Statistical tests (DP IB Psychology): Revision Note

Hypotheses

• A hypothesis is a testable statement written as a prediction of what the researcher expects to find as a result of their experiment

• Where the aim of a study is expressed in general terms and outlines the focus of the study; hypotheses must be precise and unambiguous

• There are two types of hypothesis:

  • The null hypothesis (H_₀)

  • The alternative hypothesis (H₁)

Alternative hypothesis (H₁)

• The H₁ should include the independent variable (IV) and the dependent variable (DV)

• Both the IV and the DV in the H₁ should be operationalised, which involves specifics on how each variable is to be manipulated (IV) and measured (DV)

• There are two different types of H₁:

  • Directional (one-tailed)

  • Non-directional (two-tailed)

• A directional hypothesis predicts the direction of the difference in conditions, i.e., it state that one condition will outperform the other

  • E.g., Participants who drink 200ml of caffeine before taking a memory test will correctly recall more items out of 15 than participants who drink 200ml of water before taking the same memory test

• A non-directional hypothesis does not predict the direction of the difference in conditions, i.e., it simply predicts that a difference will be shown

  • E.g., There will be a difference in the number of correctly recalled items out of 15 depending on whether participants have drunk 200ml of caffeine or 200ml of water before taking a memory test

Null hypothesis (H₀)

• All published psychological research must include the null hypothesis (H_₀); this is what all research starts with

• The H_₀ begins with the idea that the IV will not affect the DV

  • It is the default assumption unless empirical evidence proves otherwise

Testing hypotheses

• The researcher must then write the H_₀, which assumes ‘no difference’

  • E.g., There will be no difference in the number of correctly recalled items out of 15 depending on whether participants have drunk 200ml of caffeine or 200ml of water before taking a memory test

  • The researcher runs the experiment, uses statistical testing and then must form one of two conclusions:

    • If the result shows no difference between conditions (i.e., it is not statistically significant), then the H_₀ must be accepted

    • If the result shows a difference between conditions (i.e., it is statistically significant), then the H_₀ can be rejected (and the H₁ is then accepted)

Hypotheses in correlational research

• Hypotheses for correlational investigations are written in the same way as experimental hypotheses, apart from one crucial difference

  • Instead of using the term 'difference', you have to use the term 'relationship or correlation', e.g.,

    • There will be a relationship between the number of cups of caffeine drunk and the number of hours slept per night across one week

      • This is a non-directional hypothesis

    • There will be a negative correlation between the number of cups of caffeine drunk and the number of hours slept per night across one week

      • This is a non-directional hypothesis

    • There will be no relationship between the number of cups of caffeine drunk and the number of hours slept per night across one week

      • This is a null hypothesis

Factors affecting the choice of a statistical test

• A statistical test determines if a difference/correlation is statistically significant according the level of significance applied

• Applying a statistical test to a data set determines:

  • if the outcome is due to chance or to the effect of the IV on the DV

  • whether the null hypothesis can be accepted or rejected

• There are 3 distinct criteria that a researcher must consider before deciding which statistical test to use:

  • Have they conducted a test of difference or a test of correlation?

  • If they have conducted a test of difference, did they use an independent measures design, repeated measures design, or a matched pairs design?

    • an unrelated design refers to independent measures/groups

    • a related design refers to repeated measures and matched pairs

  • Have they collected nominal, ordinal or interval data?

• The table below illustrates which test should be used and when:

•  Chi-Squared is a test of both difference and association

• Spearman's rho and Pearson's r are tests of correlation

Parametric & non-parametric tests

• Parametric tests assume the following:

  • A normal distribution

    • Occurs when data is symmetrical around the mean

    • Most scores cluster near the mean; fewer are at the extremes

    • Produces the familiar bell curve shape

    • E.g., height is a measurement that has a normal distribution

  • The use of interval data or ratio data

    • Requires the most sensitive and precise level of measurement

  • Homogeneity of variance

    • If the set of scores per data set/condition are similar in terms of their dispersion

    • If both conditions have similar standard deviations, this suggests the data is equally spread and clustered around the mean

• Non-parametric tests do not follow the same criteria as parametric tests

  • There is no assumption of a normal distribution

    • Useful when data is skewed or not continuous

    • E.g., scores on a memory test

  • Non-parametric tests use nominal or ordinal data

  • Non-parametric tests do not depend on homogeneity of variance

• Parametric tests are more powerful and precise than non-parametric tests

  • More likely to detect a significant difference or correlation if one truly exists