In psychological research, replication involves repeating another scientist's experiment, often using new samples, to assess the reliability of the original findings. Because any single study carries a risk of reflecting a Type I or Type II error, researchers must be cautious when interpreting isolated results. Each successful replication of a study that produces a similar outcome provides increasing confidence that the finding represents a genuine, real-world phenomenon rather than a statistical artifact.

Replication of Studies in Psychology

Which of the following statements accurately defines a Type II error in null hypothesis testing?

A Type II error is a false negative in null hypothesis testing. It occurs when a researcher mistakenly concludes that their results are not statistically significant—thereby retaining the null hypothesis—when, in reality, the null hypothesis is false and a true relationship does exist in the population. In practical research, Type II errors typically happen because a study lacks adequate statistical power to detect the underlying relationship, often due to an insufficiently large sample size.

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Statement that says there is no relationship between the two measured items

Null Hypothesis

When a $$p$$ value is greater than the alpha criterion ($$>.05$$), researchers retain the null hypothesis, concluding there is not enough evidence to reject it. Importantly, retaining the null hypothesis is not the same as proving it is true; it simply means the data does not provide sufficient evidence to support the alternative hypothesis. Consequently, researchers use terminology like 'fail to reject the null hypothesis' or 'retain the null hypothesis,' but they never state that they 'accept' the null hypothesis.

Retaining the Null Hypothesis

The statistical power of a research design is the probability that the study will reject the null hypothesis, given a specific sample size and an expected relationship strength. For instance, if a design has a power of $$.80$$, it means there is an $$80\%$$ chance of correctly rejecting the null hypothesis when the expected relationship exists in the population. It is essentially the complement of the probability of making a Type II error, so researchers strive for high statistical power to avoid missing a real effect.

Statistical Power

Inferential statistics are a set of mathematical techniques used by researchers to determine whether a statistical result or relationship observed in a study's sample reflects something that is genuinely true of the broader population.

Inferential Statistics

https://kpu.pressbooks.pub/psychmethods4e/

KPU Research Methods in Psychology - 4th American Edition

Critics of null hypothesis testing argue that the strict convention of rejecting the null hypothesis only when $$p < .05$$ is logically flawed. This rigid threshold creates an artificial divide where a result of $$p = .04$$ is deemed significant and worthy of publication, while a nearly identical result of $$p = .06$$ is dismissed as not significant. This arbitrariness can prevent valuable research from being published and exacerbates the file drawer problem by suppressing non-significant findings.

Arbitrariness of the p-value Threshold

Bayesian statistics is an approach to inferential statistics where a researcher specifies the prior probability that the null hypothesis and alternative hypotheses are true before conducting a study. Once the study is conducted, the probabilities are updated based on the newly collected data. This approach offers a potential alternative to traditional null hypothesis testing by providing a logical framework for quantifying uncertainty using probability distributions.

Bayesian Statistics

A Type I error is a false positive in null hypothesis testing. It occurs when a researcher mistakenly concludes that their results are statistically significant—thereby rejecting the null hypothesis—when, in reality, the null hypothesis is true and there is no actual relationship in the population. These errors happen because random sampling error can occasionally produce extreme results even when no true effect exists. The predetermined alpha level dictates the probability of committing this error when the null hypothesis is true.

Type I Error

Type II Error

In the context of psychological research, which statement best defines a null hypothesis?

When the data in a study does not provide sufficient evidence to support the alternative hypothesis, which of the following is the correct terminology researchers use to describe their conclusion regarding the null hypothesis?

Brysbaert, M., & Stevens, M. (2018). Power analysis and effect size in mixed effects models: A tutorial. Journal of cognition, 1(1). https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6646942/

Power analysis and effect size in mixed effects models: A tutorial

If a research design lacks adequate statistical power, researchers can increase it by either increasing the sample size or strengthening the relationship. Strengthening the relationship can be achieved by using a stronger experimental manipulation or by carefully controlling extraneous variables to reduce data noise, such as employing a within-subjects design instead of a between-subjects design. However, the most common and practical strategy to boost power is simply to increase the sample size.

Increasing Statistical Power

Because manual computation is complex, researchers typically compute the statistical power for various research designs using online tools and downloadable programs, such as Russ Lenth’s Power and Sample Size Page or G*Power. By inputting the expected relationship strength, the sample size, and the $$\alpha$$ level, these applications calculate the study's power or determine the exact sample size required to achieve a desired power level, such as $$.80$$.

Computing Statistical Power Online

Statistical power and the probability of committing a Type II error are perfectly complementary. A Type II error occurs when a researcher fails to reject a false null hypothesis (missing a real effect). Since statistical power is the probability of correctly rejecting that false null hypothesis, statistical power is calculated as $$1 - 	ext{probability of a Type II error}$$. Therefore, maximizing a study's statistical power is the primary method for minimizing the risk of making a Type II error.

Relationship Between Statistical Power and Type II Error

In psychological research, it is generally recommended that a study's design possess adequate power prior to data collection. A widely accepted guideline is that an adequate level of statistical power is $$.80$$. This indicates that if the expected effect or relationship truly exists in the population, the study has an $$80\%$$ chance of successfully detecting it and rejecting the null hypothesis.

Adequate Statistical Power

To achieve high statistical power in psychological research, sample sizes must be larger than often realized. For an independent-samples $$t$$-test with a large population effect, it requires approximately $$26$$ participants per sample to reach a power of $$0.80$$, while reaching a power of $$0.99$$ requires $$59$$ participants per sample.

Example of Sample Size Requirements for High Statistical Power

Statistical power is heavily dependent on the expected relationship strength (effect size). Weaker relationships are harder to detect and thus provide lower statistical power for a given sample size. To compensate and achieve adequate power when investigating a weak relationship, researchers must utilize very large sample sizes.

Relationship Between Statistical Power and Relationship Strength

Which of the following best defines the statistical power of a research design?

Statistical conclusions in psychological research are fundamentally probabilistic, meaning that empirical findings are always subject to chance and the possibility of statistical errors, such as Type I or Type II errors. Because researchers cannot completely eliminate these potential errors, the results of any single empirical study can never provide absolute certainty or definitively prove that a scientific theory is true.

Probabilistic Nature of Statistics

A statistical range calculated around a sample statistic designed to contain the true population parameter a specified percentage of the time, most commonly $$95\%$$. Some researchers advocate using confidence intervals as an alternative to traditional null hypothesis testing because they are often more intuitive to interpret. Furthermore, a confidence interval inherently provides the data needed to perform a null hypothesis test; if a hypothetical population mean falls completely outside the calculated interval, the sample mean is considered statistically significantly different from that hypothetical value.

Confidence Interval

A finding is considered statistically significant when it is highly unlikely to have occurred due to random chance alone. In the context of inferential statistics, achieving statistical significance suggests that the results represent a genuine, real effect within the broader population.

Statistically Significant

In a study of sex differences in talkativeness, Matthias Mehl and his colleagues observed that the women in their sample spoke a mean of $$16,215$$ words per day while men spoke a mean of $$15,669$$ words per day. Despite finding this difference within their specific sample, they ultimately concluded that there was no evidence of a genuine sex difference in talkativeness within the broader population.

Mehl's Study on Sex Differences in Talkativeness

In a study investigating the connection between daily hassles and stress symptoms, Allen Kanner and his colleagues discovered a positive correlation of $$+.60$$ within their sample. Based on this specific sample result, they concluded that a genuine relationship between daily hassles and symptoms exists in the overall population.

Kanner's Study on Daily Hassles and Symptoms

Null hypothesis testing is the most common approach to inferential statistics in psychological research. It provides researchers with a formal, structured process to evaluate whether an observed sample result likely occurred by random chance or whether it accurately reflects a genuine relationship or difference in the broader population.

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