[STATISTICS] Introduction to Statistcal Analysis/Introduction to Statistical Analysis in Python.ipynb

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    "![title](header.png)"
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   "source": [
    "# What is Statistical Analysis?"
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    "Statistical Analysis in Python lets us draw formal conclusions from data using mathematical tests. These tests depend on a series of assumptions to work, but if they are met, can give us some powerful insight."
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   "source": [
    "# Why Python for Statistics?"
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    "R - another programming language - is purpose built, and made for statistics. So why use Python instead of R? Python allows us more flexibility with our data; Python has more options for importing data, working with controllers and image analysis that makes it more versitile than R. Prehaps more importantly is the size of the community - Python has a very large following and sees regular updates and improvements to it's ecosystem, moreso than R."
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   "source": [
    "# What libraries?"
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    "There are a number of libraries that are useful for statistical analysis in Python:\n",
    "\n",
    "* numpy and pandas give us a nice format for us to analyse our data in.\n",
    "* matplotlib and seaborn give us cool visualisation options.\n",
    "* scipy and statsmodels give us good <i>frequentist</i> options for analysis.\n",
    "* PyMC gives us good <i>bayesian</i> tools for analysis."
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   "source": [
    "# Frequentist vs Bayesian statistics"
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    "These are two different philosophies about what statistics and probability mean, resulting in different methods and outcomes. A frequentist believes in probability being the result of \"long term\" distributions, and a bayesian believes in using new data to reach new conclusions. A good analogy for this is what would happen if a frequentist and a bayesian lost their phone in their house, and rung it to find it - a frequentist would trust the sound first, whereas a bayesian would trust their knowledge of where they normally leave their phone.\n",
    "\n",
    "I recommend trying both out and seeing which one works for you - Python has more support for frequentist analysis but that shouldn't put you off trying bayesian analysis!"
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   "source": [
    "# What Problems Is This Useful For?"
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    "Strict statistical testing is useful for academics to test hypothesis in experiments and other studies - if we want to definitively test if two means are equal (eg does an antidepressant improve happiness scores over a control group?), how correlated two variables are (eg the concentration of a substance versus it's fluorescence), and if a group of means are different (eg different material elasticities)."
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