Topic: 2022FRQ真题详解

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2a - control group:

1. Isolation of Variable Effects: The control group helps researchers isolate the effects of the independent variable by providing a comparison against the experimental group. This comparison helps to determine whether the changes observed in the experimental group are due to the treatment or intervention and not due to other factors.

2. Similarity to Experimental Group: Ideally, the control group should be as similar as possible to the experimental group in all aspects except for the treatment or intervention. This similarity often involves random assignment of subjects to each group to ensure that both groups are comparable in terms of demographics, characteristics, and other variables that could influence the outcome.

3. Types of Control Groups:
• No-treatment Control Group: This group does not receive any treatment or intervention.
• Placebo Control Group: In medical or psychological research, this group receives a placebo or sham treatment, which is designed to mimic the experimental treatment but has no therapeutic effect.
• Active Control Group: This group receives an existing standard treatment or intervention, rather than a placebo, to compare the efficacy of a new treatment against the current standard.

4. Blinding: To further ensure the reliability of the results, studies often use blinding methods. Single-blind studies conceal the treatment allocation from the participants, while double-blind studies conceal it from both the participants and the researchers who interact with the participants or analyze the data. This helps to prevent bias in the treatment administration and assessment of outcomes.

5. Ethical Considerations: The use of control groups, especially placebo groups, raises ethical considerations, particularly in clinical trials where withholding treatment could harm participants. Ethical guidelines require that participants are not subjected to unnecessary risks and that they provide informed consent.

6a- bootstrapping

1. Sample with Replacement: From your original dataset of size N, randomly select N observations with replacement. This means the same observation can be chosen more than once. This new sample is called a "bootstrap sample."

2. Calculate Statistic: Calculate the desired statistic (e.g., mean, median, standard deviation) on the bootstrap sample.

3. Repeat: Repeat steps 1 and 2 many times, typically thousands or tens of thousands of times, to generate a distribution of the bootstrap samples' statistics.

4. Estimate: Use the distribution of the bootstrap statistics to estimate the standard error, confidence intervals, or bias of the statistic for the original sample.

Advantages of Bootstrapping:

• Flexibility: It can be applied to many statistical measures and used in situations where traditional parametric statistics are not applicable.

• Simplicity: It is relatively straightforward to implement and understand, especially with modern computing power.

• Non-parametric: It does not assume that your data follows a specific distribution, making it widely applicable.

Limitations:

• Accuracy: The accuracy of bootstrap methods can depend on the size of the original dataset and the statistic being estimated.

• Computationally Intensive: Requires significant computational resources for generating thousands of resamples and recalculating statistics for each.

• Edge Cases: May not work as well for statistics that are not well-approximated by the bootstrap distribution or for very small sample sizes.