Type II Error

Hypothesis Testing

In hypothesis testing, data are collected from one or more samples and then used to make an educated guess, or inference, as to the state of affairs within the relevant population(s). In any given study, this educated guess will be focused on a specific statistical characteristic of the population(s), such as the mean (μ), the variance (σ2), or the correlation between two measured variables (ρ). After a researcher chooses his or her population(s), the variable(s) of interest, the statistical focus, and the planned method for analyzing the study's data, that researcher can use hypothesis testing as a strategy for making the desired statistical inference.

There are six steps involved in the most basic version of hypothesis testing. They involve the following:

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1.
Stating a null hypothesis (H0)
2.
Stating an alternative hypothesis (Ha)
3.
Selecting a level of significance (α)
4.
Collecting data from the study's sample(s)
5.
Determining the probability, presuming H0 to be true, of getting sample data like those actually collected or sample data that deviate even further from what would be expected (if H0 were true)
6.
Deciding either to reject H0 or to fail to reject H0

An example may help clarify the way these six steps permit a researcher to engage in hypothesis testing—and how hypothesis testing may lead to a Type II error. For this example, imagine that a researcher is hired to settle a dispute between two tax-payers from New York. One believes that if all high school seniors in the state of New York were given an intelligence test, the students' mean IQ would be higher than the national average of 100. The other believes just the opposite. Also imagine that the researcher, once hired, identifies a random sample of 25 students, that each student's intelligence is measured by a trained psychologist, and that the resulting IQ scores yield a mean of 104 with a standard deviation of 15. Finally, imagine that the researcher intended from the beginning to subject the data to a one-sample t test with a level of significance equal to .05. For this example, the six steps of the hypothesis testing procedure would be as follows:

1.
H0: μ= 100.
2.
Ha ≠ 100.
3.
α= .05.
4.
In the sample, n = 25, M = 104, and SD = 15.
5.
p = 0.1949.
6.
H0 is not rejected.

As applied to this example, the logic of hypothesis testing is straightforward. If the null hypothesis were false, a random sample should most likely produce a mean that is dissimilar to the number specified in H0. However, the mean IQ of the 25 students, 104, is not very inconsistent with what would be expected if H0 were true. (With the estimated standard error of the mean being equal to 3.0, the t test's calculated value is equal to 1.33.) Because the probability associated with the sample (p = .19) is larger than the selected level of significance, the researcher decides that the evidence available is not sufficiently “at odds” with H0 to cast doubt on the null statement that the mean IQ of high school students in New York is equal to 100. Consequently, the null hypothesis is not rejected.

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