this case by the addition of a constant to the original data.
​

Taking the transformation a step further and applying the inverse transformation to the sales + constant data, again, leads to a less optimal result for this particular set of data – indicating that the skewness of the original data is not quite extreme enough to benefit from the inverse transformation.
​

There are many varieties of distribution, the below diagram depicting only the most frequently observed. If common data transformations have not adequately ameliorated your skewness, it may be more reasonable to select a non-parametric hypothesis test that is based on an alternate distribution.
​
​

SAS syntax can differ based on whether a remote versus local server is used. An example of a local server is the computer you are physically using. When you have SAS installed on the PC you are using, you are accessing it locally. A remote server, on the other hand, allows you to access SAS without having SAS installed on your PC.

Client software such as Citrix Receiver, allows you to access SAS, and other software, from a remote server. Citrix Receiver is often used by university students, new and/or light users. SAS requires different syntax in order to enable the remote server to access data files on a local computer.
For the purpose of this example we are assuming that the data file we wish to access is located, locally, on a drive of the computer we are using.

It can be difficult to find the syntax for this on Google, where search results deal more with accessing remote data (libraries) using local SAS than the other way around. This can be a source of frustration for new users and SAS Technical Support are not always able to advise on the specifics of using SAS via Citrix Receiver.

The “INFILE”statement and the “PROC IMPORT” statement are two popular options for reading a data file into SAS. INFILE offers the greater flexibility and control, by way of manual specification of data characteristics. PROC IMPORT offers greater automation, in some cases at the risk of formatting error. The INFILE statement must always be used in the context of a DATA step, whereas PROC IMPORT acts as a stand-alone procedure. The ​document below shows syntax for the INFILE statement and PROC IMPORT procedure for local SAS compared to access via Citrix Receiver.

​In SAS University Edition data file inputing difficulties can occur for a different reason. In order for the LIBNAME statement to run without error, a shared folder must first be defined. If you are using SAS University Edition, and experiencing an error when inputting data, the following videos may be helpful:
How to Set LIBNAME File Path (SAS University Edition) 
Accessing Data Files Via Citrix Receiver: for SAS University Edition

Troubleshooting check-list:

• Was the “libref” appropriately assigned?
• Was the file location referred to appropriately based on the user context?
• ​Was the correct data file extension used?

While impractical for larger data sets, if all else fails, one can copy and paste the data from a data file into SAS using the ‘DATALINES’ function.

​