Sampling and Bias in Research Methods

A distribution of a statistic calculated from multiple samples drawn from the same population.

A statistical hypothesis stating that there is no significant difference between population parameters or a relationship between variables.

A statistical hypothesis stating that there is a significant difference between population parameters or a relationship between variables.

The probability of rejecting a true null hypothesis.

The probability of failing to reject a false null hypothesis.

In probability sampling, each element in the population has an equal chance of being selected for the sample.

A starting point is chosen randomly, and then every nth element is selected from the population list.

The population is divided into groups based on a characteristic, and then samples are randomly drawn from each group.

The sampling unit is a group or cluster, not individual elements, and either the cluster or elements within are randomly selected.

Sample selection is based on convenience, using readily available elements. It's often used for quick and cost-effective research.

The researcher's judgment is used to select participants who have specific characteristics relevant to the study.

The researcher sets quotas for different subgroups within the population and selects individuals based on those quotas.

A method used to determine whether we can reject the null hypothesis based on statistical evidence. It assesses the probability of observing the data if the null hypothesis were true.

The probability of observing the data if the null hypothesis were true.

A predetermined threshold used to decide whether to reject the null hypothesis. It's the probability of rejecting the null hypothesis when it is actually true.

A value representing the level of confidence in a research finding. It is calculated as 1 - Alpha.

The probability of rejecting the null hypothesis when it should be rejected

The level of statistical significance is often expressed as P-value (α). This value represents the probability of observing the difference between the groups if there were no actual difference - basically, the chance of getting the observed results if the null hypothesis is actually true.

The null hypothesis is a statement that there is no significant difference between two groups, or no relationship between two variables. For example, a null hypothesis might state that there is no difference in bone mass between those who take a drug and those who don't.

The alternative hypothesis is a statement that there is a significant difference between two groups, or a relationship between two variables. For example, an alternate hypothesis might state that there is a difference in bone mass between those who take a drug and those who don't.

The significance level, also known as P-value (α), is the threshold we set for accepting or rejecting the null hypothesis. If the probability of the observed results occurring by chance is less than α, then we reject the null hypothesis. Typically, α is set to 0.05 (5%).

A researcher wants to test if a medication affects bone mass. They measure bone mass in a group before and after the medication. If they find a difference in these measurements, the P-value tells them how likely it is that they observed this difference by pure chance. For example, a P-value of 0.03 would indicate that there's only a 3% chance of observing this level of effect if the medication actually had no effect.

A critical value is a number that separates the rejection region from the non-rejection region. If the test statistic (a summary of the data) falls in the rejection region, then we reject the null hypothesis. If the test statistic falls in the non-rejection region, then we do not reject the null hypothesis.

The critical region is the range of values for the test statistic that indicates that there is a significant difference between groups or a significant relationship between variables, and thus we reject the null hypothesis. The non-critical region is the range of values that suggests there is no significant difference or relationship, and the null hypothesis is not rejected.

Test statistics are summary values that provide information about the differences between groups or the relationships between variables. It helps us determine if the results of a study are statistically significant based on the test statistic value. The test statistic is compared to the critical value, which is specific to a certain type of test, to see if there is a statistically significant difference between the groups or variables.

The P-value (α) defines the sensitivity of the test. If the P-value is lower, it means that the test is more sensitive to detecting smaller differences. For example, a P-value of 0.01 would indicate a more sensitive test than a P-value of 0.05, and the null hypothesis is more likely to be rejected.