Points of Significance in Biology - Nature column

http://www.nature.com/nmeth/journal/v10/n9/full/nmeth.2613.html

http://www.nature.com/collections/qghhqm

Since September 2013 Nature Methods has been publishing a monthly column on statistics aimed at providing reseachers in biology with a basic introduction to core statistical concepts and methods, including experimental design. Although targeted at biologists, the articles are useful guides for researchers in other disciplines as well. A continuously updated list of these articles is provided below.

Importance of being uncertain - How samples are used to estimate population statistics and what this means in terms of uncertainty.

Error Bars - The use of error bars to represent uncertainty and advice on how to interpret them.

Significance, P values and t-tests - Introduction to the concept of statistical significance and the one-sample t-test.

Power and sample size - Using statistical power to optimize study design and sample numbers.

Visualizing samples with box plots - Introduction to box plots and their use to illustrate the spread and differences of samples. See also: Kick the bar chart habit and BoxPlotR: a web tool for generation of box plots

Comparing samples—part I - How to use the two-sample t-test to compare either uncorrelated or correlated samples.

Comparing samples—part II - Adjustment and reinterpretation of P values when large numbers of tests are performed.

Nonparametric tests - Use of nonparametric tests to robustly compare skewed or ranked data.

Designing comparative experiments - The first of a series of columns that tackle experimental design shows how a paired design achieves sensitivity and specificity requirements despite biological and technical variability.

Analysis of variance and blocking - Introduction to ANOVA and the importance of blocking in good experimental design to mitigate experimental error and the impact of factors not under study.

Replication - Technical replication reveals technical variation while biological replication is required for biological inference.

Nested designs - Use the relative noise contribution of each layer in nested experimental designs to optimally allocate experimental resources using ANOVA.

Two-factor designs - It is common in biological systems for multiple experimental factors to produce interacting effects on a system. A study design that allows these interactions can increase sensitivity.

Sources of variation - To generalize experimental conclusions to a population, it is critical to sample its variation while using experimental control, randomization, blocking and replication to collect replicable and meaningful results.

Research methods: Know when your numbers are significant

http://www.nature.com/nature/journal/v492/n7428/fig_tab/492180a_T1.html  

When N is only 2 or 3, it would be more transparent to just plot the independent data points, and let the readers interpret the data for themselves, rather than showing possibly misleading P values or error bars and drawing statistical inferences. 

All experimental biologists and all those who review their papers should know what sort of sampling errors are to be expected in common experiments, such as determining the percentages of live and dead cells or counting the number of colonies on a plate or cells in a microscope field. Otherwise, they will not be able to judge their own data critically, or anyone else's.   Table 1: Statistics glossary: Some common statistical concepts and their uses in analysing experimental results.

Term	Meaning	Common uses
N, number of independent samples; t, the t-statistic; p, probability.
Standard deviation (s.d.)	The typical difference between each value and the mean value.	Describing how broadly the sample values are distributed.  s.d. = √−(∑ (x − mean)2/(N − 1))
Standard error of the mean (s.e.m.)	An estimate of how variable the means will be if the experiment is repeated multiple times.	Inferring where the population mean is likely to lie, or whether sets of samples are likely to come from the same population.  s.e.m. = s.d./√−N
Confidence interval (CI; 95%)	With 95% confidence, the population mean will lie in this interval.	To infer where the population mean lies, and to compare two populations.  CI = mean ± s.e.m. × t(N−1)
Independent data	Values from separate experiments of the same type that are not linked.	Testing hypotheses about the population.
Replicate data	Values from experiments where everything is linked as much as possible.	Serves as an internal check on performance of an experiment.
Sampling error	Variation caused by sampling part of a population rather than measuring the whole population.	Can reveal bias in the data (if it is too small) or problems with conduct of the experiment (if it is too big). In binomial distributions (such as live and dead cell counts) the expected s.d. is √−(N × p × (1 − p)); in Poisson dist

Points of significance: Power and sample size

Points of significance: Power and sample size

    Martin Krzywinski  
    & Naomi Altman  

    Nature Methods
    10,
    1139–1140
    (2013)
    doi:10.1038/nmeth.2738

http://www.nature.com/nmeth/journal/v10/n12/full/nmeth.2738.html

Figure 3: Decreasing specificity increases power.

(a) Observations are assumed to be from the null distribution (H₀) with mean μ₀. We reject H₀ for values larger than x^* with an error rate α (red area). (b) The alternative hypothesis (H_A) is the competing scenario with a different mean μ_A. Values sampled from H_A smaller than x^* do not trigger rejection of H₀ and occur at a rate β. Power (sensitivity) is 1 − β (blue area). (c) Relationship of inference errors to x^*. The color key is same as in Figure 1.

Figure 4: Impact of sample (n) and effect size (d) on power.
 

H₀ and H_A are assumed normal with σ = 1. (a) Increasing n decreases the spread of the distribution of sample averages in proportion to 1/√n. Shown are scenarios at n = 1, 3 and 7 for d = 1 and α = 0.05. Right, power as function of n at four different α values for d = 1. The circles correspond to the three scenarios. (b) Power increases with d, making it easier to detect larger effects. The distributions show effect sizes d = 1, 1.5 and 2 for n = 3 and α = 0.05. Right, power as function of d at four different a values for n = 3.

Frequentists vs Bayesian

http://oikosjournal.wordpress.com/2011/10/11/frequentist-vs-bayesian-statistics-resources-to-help-you-choose/

Most ecologists use the frequentist approach. This approach focuses on P(D|H), the probability of the data, given the hypothesis. That is, this approach treats data as random (if you repeated the study, the data might come out differently), and hypotheses as fixed (the hypothesis is either true or false, and so has a probability of either 1 or 0, you just don’t know for sure which it is). This approach is called frequentist because it’s concerned with the frequency with which one expects to observe the data, given some hypothesis about the world. The P values you see in the “Results” sections of most empirical ecology papers are values of P(D|H), where H is usually some “null” hypothesis.

Bayesian statistical approaches are increasingly common in ecology. Bayesian statistics focuses on P(H|D), the probability of the hypothesis, given the data. That is, this approach treats the data as fixed (these are the only data you have) and hypotheses as random (the hypothesis might be true or false, with some probability between 0 and 1). This approach is called Bayesian because you need to use Bayes’ Theorem to calculate P(H|D).

I guess I lean more towards Bayesian statistics! There's probably life on Mars =)

Biological insights from 108 schizophrenia-associated genetic loci

Biological insights from 108 schizophrenia-associated genetic loci 
Abstract: Schizophrenia is a highly heritable disorder. Genetic risk is conferred by a large number of alleles, including common alleles of small effect that might be detected by genome-wide association studies. Here we report a multi-stage schizophrenia genome-wide association study of up to 36,989 cases and 113,075 controls. We identify 128 independent associations spanning 108 conservatively defined loci that meet genome-wide significance, 83 of which have not been previously reported. Associations were enriched among genes expressed in brain, providing biological plausibility for the findings. Many findings have the potential to provide entirely new insights into aetiology, but associations at DRD2 and several genes involved in glutamatergic neurotransmission highlight molecules of known and potential therapeutic relevance to schizophrenia, and are consistent with leading pathophysiological hypotheses. Independent of genes expressed in brain, associations were enriched among genes expressed in tissues that have important roles in immunity, providing support for the speculated link between the immune system and schizophrenia.

Subject terms: Genome-wide association studies
http://www.nature.com/nature/journal/v511/n7510/full/nature13595.html

Genomic inflation factors under polygenic inheritance 
Abstract:  Population structure, including population stratification and cryptic relatedness, can cause spurious associations in genome-wide association studies (GWAS). Usually, the scaled median or mean test statistic for association calculated from multiple single-nucleotide-polymorphisms across the genome is used to assess such effects, and ‘genomic control' can be applied subsequently to adjust test statistics at individual loci by a genomic inflation factor. Published GWAS have clearly shown that there are many loci underlying genetic variation for a wide range of complex diseases and traits, implying that a substantial proportion of the genome should show inflation of the test statistic. Here, we show by theory, simulation and analysis of data that in the absence of population structure and other technical artefacts, but in the presence of polygenic inheritance, substantial genomic inflation is expected. Its magnitude depends on sample size, heritability, linkage disequilibrium structure and the number of causal variants. Our predictions are consistent with empirical observations on height in independent samples of ~4000 and ~133 000 individuals.

Keywords: genome-wide association study, genomic inflation factor, polygenic inheritance
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3137506/

In population genetics, linkage disequilibrium is the non-random association of alleles at two or more loci, that descend from single, ancestral chromosomes
linkage equilibrium D = 0, is when PA * PB = PAB (ie. A is found and B is found)

http://en.wikipedia.org/wiki/Linkage_disequilibrium

Linkage disequilibrium makes tightly linked 
variants strongly correlated producing cost 
savings for association studies



http://www.sph.umich.edu/csg/abecasis/class/666.03.pdf

 Population stratification is the presence of a systematic difference in allele frequencies between subpopulations in a population possibly due to different ancestry, especially in the context of association studies.

The two most widely used approaches to this problem include genomic control, which is a relatively nonparametric method for controlling the inflation of test statistics,[2] and structured association methods,[3] which use genetic information to estimate and control for population structure.

Genomic Control works by using markers that are not linked with the trait in question to correct for any inflation of the statistic caused by population stratification
http://en.wikipedia.org/wiki/Population_stratification 

The Hardy–Weinberg principle states that allele and genotype frequencies in a population will remain constant from generation to generation in the absence of other evolutionary influences.