Biology 3.2 Statistics Chapter: Hypothesis Testing

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Questions and Answers

What does the null hypothesis predict regarding statistical differences?

It predicts no statistical difference exists between groups. (correct)

It states that researchers will always find a significant result.

It predicts a statistical difference exists between groups.

It assumes all variables have a direct correlation.

Which of the following accurately describes a Type I error?

Rejecting the null hypothesis when it is true. (correct)

Accepting the alternative hypothesis when the data is inconclusive.

Failing to reject the null hypothesis when it is true.

Not conducting a significance test when required.

What is the significance level commonly used in hypothesis testing?

0.01

0.05 (correct)

0.20

0.10

Which term describes the probability of obtaining a statistically significant result if the null hypothesis is true?

P-value Signup and view all the answers

Which of the following represents a Type II error?

Failing to reject the null hypothesis when it is false. Signup and view all the answers

In hypothesis testing, what is indicated by a low p-value (less than 0.05)?

There is strong evidence against the null hypothesis. Signup and view all the answers

What does statistical power in hypothesis testing refer to?

The probability of correctly rejecting the null hypothesis. Signup and view all the answers

What is the consequence of setting a very low significance level in hypothesis testing?

Decreases the statistical power of the test. Signup and view all the answers

What happens to the probability of committing a Type II error as sample size increases?

It increases Signup and view all the answers

What does statistical power refer to in hypothesis testing?

The likelihood of rejecting a true null hypothesis Signup and view all the answers

At which level does significance typically represent the threshold for determining Type I error?

0.05 Signup and view all the answers

What is the relationship between sample size and statistical power?

Increased sample size increases statistical power Signup and view all the answers

Which statement is NOT true regarding parameters in biological research?

Parameters are often known quantities Signup and view all the answers

What is a Type I error in hypothesis testing?

Rejecting a true null hypothesis Signup and view all the answers

What does the standard error of the mean (SEM) indicate?

The spread of sample means around the population mean Signup and view all the answers

How is statistical power defined in the context of hypothesis testing?

The probability of detecting an effect when one truly exists Signup and view all the answers

In hypothesis testing, what does a significance level of $0.05$ imply about the corresponding confidence level?

It corresponds to a 95% confidence level Signup and view all the answers

What does it mean if the error bars representing the 95% confidence interval do not overlap?

The results are statistically significant Signup and view all the answers

Which situation describes a Type II error?

Failing to correctly reject a false null hypothesis Signup and view all the answers

What characterizes the significance level in hypothesis testing?

It defines the threshold for rejecting the null hypothesis Signup and view all the answers

Which statement accurately describes Type I Error?

Rejecting a true null hypothesis Signup and view all the answers

What is the impact of increasing the sample size on the statistical power of a test?

It can enhance the statistical power Signup and view all the answers

What is meant by the probability of committing a Type I error?

It is the likelihood of rejecting a true null hypothesis Signup and view all the answers

If a study has high statistical power, which of the following is likely true?

There is a high chance of detecting actual effects Signup and view all the answers

Which describes Type II Error in hypothesis testing?

Failing to reject the null hypothesis when it is false Signup and view all the answers

Which outcome does a researcher hope to avoid when conducting an experiment?

Committing a Type II error Signup and view all the answers

Which of the following statements is correct regarding significance levels?

A significance level of $0.01$ indicates a 99% confidence level Signup and view all the answers

In hypothesis testing, which scenario is evidence of a Type I error?

Rejecting the null hypothesis when it is true Signup and view all the answers

How do confidence intervals contribute to understanding measurement error?

They provide a range of values for the true population value Signup and view all the answers

What does statistical power primarily indicate in research studies?

The likelihood of correctly rejecting the null hypothesis when it is false Signup and view all the answers

What is implied when experimental validity is low?

The conclusions may not accurately represent the scientific issue Signup and view all the answers

What does it mean for measurements to be statistically different?

They indicate different sample means Signup and view all the answers

What type of error occurs when a researcher mistakenly rejects a true null hypothesis?

Type I Error Signup and view all the answers

Which of the following correctly represents the probability of committing a Type I Error?

$ ext{alpha}$ Signup and view all the answers

Increasing the significance level from 0.01 to 0.05 primarily affects which type of error?

Type I Error only Signup and view all the answers

What is the consequence of choosing a lower significance level, such as 0.01?

Increased risk of Type II Error Signup and view all the answers

What is indicated by the term 'statistical power'?

The ability to correctly reject a false null hypothesis Signup and view all the answers

When a researcher fails to reject a false null hypothesis, which type of error has occurred?

Type II Error Signup and view all the answers

What effect does lowering the significance level have on the confidence of the results?

It increases confidence in the results Signup and view all the answers

Which statement best describes a Type II Error in hypothesis testing?

Failing to reject the null hypothesis when it should be rejected Signup and view all the answers

How does the choice of significance level influence Type I and Type II Errors?

Increasing significance level decreases Type II Error but increases Type I Error Signup and view all the answers

Study Notes

Null and Alternative Hypotheses

The null hypothesis is the starting point of a research study, assumed to be true before the experiment is conducted.
Researchers use experimental results to determine whether there is enough evidence to reject the null hypothesis.
If there is not enough evidence to reject it, the null hypothesis is not rejected.

Statistical Significance

Statistical significance pertains to the probability that a null hypothesis is true, given a predetermined margin of error.
Results that are statistically significant are unlikely to be due to chance alone.
The p-value of a study is the probability of observing the study's results due to chance alone.
P-values between 0 and 0.05 are considered statistically significant, while p-values greater than 0.05 are not.

Confidence Intervals

Confidence intervals are calculated with a specified confidence level (eg. 95%).
Confidence intervals provide a range of values within which a population parameter is likely found.
When confidence intervals calculated for different measurements do not overlap, the results are considered statistically significant, even if the exact values differ.
95% confidence intervals are typically presented as sample mean ± 2 SEM.

Error Bars in Research Studies

Error bars represent the variability of the data in a research study.
When error bars for different measurements do not overlap, this implies a statistically significant difference between the measurements.

Experimental Validity

Experimental validity refers to how accurately an experiment tests its intended objective and whether the results can be trusted.
If an experiment is valid, its conclusions can be applied to real-world situations.

Types of Error in Experiments

Type I error occurs when the null hypothesis is rejected when it should not be.
The probability of committing a Type I error is called the alpha value (α).
Type II error occurs when the null hypothesis is not rejected when it should be.
The probability of committing a Type II error is called the beta value (β).
Statistical power describes the probability that a test will detect an effect when such an effect exists, also defined as the probability of correctly rejecting the null hypothesis.

Confidence Levels

Biological research often involves drawing conclusions from samples of a population.
Values calculated from samples are called statistics.
Values that describe whole populations are called parameters.
Confidence intervals provide a range of values within which a population parameter is likely to be found.

Statistical Power

Statistical power is the ability of a test to detect an effect when one exists.
It is also the probability of correctly rejecting the null hypothesis.
Power can also be described as the probability of avoiding a Type II error.
Statistical power is increased with larger sample sizes.

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Description

This quiz covers key concepts in hypothesis testing, including null and alternative hypotheses, statistical significance, and confidence intervals. Test your understanding of p-values and their implications on research findings. Perfect for students studying statistics at various levels.