01_chapter1.Rmd

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# Introduction {#ch1}

> "So never lose an opportunity of urging a practical beginning, however small, for it is wonderful how often in such matters the mustard-seed germinates and roots itself." 
>
> --- Florence Nightingale


<div class="objective-container">
<div class="objectives"> Learning objectives </div>
1. Describe the field of statistics and its importance in scientific inquiry  
2. Learn the scientific method, its purpose, and its connection to statistics
3. Understand the concepts in the general statistical framework
</div>

## Statistics and Evidence-based Research {#ch1_s1}

There are many definitions of statistics: 

* the science of learning from experiences
* the study of collecting, analyzing, and interpreting data
* the mathematics of uncertainty
* a required college course designed to make everyone miserable

All of these definitions hold a degree truth (some more than others -- we'll let you 
guess which `r emo::ji("wink")`). Statistics is a highly versatile field, with methods 
applicable to and used by a wide variety of disciplines. The importance of the
field of statistics lies in it's ability to quantify our uncertainty about a 
potential outcome -- such as the most likely cause and treatment for a headache.
Almost everything in life is associated with some uncertainty -- the weather, 
your career, the connection between your genetics and your response to certain
medications; however, just because something isn't known with 100% certainty 
doesn't mean we can't understand it better. Statistics helps us understand the 
world better by allowing us to quantify our uncertainty, describe associations 
between phenomena, and make informed decisions.

And how exactly do researchers use statistics to quantify their uncertainty? 
Well, this is achieved by collecting data, or evidence, about whatever process
is of interest. For example, if you want to know how likely it is to rain 
tomorrow, you might look at the weather in your location the past few days.
Since rain can travel, you might also look at the recent weather in the surrounding
areas. You could also evaluate historical weather records to determine if
this season is known for being particularly rainy or dry in the past. These are
all various examples of data you can collect to inform your weather prediction.
In scientific research, data is obtained and investigated through statistical
inquiry to help answer important questions: 

* Which drug should a doctor prescribe to treat an illness?  
* Can we predict the longevity of the national population to inform government decisions regarding Social Security?  
* What factors increase the risk of an individual developing coronary heart disease?  

These questions are too important to be left to opinion, superstition, or 
conjecture. Consequently, there has been a tremendous push for objective, 
**evidence-based** decision making in medicine, public health, and policy making. 
Statistics and biostatistics are the sciences that allows us to make these difficult
decisions. When studying humans, we can't control every aspect of their life, 
such as what they eat or where they work. There are ethical considerations - if 
we wanted to research the effects of smoking on lung cancer, we would not be 
able to force people to smoke (or not). Humans are also incredibly diverse and 
variable, not to mention expensive to perform research upon. Despite these 
issues, there is a moral imperative to make decisions on potentially life-saving
therapies as fast as possible. To make evidence-based conclusions, we need to 
collect, process, analyze, and interpret data in order to draw conclusions in an 
objective manner. 

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<div class="definition-container">
<div class="definition"> &nbsp; </div>
<div class="text">
**Evidence-based practice:** <em> Using sound research findings based on observed or collected data to make decisions </em>
</div>
</div>


## Scientific Method {#ch1_s2}

In principle, people collect and process information every day of their lives. 
Since it's something we do frequently, you might think we would be really good 
at it...but we're not. Unfortunately, humans are not natural statisticians. We 
are not good at picking out patterns from a sea of noisy data. And, on the flip 
side, we are *too good* at picking out non-existent patterns from small numbers 
of observations. We also find it difficult to sort out the effects of multiple
factors occurring simultaneously and we are subject to all sorts of biases 
depending on our personalities, emotions, and past experiences.

In order to mitigate any of our own personal biases when answering important 
questions about the way the world works (i.e., to do good science), we must be
careful to be rigorous in the way we proceed. The **scientific method** is the 
process used to answer scientific questions.
 
1) Ask a question
2) Construct a hypothesis
3) Test your hypothesis with a study or an experiment
4) Analyze data and draw conclusions
5) Communicate results

As an example of the scientific method, consider that you would like to start a
garden, but you are not sure which type of fertilizer is best. If there are three
types of fertilizer you cannot decided between, you might proceed through the 
scientific method as follows:

1) Ask a question

Of fertilizers A, B, and C, which will yield the fastest plant growth in my garden?

2) Construct a hypothesis

You may have read some reviews for each type of fertilizer online. Fertilizer A
has 4.5 stars, fertilizer B as 4.2 stars, and fertilizer C has 4.6 stars. Thus,
you may hypothesize that fertilizer C leads to the fastest plant growth, followed
by fertilizer A, and that fertilizer B has the slowest plant growth.

3) Test your hypothesis with a study or an experiment

To test your hypothesis, you can section off three areas of your garden. In each 
area, you use one of the three fertilizers and plant the same number and type of
plants. In order for your experiment to be fair, you will want to make sure each
of the three areas is equal-size, gets the same amount of sunlight, is watered 
the same amount, etc.

4) Analyze data and draw conclusions

After 5 weeks, you measure the height of each plant which use each type of 
fertilizer. Taking the average plant height from each of the three sections of 
your garden, you find that when fertilizer A was used, the average plant height 
was the tallest and thus you conclude that fertilizer A is the best for your
garden.

5) Communicate results

Other gardeners in your area may be interested in your results. You may share
with them your recommendation for fertilizer A, which is backed by a 
well-controlled experiment.

Even in this relatively simple example, you can see how much care is required to
have a valid experiment. There are many other factors that may also influence
your decision on the best fertilizer, such as the price and availability. It's
also possible that fertilizer A ended up with the fastest average plant growth
just due to random chance, and if you repeated the entire experiment again you
might find fertilizer B or C to result in taller plants. 

---

<div class="definition-container">
<div class="definition"> &nbsp; </div>
<div class="text">
**Scientific method:** <em> Five steps that can be used to acquire knowledge 
  without incorporating personal opinion </em>
</div>
</div>


## Statistical framework {#ch1_s3}

As we saw in the fertilizer example, collecting and analyzing data can be complicated.
Statistics helps us design studies, test hypotheses, and use data to make scientifically
valid conclusions about the world. In general, scientists use the scientific method 
to make generalizations about classes of people on the basis of their studies. 
The class of people that they are trying to make generalizations about is called 
the **population**. Most of the time, it is impractical and expensive to study 
all individuals in a population - although many governments do  the best they 
can every 10 years. Instead of sampling everyone in the population, or taking a 
**census**, typically we study only a portion of the population called the
**sample**. In order to determine how best to obtain a sample to answer the 
research questions, we must be cautious about the **study design**. Then, 
researchers make generalizations, or **inference**, about the entire population 
based on studying the sample. We can visualize the statistical framework using 
this diagram:

```{tikz statFramework, fig.cap = "Statistical Framework", fig.ext = 'png', echo = F, fig.align='center'}
\usetikzlibrary{decorations.pathreplacing,positioning, arrows, shapes, calc,shapes.multipart}
\tikzstyle{block1} = [rectangle, draw, fill=yellow!20, 
    text width=10em, text centered, rounded corners, minimum height=6em]
\tikzstyle{block2} = [rectangle, draw, fill=yellow!20, 
    text width=5em, text centered, rounded corners, minimum height=3em]
\tikzset{
    %Define standard arrow tip
    >=stealth,
    % Define arrow style
    pil/.style={
           ->,
           thick,
           shorten <=2pt,
           shorten >=2pt,}
}
\tikzstyle{line} = [draw, -latex]
\begin{tikzpicture}[node distance = 3cm, auto]
            % Place nodes
            \node [block1] (pop) {Population \\ (Parameters)};
            \node [block2, below of=pop] (samp) {Sample \\ (Statistics)};
            
            % Draw edges
            \draw[->, >=latex, shorten >=2pt, shorten <=2pt, bend right=45, thick]  (pop.west) to node[auto, swap] {Study Design}(samp.west);
            \draw[->, >=latex, shorten >=2pt, shorten <=2pt, bend right=45, thick] (samp.east) to node[auto, swap] {Inference}(pop.east); 
            
        \end{tikzpicture}
```

Throughout this book, we will dive deeper in to each aspect of the statistical
framework. We consider two broad categories of statistical 
analysis: **descriptive statistics**, which deals with methods for summarizing 
and/or presenting data and **inferential statistics**.

---

<div class="definition-container">
<div class="definition"> &nbsp; </div>
<div class="text">
**Population: ** <em> The group towards which scientists attempt to generalize </em>

**Census: ** <em> A study which includes all members of the population </em>

**Sample: ** <em> A portion of the population which is part of the study </em>

**Study design: ** <em> The process of obtaining the best sample to answer the research questions </em>

**Inference: ** <em> The process of making generalizations about the population </em>

**Descriptive statistics: ** <em> Methods for summarizing and/or presenting data </em>

**Inferential statistics: ** <em> Methods for making generalizations about a population
  using information contained in the sample </em>
</div>
</div>