Hypothesis testing

Introduction to Hypothesis TestingWorking With Geographic InformationWeek 7: Hypothesis TestingKey Topics:

  • Hypotheses

  • Significance

  • Steps for Hypothesis Testing

Understanding HypothesesDefinition: A hypothesis is a formal statement that can be tested statistically.Examples of Testable Hypotheses:

  • The onset of spring in 2013-2023 was earlier than during the previous decade.

  • Indigenous women in Australia exhibit higher stress indicators than any other racial minority.Non-examples:

  • The extent of temperature rise over the last decade.

  • How GIS can enhance conservation efforts.

Null and Alternative HypothesesNull Hypothesis (H0): The claim being tested; usually states "no effect" or "no difference."Alternative Hypothesis (H1 or Ha): What we seek evidence for; may be one-sided (greater or smaller than the null) or two-sided (different from the null).

Examples of Null HypothesesExamples:

  • The timing of spring onset in 2020-2023 was the same as the previous decade.

  • Stress indicators for Indigenous women are the same as those of other racial minority groups.

Purpose of the Null HypothesisSignificance of Null Hypothesis:

  • It is a statement we aim to refute through testing.

  • Differences observed may not be “true,” but statistically unlikely to occur randomly.

Examples of Alternative HypothesesOne-sided Hypotheses:

  • The onset of spring in 2013-2023 was earlier than the previous decade.

  • Indigenous women in Australia exhibit higher stress indicators than other racial minorities.Two-sided Hypotheses:

  • The onset of spring in 2013-2023 was different from the previous decade.

  • Indigenous women in Australia exhibit different stress levels from other racial minorities.

Significance in Hypothesis TestingHypothesis testing often involves differences between two datasets.Various tests for differences can be applied based on research questions and data characteristics.Outputs of statistical tests usually include a test statistic and an associated significance (p-value).

Understanding Statistical SignificanceDefinition of Significance:

  • In daily language, it often means "importance," but in statistics, it has a specific meaning.

  • Avoid confusing significance with importance in academic writing.

Probability and Statistical SignificanceStatistical significance relates to probability.Example of probability: The likelihood of getting "heads" when flipping a coin.

Interpreting Test Statistics and P-valuesThe test statistic results are not always intuitively understood; however, p-values are more interpretable.P-value: Indicates the likelihood of observing the test result due to random variability.A p-value of 0.5 suggests the result is observed half the time by chance.A small p-value indicates it is unlikely due to random chance.

Determining Statistical SignificanceA small p-value allows us to reject the null hypothesis.Alpha (α) Value:

  • The predetermined significance level.

  • Common values: 0.01 or smaller for physical geographers and 0.05 or smaller for human geographers.

Statistical Significance LevelIf p-value ≤ α, the data are considered statistically significant at the significance level α.

Steps for Hypothesis Testing (Preparation)Define Your Research Question:Examples:

  • Is spring onset occurring earlier in the last decade?

  • Do Aboriginal Indigenous women experience more stress than other racial minorities?Collect and Understand Data:

  • Timing of spring onset from remotely sensed observations.

  • Stress indicators for Indigenous women and other racial minorities.Describe and Compare Data:

  • Assess if the data follows a normal distribution.

  • Explore multi-modal distributions or skewed data through transformations.

Steps for Hypothesis Testing (Execution)Testing Differences for Statistical Significance:Actions:

  • Choose an appropriate statistical test.

  • Set up null and alternative hypotheses.

  • Decide on the significance level (α).

  • Calculate the test statistic.

  • Interpret the results of the test statistic.

Concluding Hypothesis TestingConclude Findings:

  • Your conclusion will depend on the significance of the test result.

  • If p-value < α, reject the null hypothesis.

  • This conclusion does not confirm the alternative hypothesis but indicates the results are unlikely due to random variability.Examples of Conclusions:

  • Mean spring onset timing was earlier for 2013-2023 than in the previous decade.

  • Indigenous women in Australia experience higher stress levels than other racial minorities.