Statistics: Sampling Error and Hypothesis Testing

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Questions and Answers

What defines independent events in probability?

Both events must happen together

The occurrence or nonoccurrence of one event has no effect on the other (correct)

The occurrence of one event negates the occurrence of another

The occurrence of one event affects the occurrence of another

Which rule applies to the probability of mutually exclusive events?

The average of individual probabilities

The absolute difference of individual probabilities

The sum of individual probabilities of events (correct)

The product of individual probabilities of events

What is subjective probability based on?

Mathematical calculations of frequency

Predefined probabilities based on historical data

Statistical likelihood of events

An individual's belief about an event's likelihood (correct)

What does it mean for events to be exhaustive?

They include all possible outcomes Signup and view all the answers

What is the purpose of the multiplicative law of independent events?

To calculate joint probabilities of independent events Signup and view all the answers

When are two random variables considered independent?

When their marginal probabilities are equal to the conditional probabilities for all conditions. Signup and view all the answers

What does the general law of probability state about two independent events?

The chance that both events happen at the same time is the product of their probabilities. Signup and view all the answers

What is meant by conditional probability?

The probability of one event occurring given that another event has occurred. Signup and view all the answers

Which of the following statements is true regarding independent events?

The conditional and marginal probabilities are the same for all conditions. Signup and view all the answers

In hypothesis testing, what is being assessed with respect to H0?

The probability of obtaining a score more extreme than the observed score, given that H0 is true. Signup and view all the answers

What does a lower p-value indicate regarding the null hypothesis (H0)?

More evidence against H0. Signup and view all the answers

What is the typical significance level used to decide whether to reject H0?

0.05 Signup and view all the answers

If a researcher commits a Type I error, what have they done?

Rejected H0 when it is true. Signup and view all the answers

What is a critical value in hypothesis testing?

The cutoff point that determines the rejection region. Signup and view all the answers

Which statement correctly describes the power of a test?

Probability of rejecting H0 when it is false. Signup and view all the answers

What characterizes a two-tailed test compared to a one-tailed test?

It tests for extreme values in both directions. Signup and view all the answers

If Type I error rates are reduced, what is the expected impact on Type II errors?

Increase in Type II error rates. Signup and view all the answers

What does it mean to reject the null hypothesis?

Concluding that there is enough evidence against H0. Signup and view all the answers

What is eta squared used for in t-tests?

Measuring the proportion of variance accounted for Signup and view all the answers

What does a higher score in absolute effect sizes indicate?

A clear interpretation of the effect Signup and view all the answers

Which aspect influences the precision of confidence intervals?

The level of variation in the sample Signup and view all the answers

For which analysis is the sd of difference scores particularly beneficial?

Paired sample tests Signup and view all the answers

What does a confidence level of 95% suggest about findings?

There is a 5% chance the findings could be incorrect Signup and view all the answers

What is categorical data primarily composed of?

Frequencies of observations in multiple categories Signup and view all the answers

What is the primary purpose of the chi-square test?

To test the independence of two categorical variables Signup and view all the answers

What do observed frequencies represent in a chi-square test?

The actual counts gathered in the sample Signup and view all the answers

In the context of a goodness-of-fit test, what does the term 'expected frequencies' refer to?

Counts we would expect if the null hypothesis were true Signup and view all the answers

What is the interpretation of the degrees of freedom in the chi-square test?

The number of categories minus one Signup and view all the answers

How do we determine the significance of the chi-square statistic obtained?

By using the chi-square distribution table and degrees of freedom Signup and view all the answers

What does the expected frequency in a contingency table represent?

What we would expect if the two variables were independent Signup and view all the answers

How is the degrees of freedom calculated for a contingency table?

Df = (R - 1)(C - 1) Signup and view all the answers

What does a low p value indicate in statistical testing?

We have found evidence against the null hypothesis Signup and view all the answers

What does a high p value indicate in statistical hypothesis testing?

There is an absence of evidence against the null hypothesis Signup and view all the answers

Which statement about statistical significance is accurate?

Statistical significance does not equate to practical relevance Signup and view all the answers

What does the term 'nonocurrences' refer to in statistical analysis?

Responses indicating disagreement Signup and view all the answers

Study Notes

Sampling Error

Sampling error refers to the variability of a sample statistic from a population parameter.
A sample statistic will likely deviate from the population parameter due to chance.
For example, if a population has a mean of 50, a sample of ten people might have a mean of 49 or 51.

Hypothesis Testing

Hypothesis testing is used to determine if observed differences in data are due to chance.
A hypothesis is a statement about a population parameter.
Sampling distributions can be used to understand the variability of a statistic.

Sampling Distributions

Sampling distributions show how sample statistics vary over repeated samples.
They are distributions of sample means.
They are not distributions of scores.

Distribution of Values

The distribution of values obtained from a sample statistic is used over repeated sampling.
This distribution can help determine if chance is the reason for the differences or not.

Probability of Population Means

Probability of having the same sampling difference if population means were equal.
A low probability suggests independent variable change.

Hypothesis Testing Process

Begin with a research hypothesis.
Establish null hypothesis (no change/no effect).
Create sampling distribution under the null hypothesis.
Collect some data.
Compare sample statistic to established distribution.
Reject or retain null hypothesis based on probability calculations.

Error Types

Type I error: Rejecting a true null hypothesis (false positive).
Type II error: Failing to reject a false null hypothesis (false negative).
Significance level (alpha) is the probability of a Type I error.

Using Conventions

Rejection levels/significance levels indicate the differences are statistically significant.
- For instance, a .05 level means a difference that occurs less than 5% of the time under the null.

Other Statistical Concepts

Standard error: The standard deviation of a sampling distribution.
- Used to assess variability in sample means from repeats.
Central Limit Theorem: Sampling distribution of the mean tends towards a normal distribution as sample size increases.
Test statistics: Associated with specific statistical procedures, they have their own sampling distributions.

Additional Concepts

Bootstrapping: Sampling with replacement from the obtained data/sample.
A method helpful for assessing distributions of samples with characteristics similar to the examined sample.
Confidence interval: the range within which the true population mean is likely to fall with a given confidence level.

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Description

This quiz covers key concepts in statistics, focusing on sampling error, hypothesis testing, and sampling distributions. Understand how sample statistics can vary from population parameters and learn about the implications of these concepts in data analysis. Engage with scenarios to test your knowledge on statistical variability and inference.