Hypothesis Testing in Statistics

Study Notes

Null Hypothesis (H0): a statement of no difference or no effect, predicting that the observed phenomenon is due to chance
Alternative Hypothesis (H1): a statement of difference or effect, predicting that the observed phenomenon is real
One-Tailed Test: tests whether the sample mean is significantly greater than (or less than) the population mean
Two-Tailed Test: tests whether the sample mean is significantly different from the population mean (in either direction)
Type I Error: rejecting the null hypothesis when it is actually true (false positive)
Type II Error: failing to reject the null hypothesis when it is actually false (false negative)
Level of Significance (α): the maximum probability of committing a Type I error, typically set at 0.05
P-Value: the probability of obtaining the observed results (or more extreme results) assuming the null hypothesis is true
Test Statistic: a numerical value that summarizes the difference between the sample data and the null hypothesis

Independent Variable: the variable being manipulated by the researcher
Dependent Variable: the variable being measured or observed in response to the independent variable
Control Group: a group that does not receive the treatment or manipulation, used as a baseline for comparison
Experimental Group: a group that receives the treatment or manipulation
Randomization: the process of randomly assigning participants to either the control or experimental group
Replication: repeating the experiment multiple times to increase the reliability of the results
Confounding Variables: variables that can affect the outcome of the experiment and are not controlled for
Blind Study: a study in which the participants or researchers are unaware of the group assignments or treatment conditions
Double-Blind Study: a study in which both the participants and researchers are unaware of the group assignments or treatment conditions

A null hypothesis (H0) proposes no real effect or difference, attributing observed outcomes to chance
An alternative hypothesis (H1) proposes a real effect or difference, suggesting observed outcomes are genuine
One-tailed tests examine if sample means are significantly greater or less than population means
Two-tailed tests examine if sample means differ significantly from population means in either direction
Type I errors occur when rejecting a true null hypothesis (false positive), with a 5% chance of occurrence (α = 0.05)
Type II errors occur when failing to reject a false null hypothesis (false negative)
P-values represent the probability of achieving observed results (or more extreme) assuming a true null hypothesis
Test statistics numerically summarize differences between sample data and the null hypothesis

Independent variables are manipulated by researchers to observe effects
Dependent variables are measured or observed in response to independent variables
Control groups serve as baselines, unaffected by the treatment or manipulation
Experimental groups receive the treatment or manipulation, allowing for comparison with control groups
Randomization ensures participants are randomly assigned to control or experimental groups
Replication involves repeating experiments to increase result reliability
Confounding variables can affect experiment outcomes and require control
Blind studies conceal group assignments or treatment conditions from participants or researchers
Double-blind studies conceal group assignments or treatment conditions from both participants and researchers

The first step in the scientific method, involving careful and systematic observations about the world around us
Can be done through direct observation (using senses) or indirect observation (using tools or instruments)
A good observation must be:
- Accurate (free from bias and error)
- Precise (detailed and specific)
- Relevant (related to the problem or question being studied)

A proposed explanation for the observations made, predicting the outcome of an experiment
Characteristics of a good hypothesis:
- Specific (clearly states what is being tested)
- Testable (can be proven or disproven through experimentation)
- Falsifiable (can be proven wrong if data doesn't support it)
- Simple (easy to understand and communicate)
Types of hypotheses:
- Null hypothesis (states no significant difference or relationship)
- Alternative hypothesis (states significant difference or relationship)