A population is all possible cases of a certain entity with similar characteristics.
Can be defined broadly (e.g., all people) or more narrowly (e.g., people in Texas, people at a school).
Full population study is often impractical due to changing demographics and costs.
Example: A census collects data that quickly becomes outdated.
Researchers often rely on samples that ideally resemble the larger population.
Random Sampling: Minimizes bias; includes:
Simple Random Sampling: Every individual has an equal chance.
Systematic Random Sampling: Collect data at fixed intervals (e.g., every 10th person).
Stratified Sampling: Population divided into smaller groups (strata) like age, gender, ethnicity, with equal representation from each group.
Non-Random Sampling: Used when random sampling isn't practical, such as convenience samples.
Sampling Criteria: Specific requirements for selecting a sample relevant to the study type.
Example: Studying students with disabilities requires targeted sampling rather than random.
Defined as the degree to which a sample differs from the population.
Larger samples generally produce results that resemble the population more closely, reducing sampling error.
Standard Error: Inversely related to sample size; as sample size increases, standard error decreases.
Null Hypothesis (H0): Assumes no relationship or difference exists.
Example: No relationship between cholesterol levels and heart disease incidence.
Always stated negatively in relation to the alternative hypothesis.
Research Hypothesis: Posits a relationship or difference that the study will investigate.
Example: An exercise group will differ from a non-exercising group in outcome.
Number of null hypotheses increases with the number of independent variables.
Example: One independent variable leads to one null hypothesis; two variables lead to three null hypotheses; three lead to seven, etc.
Null hypotheses are foundational for statistical tests; often retained or rejected based on analysis results.
As sample size grows, confidence in the findings increases, allowing for the null hypothesis to be tested appropriately.
One-Directional Null Hypothesis: Predicts a specific direction of impact (improvement expected).
Example: New fertilizer will increase crop yield.
Two-Directional Null Hypothesis: Examines change without specifying direction (increase or decrease).
Example: Fertilizer could either increase or decrease yield, thus both tails of the distribution are evaluated.
Alpha Level (α): Represents the significance level for rejecting the null hypothesis; often set at 0.05 or 0.01.
One-tailed test: 5% rejection area in one tail means focusing only on increases or decreases.
Two-tailed test: 5% rejection area split between two tails; needs to consider both potential changes.
Null hypothesis is rejected if sample mean lies in the rejection region based on calculated Z scores.
Example: A Z score of 2.54 would lead to rejection if it exceeds the critical Z score threshold for the set alpha.
Type I Error: Rejecting a true null hypothesis (false positive).
Example: Finding a drug effective in lowering cholesterol when it is not impactful in the population.
Type II Error: Failing to reject a false null hypothesis (false negative).
Example: Not finding an effect that does exist, often problematic with small sample sizes.
Test Power: Likelihood of correctly rejecting a false null hypothesis; increases with larger sample sizes.
Emphasis on accurate hypothesis creation; hypothesis should be concise and reflect research aims.
Different methodologies (parametric and non-parametric) discussed:
Parametric Methods: Use when data meet normality assumptions (e.g., Pearson's correlation, T-tests).
Non-Parametric Methods: Employed when data doesn't meet parametric assumptions.
Other important concepts include: Levine's test to check group variances for equality before analysis.
Encourage further discussion with the instructor for clarifications and deeper understanding.
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