Experiment D is very different.
Always show and emphasize the effect size as difference, percent difference, ratio, or correlation coefficient along with its confidence interval. Statistical hypothesis testing is a way to make a crisp decision from one analysis. If the P value is less than a preset value usually 0. This is helpful in quality control and some clinical studies.
It also is useful when you rigorously compare the fits of two scientifically sensible models to your data, and choose one to guide your interpretation of the data and to plan future experiments. Here are five reasons to avoid use of statistical hypothesis testing in experimental research:. The need to make a crisp decision based on one analysis is rare in basic research. A decision about whether or not to place an asterisk on a figure does not count! If you are not planning to make a crisp decision, the whole idea of statistical hypothesis testing is not helpful.
Statistical hypothesis testing has even been called a cult Ziliak and McCloskey The question we want to answer is: Given these data, how likely is the null hypothesis? The question that a P values answers is: Assuming the null hypothesis is true, how unlikely are these data? These two questions are distinct, and so have distinct answers. Scientists who intend to use statistical hypothesis testing often end up not using it.
If the P value is just a bit larger than 0. If you use a P value to make a decision, of course it is possible that you will make the wrong decision. In some cases, the P value will be tiny just by chance, even though the null hypothesis of no difference is actually true. In these cases, a conclusion that a finding is statistically significant is a false positive and you will have made what is called a type I error. If you only look at experiments where the P value is just a tiny bit less than 0. Ioannidis used calculations like these and other considerations to argue that most published research findings are probably false.
If you do obtain a small P value and reject the null hypothesis, you will conclude that the values in the two groups were sampled from different distributions. As noted above, there may be a high chance that you made a false positive conclusion due to random sampling. When thinking about why an effect occurred, ignore the statistical calculations, and instead think about blinding, randomization, positive controls, negative controls, calibration, biases, and other aspects of experimental design. One meaning is that a P value is less than a preset threshold usually 0.
These two meanings are completely different, but are often confused. Only report statistical hypothesis testing and place significance asterisks on figures when you will make a decision based on that one analysis. If you use statistical hypothesis testing to make a decision, state the P value, your preset P value threshold, and your decision. When discussing the possible physiological or clinical impacts of a finding, use other words. Pharmacology journals are full of graphs and tables showing the mean and the standard error of the mean SEM. A quick review. With large samples, the SEM will be tiny even if there is a lot of variability.
The SEM gives information about how precisely you have determined the population mean.
If you want to display the variability among the values, show raw data which is not done often enough in my opinion. If showing the raw data would make the graph hard to read, show instead a box-whisker plot, a frequency distribution, or the mean and SD. Standard error bars do not show variability and do a poor job of showing precision.
The figure plots one data set six ways. The leftmost lane shows a scatter plot of every value, so is the most informative. The next lane shows a box-and-whisker plots showing the range of the data, the quartiles, and the median whiskers can be plotted in various ways, and do not always show the range. The third lane plots the median and quartiles.
This shows less detail, but still demonstrates that the distribution is a bit asymmetrical. The fourth lane plots mean with error bars showing plus or minus one standard deviation. Note that these error bars are, by definition, symmetrical so give you no hint about the asymmetry of the data. The next two lanes are different than the others as they do not show scatter. Instead, they show how precisely we know the population mean, accounting for scatter and sample size. The sixth rightmost lane plots the mean plus or minus one standard error of the mean, which does not show variation and does a poor job of showing precision.
The methods section of every paper should report the methods with enough detail that someone else could reproduce your work. This applies to statistical methods just as it does to experimental methods. When reporting a sample size, explain exactly what you counted.
Did you count replicates in one experiment technical replicates , repeat experiments, the number of studies pooled in a meta-analysis, or something else?
About the Companion Book. A book has been written specifically to accompany this web site. Its title is Statistical Misconceptions. This book discusses each of. Summary. This engaging book helps readers identify and then discard 52 misconceptions about data and statistical summaries. The focus is on major concepts.
If you eliminated any outliers, state how many outliers you eliminated, the rule used to identify them, and a statement whether this rule was chosen before collecting data. When possible, report the P value up to at least a few digits of precision, rather than just stating whether the P value is less than or greater than an arbitrary threshold.
For each P value, state the null hypothesis it tests if there is any possible ambiguity. When reporting a P value that compares two groups, state whether the P value is one- or two-tailed. If you report a one-tailed P value, state that you recorded a prediction for the direction of the effect for example increase or decrease before you collected any data and what this prediction was. If you did not record such a prediction, report a two-tailed P value.
Explain the details of the statistical methods you used.
For example, if you fit a curve using nonlinear regression, explain precisely which model you fit to the data and whether and how data were weighted. Also state the full version number and platform of the software you use. Consider posting files containing both the raw data and the analyses so other investigators can see the details. The physicist E. In these fields, statistical analysis may not be necessary.
But if you work in a field with a lower signal-to-noise ratio, or are trying to compare the fits of alternative models that do not differ all that much, you need statistical analyses to properly quantify your confidence in your conclusions. The suggestions I propose in this commentary can all be summarized simply: If you are going to analyze your data using statistical methods, then plan the methods carefully, do the analyses seriously, and report the data, methods, and results completely.
The first argument 1. This commentary evolved from multiple conversations between the author and editors of several pharmacology journals. This work represents solely the opinions of the author. Publication of this article does not represent an endorsement of GraphPad Software. National Center for Biotechnology Information , U.
Naunyn-Schmiedeberg's Archives of Pharmacology. Naunyn Schmiedebergs Arch Pharmacol. Published online Sep Harvey J. Motulsky GraphPad Software Inc. Author information Article notes Copyright and License information Disclaimer.
GraphPad Software Inc. Motulsky, Email: moc. Corresponding author. Received Aug 8; Accepted Aug The license does not allow the distribution of modified versions of the article. This article has been cited by other articles in PMC. Abstract Ideally, any experienced investigator with the right tools should be able to reproduce a finding published in a peer-reviewed biomedical science journal.
Introduction Ideally, any experienced investigator with the right tools should be able to reproduce a finding published in a peer-reviewed biomedical science journal. Misconception 1: P-Hacking is OK Statistical results can only be interpreted at face value when every choice in data analysis was performed exactly as planned and documented as part of the experimental design.
Open in a separate window. Table 1 Identical P values with very different interpretations.
asvilaligh.tk Those data simply do not help answer your scientific question Similarly, experiments C and D have identical P values, but should be interpreted differently. My suggestions for authors: Always show and emphasize the effect size as difference, percent difference, ratio, or correlation coefficient along with its confidence interval. Consider omitting reporting of P values. Here are five reasons to avoid use of statistical hypothesis testing in experimental research: The need to make a crisp decision based on one analysis is rare in basic research. Misconception 4: the standard error of the mean quantifies variability Pharmacology journals are full of graphs and tables showing the mean and the standard error of the mean SEM.
Misconception 5: you do not need to report the details The methods section of every paper should report the methods with enough detail that someone else could reproduce your work. My suggestions for authors: When reporting a sample size, explain exactly what you counted. Summary The physicist E. References Anonymous Trouble at the lab. Raise standards for preclinical cancer research.