Research Methods Chapter 8

What determines beta, probability of making a type 2 error?

- High power o High effect size + high sample size

Type 1 Error:

- Occurs when we reject the null hypothesis when it is in fact true. - When your results are not actually significant but you misinterpret them as being significant and therefore reject the null. - Psychologist concludes that his or her therapy reduced anxiety when it did not.

The Tradeoff Between Type 1 and Type 2 Errors:

- We want a small alpha to prevent type 1 errors. - However, for any given sample size, when alpha is set lower, beta will be higher. - Setting a small alpha makes it more difficult to find data that are strong enough to allow rejecting the null hypothesis and makes it more likely that weak relationships will be missed. - The difficulty is that although setting a lower alpha protects us from type 1 errors, doing so may lead us to miss the presence of weak relationships. - As N increases, the likelihood of the scientist detecting relationships with small effect sizes increases, even when alpha remains the same. - Rejecting a null hypothesis does not necessarily mean that the null hypothesis is actually false, but rather it means that the null hypothesis does not seem to be able to account for the collected data.

Steps for hypothesis testing:

1. Develop hypothesis 2. Set alpha (usually .05 or .01) 3. Calculate the power to determine the sample size that is needed 4. Collect data 5. Calculate statistic and p-value 6. Compare p-value to alpha (.05) 7. Either reject null (p<.05) or accept null (p>.05)

Significance level:

Alpha= The standard that the observed data must meet o Meaning we can reject the null hypothesis only if the observed data are so unusual that they would have occurred by chance at most 5 percent of the time. o Less than a 5% chance that the results occurred by chance.

Effects of Sample Size

Increasing sample size will increase the statistical significance of a relationship whenever the effect size is greater than zero. - The p-value is influenced by sample size, as a measure of statistical significance the p-value itself is not a good indicator of the size of a relationship. - Effect size is an index of the strength of a relationship that is not influenced by sample size. Importance of variance statistic:

Correlational and experimental research:

Meant to investigate relationships between or among 2 or more variables.

p-value:

Probability value= The likelihood of an observed statistic occurring on the basis of the sampling distribution. - Two-sided p-values: Scientists generally use these to test their research hypotheses. Type-sided p-values take into consideration that unusual outcomes may occur in more than one way.

Type 2 Error

Refers to the mistake of failing to reject the null hypothesis when the null hypothesis is really false - Psychologist concludes that the psychotherapy program is not working, when it really is. - Beta = probability of making a type 2 error - Type 2 errors are more common when the power of a statistical test is low

Statistical power: T

Statistical power: The probability that the researcher will, on the basis of the observed data, be able to reject the null hypothesis given that the null hypothesis is actually false and should be rejected. - Power written in terms of beta= 1-Beta - Beta can only be estimated - High sample size (N) à higher power for the test

Statistical significance formula

Statistical significance = effect size x sample size.

Null hypothesis:

The assumption that the observed data reflect only what would be expected under the sampling distribution

Importance of variance statistic:

The proportion of explained variability in the dependent variable is indicated by the square of the effect-sized statistic. - Portion of the dependent variable that is explained by the independent variable(s).

Effect Size:

The size of a relationship is indicated by effect size. - The effect size indicates the magnitude of a relationship. - Larger effect sizes indicate stronger relationships - The problem is that since a researcher doesn't know the effect size for the relationship they are examining, statistical power cannot be calculated. However, the researcher can estimate the effect size based on the effect sizes of previous research in the field - Effect size of a relationship can be more important than the statistical significance of the relationship bc it provides a better index of a relationships' strength. - Effect size can help if trying to decide between two experiments based on cost

Sampling distribution:

all the possible values of a statistic - For example: the sampling distribution for events that have two equally as likely possibilities, such as the distribution of correct/incorrect answers is called a binomial distribution

Inferential statistics

use sample data to draw inferences about the true state of affairs