## SD vs SEM

While the mean and standard deviation are descriptive statistics, the mean and standard error describes bounds for a random sampling process. This difference changes the meaning of what is being reported: a description of variation in measurements vs a statement of uncertainty around the estimate of the mean.

In other words standard error shows how close your sample mean is to the population mean. Standard deviation shows how much individuals within the same sample differ from the sample mean. This also means that standard error should decrease if the sample size increases, as the estimate of the population mean improves. Standard deviation will not be affected by sample size.

Gregory Verleysen, ResearchGate

The SD indicates the dispersion of individual data values around their mean, and should be given any time we report data. The SE is an index of the variability of the means that would be expected if the study were exactly replicated a large number of times. By itself,this measure doesn’t convey much useful information. Its main function is to help construct 95% and 99% CIs, which can supplement statistical significance testing and indicate the range within which the true mean or difference between means maybe found.

Maintaning Standards: Differences between the Standard Deviation and Standard Error, and When to Use Each

The Standard Deviation of the means is called The Standard Error.

Standard deviaton, tells us how the data is distributed around the mean. Standard error, tells us how the mean is distributed. Confidence Intervals are related to standard errors. Since we are trying to interpret the confidence interval of the average value. We are considering how averages (means) are distributed.

## Skewness & Kurtosis

What’s the acceptable range of skewness and kurtosis ?

-2 +2 are usually fine.

(Trochim & Donnelly, 2006; Field, 2000 & 2009; Gravetter & Wallnau, 2014) (George & Mallery, 2010) SPSS for Windows Step by Step: A Simple Guide and Reference, 17.0 update (10a ed.)

It depends on mainly the sample size. Most software packages that compute the skewness and kurtosis, also compute their standard error. Both S = skewness/SE(skewness) and K = kurtosis/SE(kurtosis) are, under the null hypothesis of normality, roughly standard normal distributed. Thus, when |S| > 1.96 the skewness is significantly (alpha=5%) different from zero; the same for |K| > 1.96 and the kurtosis.

Source: Casper J Albers

How to compute SE of skewsness and SE of kurtosis? Roughly,

 1 2 SE(skewness) = SQRT(6/N) SE(kurtosis) = SQRT(24/N)
Published on 10.11.2018 by Mert Bakır with commit 4fa6ba7.
statistics
#math #statistics

Bir küme içerisinden seçilen her bir iki nokta için; bu iki nokta bir doğru ile birleştirildiğinde eğer bu doğru küme içerisinde kalıyorsa bu set convex settir. […] Any two convex set that don’t touch each other(don’t intersect) can be seperated by a simple straight line. …

$$y=mx+b$$ m is the slope of the line. How to find the slope of a line or the equation of a line where you have 2 points? $$\frac{\Delta y}{\Delta x}=\frac{y_1-y_2}{x_1-x_2}$$ […] $f'(x)$ returns the slope of a tangent line to $f(x)$ at $x$. […] $$f(x) = x^3-6x^2+x-5$$, Find the …

Bu yazının amacı linear regresyona detaylı bir giriş yapmaktır. Regresyon analizinin amacı, değişken setleri arasındaki ilişkiyi tanımlamaktır. Bir bağımlı değişkeni, bir ya da birden fazla bağımsız değişkene bağlı olarak tahmin etmek için kullanılan modellerdir. […] Linear Regresyon Nedir? …

Tanımlayıcı istatistiklerden ortalama ve ortanca. Analiz yapılırken iş bu ikisinden hangisinin anlamlı olduğuna geldiğinde sık sık hata yapılmaktadır. Hataların yanısıra, dünyada bu istatistiklerin manipüle edilerek kötüye kullanıldığı örnekler de ne yazık ki çoktur. (bknz: statistical lies) Ne …

Some time ago, I wanted to display image galleries on my Hugo website and searched for Hugo themes for photography and gallery. I can’t say I find much. Then, I met with a javascript library called nanogallery2 which is using another javascript library as an image viewer lightbox2. In this …

Image processing may seem complicated at first but it’s actually easy and definitely worth implementing since it’ll help you decrease page load times. As you probably know, we don’t want to load raw images with huge sizes for small thumbnails or blog-posts. We want to load a small …

I’ve, recently, published a blog post called Perfect Workflow for Publishing Python Notebooks. I talked about some of the benefits of using Rmarkdown and reticulate. In this post, I’ll try HTML widgets and explain how we can embed those in our blog post using nothing but R. […] 1 …

Resume A4 is a side project of mine. It’s one page Hugo Theme that allows you to write your resume in YAML format and keep track of it using git. Also, you can publish it online as a static site using GitLab, GitHub Pages, Netlify, or some other service you are familiar with. A few months …

I’ve been searching for a good workflow for publishing Jupyter or RMarkdown Notebooks as static blog posts. I think I’ve found the optimal solution for my use case. In this post, I’ll explain my workflow and why chose this way with examples. […] In reality my main purpose to …

Plotly is a visualization library that allows us to write code in Python, R, or Julia and generates interactive graphs using Javascript. So, we don’t have to deal with Javascript. You can checkout Plotly gallery, there are interesting works. Anyway, last week, I’ve started learning …