✍️ Free Response Questions (FRQs)
👆 Unit 1 - Exploring One-Variable Data
1.4Representing a Categorical Variable with Graphs
1.5Representing a Quantitative Variable with Graphs
1.6Describing the Distribution of a Quantitative Variable
1.7Summary Statistics for a Quantitative Variable
1.8Graphical Representations of Summary Statistics
1.9Comparing Distributions of a Quantitative Variable
✌️ Unit 2 - Exploring Two-Variable Data
2.0 Unit 2 Overview: Exploring Two-Variable Data
2.1Introducing Statistics: Are Variables Related?
2.2Representing Two Categorical Variables
2.3Statistics for Two Categorical Variables
2.4Representing the Relationship Between Two Quantitative Variables
2.8Least Squares Regression
🔎 Unit 3 - Collecting Data
3.5Introduction to Experimental Design
🎲 Unit 4 - Probability, Random Variables, and Probability Distributions
4.1Introducing Statistics: Random and Non-Random Patterns?
4.7Introduction to Random Variables and Probability Distributions
4.8Mean and Standard Deviation of Random Variables
4.9Combining Random Variables
4.11Parameters for a Binomial Distribution
📊 Unit 5 - Sampling Distributions
5.0Unit 5 Overview: Sampling Distributions
5.1Introducing Statistics: Why Is My Sample Not Like Yours?
5.4Biased and Unbiased Point Estimates
5.6Sampling Distributions for Differences in Sample Proportions
⚖️ Unit 6 - Inference for Categorical Data: Proportions
6.0Unit 6 Overview: Inference for Categorical Data: Proportions
6.1Introducing Statistics: Why Be Normal?
6.2Constructing a Confidence Interval for a Population Proportion
6.3Justifying a Claim Based on a Confidence Interval for a Population Proportion
6.4Setting Up a Test for a Population Proportion
6.6Concluding a Test for a Population Proportion
6.7Potential Errors When Performing Tests
6.8Confidence Intervals for the Difference of Two Proportions
6.9Justifying a Claim Based on a Confidence Interval for a Difference of Population Proportions
6.10Setting Up a Test for the Difference of Two Population Proportions
😼 Unit 7 - Inference for Qualitative Data: Means
7.1Introducing Statistics: Should I Worry About Error?
7.2Constructing a Confidence Interval for a Population Mean
7.3Justifying a Claim About a Population Mean Based on a Confidence Interval
7.4Setting Up a Test for a Population Mean
7.5Carrying Out a Test for a Population Mean
7.6Confidence Intervals for the Difference of Two Means
7.7Justifying a Claim About the Difference of Two Means Based on a Confidence Interval
7.8Setting Up a Test for the Difference of Two Population Means
7.9Carrying Out a Test for the Difference of Two Population Means
✳️ Unit 8 Inference for Categorical Data: Chi-Square
📈 Unit 9 - Inference for Quantitative Data: Slopes
🧐 Multiple Choice Questions (MCQs)
Best Quizlet Decks for AP Statistics
⏱️ 4 min read
June 3, 2020
This part focuses on the components in designing an experiment and how to increase the accuracy of the results. Understanding how to avoid bias from the previous sections above relates to experiments too.
Response variables measure the outcomes of a study. An explanatory variable can help explain or predict changes in a response variable.
An experiment intentionally imposes some treatment on individuals to measure their responses.
A specific condition applied to the individuals in an experiment is called a treatment. If there are several explanatory variables, a treatment is a combination of specific values of these variables. An experimental unit is the object to which a treatment is randomly assigned. When the experimental units are human beings, they are referred to as subjects.
A factor is a variable that is manipulated and may cause a change in the response variable. This often occurs when there are multiple explanatory variables. The different values of a factor are called levels.
Random Assignment: this means that the experimental units are assigned to treatments using a chance process. The process creates roughly equivalent groups with the potential differences between the variables evenly distributed among the groups. This is used in both studies and experiments.
Control: This implies that the other variables are constant for all experimental units in an experiment. Helps avoid confounding and reduces variability in the response variable.
Replication means that you need to use enough experimental units to distinguish a difference in the effects of treatments from chance variation due to the random assignment. *Replication means repeatability.
Start with the most simple elements of an experiment which is the experimental units first, next the treatments, and finally measuring the responses.
Control group is used to provide a baseline for comparing the effects of the other treatments to a certain standard. Although this may vary depending on the experiment, a control group may be given inactive treatment (placebo), an active treatment, or no treatment at all. Control groups help deal with confounding because you remove the chance that an outside influence would affect the results.
Random Assignment to the experimental units is extremely important because you eliminate confounding and large differences between the treatment groups.
Replication ensures the validity of your data because if you repeatedly get similar responses, that means your conclusion and analysis is accurate.
Avoiding Confounding is vital because if you need to establish causation but can’t identify the effects of the explanatory variables, the experiment data is useless.
A Placebo is a treatment that has no active ingredient but is otherwise like the other treatments. Sometimes, it won’t make sense for there to be a placebo group. The placebo effect occurs when some subjects in an experiment responded favorably to any treatment, even an inactive one.
In a double blind experiment, neither the subjects nor those who interact with them and measure the response variable know which treatment a subject receives. This helps avoid confounding and personal bias towards a certain outcome. In a single blind experiment, the subjects don’t know which treatment they are receiving or the people who interact with them and measure the response variable don’t know which subjects are receiving the treatment. In this type, one or the other (subject or administrator) knows, not both.
In a completely randomized design, the experimental units are assigned to the treatments completely by chance. Assignment of treatment to the groups must be random. The group sizes won’t always be exactly even. This is the simplest statistical design for experiments but when there are clear distinctions or similarities within the chosen experimental units, that’s when you need a more specific experimental design.
Example of assigning treatments to Block Experiments
Image Courtesy of Elign Community College
A matched pairs design works when you need to compare two treatments that uses blocks in pairs of size 2. In some matched pairs designs, two very similar experimental units are paired and the two treatments are randomly assigned within each pair. In others, each experimental unit receives both treatments in a random order.
It is possible to establish causation with experiments only because treatment is imposed. That’s a major difference between studies and experiments.
*Remember: Control what you can, block on what you can’t control, and randomize to create comparable groups. Be careful with combining study lingo with experiments.
🎥Watch: AP Stats - Experiments and Observational Studies
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