What are the Fundamentals of Applied Statistics? Would the knowledge of the following topics suffice for a crash course on fundamentals of applied statistics?


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*Basics of Probability

*Descriptive Statistics

*Estimation Theory

*Hypothesis Testing


The targeted audience are those with little or no exposure to statistics. The course should bring about a clear understanding of what is statistics and its basic outline. It should also serve as a start for those who are interested in the subject but don't know where to begin. 
The "applied" part comes with the implementation of the above theories in practical examples and exercises.
 A: If these are subject-matter-experts I would spend more time discussing:


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*How to ask the right question in a way that it can be answered.

*How to collect data so that you can answer the question.

*How to select a statistical procedure that can answer your question.

*What the result of the statistical analysis means and how to know if it is of any practical value.

*When to call in professional statisticians and how to effectively work with them.
A: 
The targeted audience are those with little or no exposure to statistics.

My favourite audience!

It should also serve as a start for those who are interested in the subject but don't know where to begin.

Your choice of textbook is going to be crucial. My strategy is to have one very short stats textbook (e.g. Urdan, Stats in Plain English), and to do everything else through code and tutorials.

The "applied" part comes with the implementation of the above theories in practical examples and exercises.

This is the crucial part. Make the examples relevant: no synthetic data, and of the right dimensions for your audience (don't teach flower or airplane data to would-be survey analysts).


*

*Basics of Probability

*Descriptive Statistics

*Estimation Theory

*Hypothesis Testing


That's one way to put it. I would stress:

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*Data. What it is (observations, variables, samples), how is it produced.

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*Data collection, sample design, measurement issues.

*Question(s) -> Data -> Question(s) -> Data -> etc.



*Distributions. How do we describe one variable, several variables.

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*Your descriptive stats are here.

*Tons of EDA (exploratory data analysis) / data visualization always helps.

*Concentration indices, quantiles, ECDFs. Invaluable.



*Estimation. When we have $\bar x$, how do we estimate $\mu$?

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*A bit of probability and estimation theory here.



*Inference. When we observe an association, how do we measure its robustness?

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*Hypothesis testing happens here. More probability here.

*Downplay $p$-values, emphasize standard errors.

*If you have time, models.
My strategy:
Anticipate that students will forget (3) and (4). That's alright, the next course will take it up again. But (1) and (2), your students need to be familiar with the jargon, and should be critical quantifiers, who know that data are dirty, that sampling is complex, that "raw data" is an oxymoron, etc.
General philosophy:

Source.
