Glossary
Alternative Hypothesis (Hₐ)
A statement that contradicts the null hypothesis, proposing that there is an effect, a difference, or a relationship between variables.
Example:
If the null hypothesis is that a new drug has no effect, the alternative hypothesis might be that the drug does reduce symptoms.
Bias
A systematic error in a study's design, data collection, or analysis that leads to results that consistently deviate from the true value.
Example:
If a survey about preferred ice cream flavors is only conducted at a chocolate factory, the results might have a bias towards chocolate.
Correlation vs. Causation
Correlation indicates that two variables move together, while causation means one variable directly influences another; correlation does not imply causation.
Example:
Observing that ice cream sales and shark attacks both increase in summer shows a correlation, but ice cream doesn't cause shark attacks; both are influenced by warm weather, illustrating correlation vs. causation.
Non-Random Patterns
Systematic and somewhat predictable variations in data, often indicating a genuine effect, a relationship between variables, or the presence of bias.
Example:
Observing that the number of hours studied consistently correlates with higher exam scores demonstrates a non-random pattern.
Null Hypothesis (H₀)
A statement of no effect, no difference, or no relationship between variables, which is assumed to be true until sufficient evidence suggests otherwise.
Example:
For a study testing a new energy drink, the null hypothesis would state that the drink has no effect on athletic performance.
P-value
The probability of observing a test statistic as extreme as, or more extreme than, the one calculated from the sample data, assuming the null hypothesis is true.
Example:
A p-value of 0.01 means there's only a 1% chance of getting results as extreme as yours if the null hypothesis were true, suggesting strong evidence against the null.
Practical Significance
Refers to whether a statistically significant result is large enough or meaningful enough to have real-world importance or utility.
Example:
A new diet might show a statistically significant weight loss of 0.5 pounds, but this might not have much practical significance for someone trying to lose a lot of weight.
Random Patterns
Variations in data that are unsystematic, unpredictable, and often attributed to natural variability or random error.
Example:
The sequence of heads and tails in a series of fair coin flips typically exhibits random patterns, with no discernible order.
Randomized Controlled Trials
An experimental design where participants are randomly assigned to different groups (e.g., treatment or control) to minimize bias and allow for causal inferences.
Example:
To test a new vaccine, participants are assigned to receive either the vaccine or a placebo in a randomized controlled trial to ensure any observed effects are due to the vaccine.
Statistical Significance
A determination of whether an observed effect or relationship in data is likely genuine and not merely due to random chance.
Example:
If a new teaching method leads to a statistically significant improvement in test scores, it suggests the method, not just luck, caused the change.
Test Statistic
A value calculated from sample data during a hypothesis test, used to measure how far the observed sample result deviates from what is expected under the null hypothesis.
Example:
In a t-test, the calculated test statistic indicates how many standard errors the sample mean is away from the hypothesized population mean.