1. AP Seminar: Statistics Primer
Goal: Be able to determine the usefulness and reliability a primary resource document will have for your paper by assessing some basic statistical parameters.
To achieve this goal, you need to be able to…
Evaluate the experimental design/study techniques
Qualify the validity of conclusions in a paper based on the experimental design and statistical analyses

2. Primary Source Articles
The general structure of a primary source article is:
Abstract (how can you find what you need to know from only the abstract?)
Introduction
Materials & Methods/Research Methodology
Results
Discussion
Sources
How do these articles eventually get published?

3. Basic Statistical Vocabulary
Controlled variables & control groups
Sample size (N)
Sampling techniques (random, stratified, cluster)
Significance and P value
Confidence, error, and “true value”

4. Controlled Variables & Control Groups
Manipulated Variable: The variable you intentionally change to measure if there is a difference in the responding variable.
Responding Variable: The variable that might change as a result of the manipulated variable.
Controlled Variables: Variables kept the same in all trials so that the manipulated variable is the only source of variation.
Control Group(s): Trial group with no manipulated variable. A complex experiment can have multiple control groups (see dolphin example).

5. What is “good” experimental design?
The results from an experiment are only useful if they are reliable and valid. What does that mean?
Reliability means that every time the experiment is performed, the results will be the same. We ensure reliability by doing multiple trials.
Validity means the experimental design actually tests the hypothesis. We ensure validity by having adequate control groups and controlled variables.
A hypothesis is a claim that there is a relationship between 2 or more observed phenomena. The null hypothesis is the opposite; there is no relationship. Ultimately an experiment allows you to accept or reject the null hypothesis.

6. Sample Size (N) “N” means the number of individuals used in the study.
Generally, the more test subjects, the better. This allows you to reduce bias, reduce the risk of outliers, reduce error, and increase confidence level.
Determination of the appropriate sample size can be mathematically complex and varies widely based on what is being studied. The more complex the relationship being investigated, the more individuals are needed to ensure valid results. However, you don’t always have a choice. Compare diet studies to wildlife biology… time and money are always limiting!

7. Sampling Techniques
Most of the time, you can’t get census data (what’s a census?) so you have to obtain a representative sample that will allow you to extrapolate your conclusions to the total population.
Simple random sample (SRS): Random number generators are often used to select certain individuals from the total population. This is a simplistic technique and is rarely used in published studies.
Stratified sample: When there are multiple categories within a population, they are arranged as homogenous strata and then a SRS can be pulled from each strata. This is better than a SRS because it increases the variability of samples and reduces sampling error by ensuring all categories in a population will be represented.
Cluster sample: heterogenous groups are formed based on geographic proximity and then a SRS is used. This is also better than SRS!
Randomly generate Student ID #s to complete a survey.
Divide by grade, gender, etc. and then randomly select from the strata
Walk through the hallways and randomly select a student from each group you see. $

8. Significance & P value Let’s get back to the null hypothesis (H0).
The P value sets an arbitrary value that the data collected in an experiment must be below in order to reject the null hypothesis. Remember, the null hypothesis means there is no relationship. Rejecting the null hypothesis means there could be a relationship and the data are, therefore, significant.
When P ≥ 0.05, the researchers are unable to reject the null hypothesis and they cannot conclude there was a relationship.
This can happen because the sample size was too small (“lacking statistical power”) or because there is truly no relationship.

9. True Value, Error, and Confidence
The true value is the “answer.” If we want to know the average height of an American adult, we can sample people or take a census, but we can never truly know the answer. True values are unknowable. We contrast this with expected values, which are accepted mean values.
Error is the amount that a data point deviates from the expected value (not the true value, because we can’t know it).
The degree to which we are confident that we will capture the true value in a range of values is the confidence interval. Often we use 95% as our confidence interval, but you may see 90 or 99%.

11. Correlation & Causation
You are aware that correlation does not prove causation. Proving causation can be statistically complex.
This is a common misinterpretation and abuse of statistics in the media. No peer-reviewed scientific paper will ever make this mistake- be wary!

12. Bad Statistics Common problems include: Bias Misrepresenting the data
Jumping from a correlation to a causation
Sometimes this is unintentional and sometimes the slant is purposeful. A great way to avoid this making its way into your paper is to use only peer-reviewed, primary source documents. The biggest culprit of the abuse of statistics (intentional or accidental) is the media. Be especially critical when analyzing secondary source documents.

13. Applications: What does it all mean?
Let’s look at a few examples of primary resource documents that have used and reported statistics appropriately and compare that to some examples of secondary resource documents that have not.

14. When you Google “New study proves…”
No scientist would EVER use the word “prove” or make claims this bold.