topic 3 Flashcards
What are the non-parametric equivalents of the Independent samples T-test and the Paired T-test?
Mann Whitney U-test and Wilcoxon Signed Rank Test respectively.
Why would you use ANOVA instead of T-tests to compare means?
ANOVA can compare any two of an input of two or more means, wheres T-tests can only compare two.
Also, conducting multiple T-tests would incur a larger chance of gaining a false positive e.g. 10 comparisons would require 0.95 to the power of 10 = 60%; therefore a 40% chance of a false positive.
ANOVA can also analyse data that comprises of two variable factors.
What does ANOVA analyse?
ANOVA analyses the chance that all the samples belong to the same population. It functions on the same critical threshold of 0.05%; a smaller p-value than this would indicate that the samples are from the same population.
How does ANOVA work and which figure would you use to aid a decision to reject or accept the null hypothesis?
ANOVA functions by splitting the data into two: between groups variance and within groups variance. i.e. how much do the values in each sample deviate away from the mean and how much do the different samples deviate away from one another?
The F-value with associated P-value is indicative of whether the hypothesis is false. A large F-ratio indicates a significant results whereas a small ratio indicates that the variance is due to random chance.
How do you calculate the F-ratio? Provide an example.
You divide the between groups variance by within groups variance. See pp.
How are the degrees of freedom calculated for an ANOVA?
Total degrees of freedom: n - 1
Between groups: groups - 1
within groups: total - between
How must you input your data in SPSS when performing an ANOVA?
The data must be aligned so that observations are in one column and the corresponding group code is in the adjacent column.
What are the significant values in the SPSS ANOVA output?
Degrees of freedom.
The mean square column holds the between and within groups variance.
The F-ration and the corresponding P-value.
e.g. low F-value and significant p-value means there is a lot of variation within groups compared to between but we still reject the hypothesis that there is no difference between varieties.
R squared value indicates how much of variation is explained by the variable.
How do you validate the results of an ANOVA?
Store the residuals when performing the test; only achievable when the test is accessed through the pathway: General linear model> univariate.
ANOVA requires that these are normally distributed, which can be shown though line graphs or Q-Q plots (‘normal’ residuals mean the dots will roughly lay on the fitted line for observed values against expected values).
Q-Q plots are accessed through: analyse> descriptive statistics> Q-Q plots.
What is the purpose of a Turkey post hoc test?
ANOVA only reveals if there is a significant difference in variation or not. This test reveals which two samples were significantly different to one another.
Which test must you use if the residuals from an ANOVA are not normally distributed?
Use a Kruskal Wallis test.
Accessed via: Analyse> non-parametrics> K independent samples.
What is a 2-way ANOVA?
An analysis of the influence of two factors on a dependent variable.
What are the 3 hypotheses used for a 2-way ANOVA?
The first factor has no influence on the dependent variable; the second factor has no influence on the dependent variable; the first and second factors do not interact.
Therefore, you are testing 3 null hypotheses simultaneously.
How would you organise the data in SPSS to perform a 2-way ANOVA?
Observations in one column with the other two factors in the following two adjacent columns; each of the factors with the levels of variation coded.
What are the important figures in a 2-way ANOVA output when deciphering whether to reject or retain the 3 null hypotheses?
There are 3 p-values that need to be assessed; each for corresponding to one of the 3 null hypotheses.
One for each of the factors and then: factor*factor.
Each p-value follows the same rule of 0.05 being the critical threshold.
