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Block 1 Unit 3 Type I and Type II Errors

i) What is a Comparison Distribution?

A comparison distribution is a theoretical distribution that represents the population situation if the null hypothesis is true. In hypothesis testing, you compare the actual sample's score to this comparison distribution to determine the probability of obtaining your results if the null hypothesis were true.

ii) What is a Research Hypothesis?

A research hypothesis is a statement that proposes a specific relationship or effect between variables. It is the prediction that researchers aim to support through their study. For example, a research hypothesis might state that "a new drug will reduce blood pressure more effectively than the existing drug".

iii) What is a Directional Hypothesis?

A directional hypothesis predicts the direction of the effect, stating whether one variable will be higher or lower than the other. For instance, a directional hypothesis might predict that "participants who receive cognitive-behavioural therapy will experience lower levels of anxiety compared to those who receive no treatment".

iv) What is a Type I Error?

A Type I error, also known as a "false positive," occurs when you reject the null hypothesis when it is actually true. This means you conclude there is a significant effect or relationship when there is none. For example, you might conclude that a new teaching method is more effective when it is not, based on the sample data.

v) What do you Mean by a Two-Tailed Test?

A two-tailed test is used when the research hypothesis does not specify a direction for the effect, only that there will be an effect. The critical region for rejecting the null hypothesis is divided between both tails of the comparison distribution. This is in contrast to a one-tailed test, which focuses on one direction of effect.

vi) Describe Briefly the Relationship Between Type I & Type II Errors.

There is an inverse relationship between Type I and Type II errors. When you decrease the probability of making a Type I error (by setting a more stringent significance level), you increase the probability of making a Type II error. Conversely, when you decrease the probability of making a Type II error (by setting a more lenient significance level), you increase the probability of making a Type I error. Researchers must balance these risks when choosing a significance level for their study.

Important Points

i) The research hypothesis and null hypothesis are completely opposite. The research hypothesis proposes a specific relationship or effect, while the null hypothesis states that there is no such relationship or effect.

ii) Cutoff sample scores are also known as critical values. These values mark the threshold beyond which the null hypothesis is rejected.

iii) In a Type I error, we reject the null hypothesis when it is true. This is also known as a "false positive" and occurs when the sample data lead to the incorrect rejection of a true null hypothesis.

iv) The hypothesis in which we fail to reject the null hypothesis is called not statistically significant. Note that we do not "accept" the null hypothesis, as the results might be inconclusive.

v) The probability of making a Type II error is called beta (β).

vi) The significance level, which is the chance of making a Type I error, is called alpha (α). The significance level (α) is the probability of rejecting the null hypothesis when it is actually true (Type I error).

vii) A one-directional hypothesis is tested with a one-tailed test. A one-tailed test is used when the research hypothesis predicts the direction of the effect (e.g., higher or lower).

viii) A hypothesis that predicts an effect but does not predict a particular direction for the effect is called a non-directional hypothesis.

ix) A one-tailed test has either direction only. It focuses on a specific direction of effect, either positive or negative.