Retaining the Null Hypothesis

Trade-off Between Type I and Type II Errors

Type I Error

In the context of psychological research, what does it mean for a researcher to set the level of significance (alpha, or $\alpha$) at .05?

A researcher investigating the impact of social media on self-esteem sets the level of significance ($\alpha$) at $.05$. After collecting and analyzing the data, they obtain a $p$ value of $.06$. True or False: The researcher should reject the null hypothesis because the result is very close to the significance level.

A researcher is evaluating the results of a psychological study using a standard significance level ($\alpha$) of $.05$. Match each component of the null hypothesis testing process to its correct analytical role or logical condition in the decision-making process.

Rank the following significance levels ($\alpha$) based on their effectiveness in preventing a researcher from incorrectly rejecting the null hypothesis, from the 'most protective' (strictest) level to the 'least protective' (most lenient) level.

In the context of null hypothesis testing within psychological research, what is the numerical value almost always used as the level of significance ($\alpha$)?

Match each component of the level of significance ($\alpha$) to its conceptual role in the process of null hypothesis testing.

A researcher sets her significance level at $\alpha = .05$ before beginning a study on caffeine and reaction time. After data collection and analysis, she obtains a $p$ value of exactly $.05$. True or False: This result meets the alpha criterion, and the researcher should reject the null hypothesis.

When the null hypothesis is actually true and a researcher has set $\alpha = .05$, the researcher will mistakenly reject the null hypothesis _____ % of the time—demonstrating that alpha simultaneously functions as both the decision threshold for the $p$ value and the long-run rate of a specific type of decision error.

A psychology student is designing a study on mindfulness training and stress levels. Evaluate the logical order of the following steps involved in correctly applying alpha ($\alpha$) within null hypothesis testing, arranging them from first (1) to last (5).

In null hypothesis testing, the predetermined criterion used to decide how low a $p$ value must be before a sample result is considered unlikely enough to reject the null hypothesis is called _____.

Define the term alpha ($\alpha$) in the context of null hypothesis testing and state its most commonly used numerical value in psychological research.

Based on the definition of alpha ($\alpha$), explain what setting this criterion to $.05$ means regarding the probability of making a decision error if the training program actually has no effect (i.e., if the null hypothesis is true).

A clinical psychologist designs an experiment to test whether a new therapy reduces depressive symptoms and sets the level of significance ($\alpha$) to $.05$. After analyzing their sample data, they obtain a $p$ value of $.03$. Apply the rules of null hypothesis testing to determine and justify whether the psychologist should reject or retain the null hypothesis.