Research Methods B Flashcards
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What do parametric tests assume (3)
Normal distribution
Homogeneity of variance (if comparing 2 or more groups)
Interval or ratio data
What do non-parametric tests assume
Nothing
Advantage and disadvantage of parametric tests compared to non-parametric
Adv: More powerful - can detect differences better
Disadv: Less flexible
How can a parametric test still be used if parametric assumptions are not met
Transform the data to normalise data distributions
Kolmogorov-Smirnov test (K-S)
Tests the probability the data belongs to a normal distribution
Hypothesis and null hypothesis of Kolmogorov-Smirnov test
H1: Variable is not normally distributed
H0: Variable is normally distributed
Conclusion if p < 0.05 in Kolmogorov-Smirnov test
Significant, reject H0, therefore not normally distributed
Conclusion if p > 0.05 in Kolmogorov-Smirnov test
Not significant, accept H0, therefore is normally distributed
What should be reported if SPSS gives p = 0.000 and why
0.001, SPSS cannot round past 3 decimal places and p can never be 0
Levenes test
Tests the homogeneity of variance, determines data sets are from the same population or not
Hypothesis and null hypothesis of the Levenes test
H1: Variance is not equal
H0: Variance is equal (homogenic)
Conclusion if p < 0.05 in the Levenes test
Significant, reject H0, variance is not equal
Conclusion if p > 0.05 in the Levenes test
Not significant, accept H0, variance is equal
How to test whether to use a parametric test
Conduct a Kolmogorov-Smirnov test and Levenes test, if p > 0.05 in both then assumptions have been met and a parametric test can be performed
What kind of data is needed for all parametric tests
Interval or Ratio
Chi-squared ‘goodness of fit’’ test (GF)
Compares a samples proportions to that of the population
How a Chi-squared test works
Frequencies of participants are compared to generated expected frequencies based on the null hypothesis (that nothing is going on). If significantly different from observed, results are significant
Different null hypothesis’ for Chi-squared goodness of fit (2) and examples
1) No difference between the categories
Eg - the number of men and women are equal
2) No difference between the categories’ frequency distribution
Eg - number of men and women in computing reflects the proportions at the university
(which one is chosen changes the expected frequencies)
Expected frequencies (for Ch-squared goodness of fit) = …
proportion of population x sample size
Proportion depends on which null hypothesis chosen
Chi-squared (X^2) = …
sum of ( (frequency observed - frequency expected)^2 / frequency expected )
Chi-squared ‘test for independence’ (TI)
Tells whether two groups are associated or independent of influence
Chi-squared ‘test for independence’ (TI) example
Does gender influence smoking frequency
Chi-squared ‘goodness of fit’’ test (GF) example
Are there more men in the computing department than there would be by chance
How is expected frequencies calculated for Chi-squared test for independence
What the results would be completely down to chance…
= column total x row total / n
Conclusion if Chi-squared value is lower than critical value found in the table
Results are not significant, accept H0 that nothing is going on
How many variables can a Chi-squared test compare at a time
2
T-tests
Compare the means of two groups, looking for differences between them (H1), telling us if the difference in means falls n the most extreme 5%
Types of t–test (3)
Independent, dependent, one sample
Other names for independent t-tests (2)
Unrelated, between groups
Other names for dependent t-tests (4)
Related, paired sample, within groups, repeated measures
Requirements to conduct a t-test (2)
Data meets parametric assumptions
and is interval or ratio data
Independent t-test example H1
Students who do extra reading for their module get higher grades (IV = extra reading, DV = Higher grades)
Conclusion if p < 0.05 for an independent t-test
There is an extreme, real difference in groups means, they are a part of different populations
Sample distribution of the difference between means
Theory that, if the null hypothesis is correct, plotting all the difference means of randomly selected participants from each group would form a normal distribution curve
What does the t statistic from t-tests show
How many standard deviations the difference between the means is from 0
One sample t-test
Compares the sample mean with that of a known populations’
One sample t-test example
Are 1st year psychology students more intelligent than the population in general (mean IQ = 100)
How to report t-tests
t (df) = t-value, p = p-value
What does a larger t-value mean
the larger the difference of the means
One sample Wilcoxon signed rank test
Tests if the median of the measurement is equal to a specific value (population median), determining whether the sample is part of the general population
Requirements for using the One sample Wilcoxon signed rank test (3)
Non-parametric, comparing independent groups (sample and population), interval or ratio data
Hypothesis and null hypothesis for the One sample Wilcoxon signed rank test
H1: Median significantly different from population median (can be one-directional)
H0: Median similar to population median
Conclusion if p < 0.05 in the one sample Wilcoxon signed rank test
Significant, so the median is significantly different from the populations
Example of independent t-test
Is there a difference between male and female numerical ability scores
Requirements for an independent t-test (2)
Parametric assumptions met, interval or ratio data
Conclusion if p < 0.05 for an independent t-test
Significant difference between the groups, a part of different populations
For an independent t-test, when should the row ‘equal variance not assumed’ be used?
Questionable but can be in occasional circumstances when a Levenes test is significant so equal variance cannot be assumed
Requirements for Mann-Whitney test (2)
Interval, ratio data (sometimes ordinal)
Non-parametric so no assumptions
Mann-Whitney test (U)
Equivalent to independent t-test, it tests whether the distributions of both groups are equal or significantly different
What does the U value for Mann Whitney tests mean
the closer to 0, the more the groups medians are equal (H0 being true)
Conclusion if p < 0.05 for Mann Whitney test
Significant difference between the groups medians, reflecting a real difference in populations
When to use the ‘exact sign.’ U and p values in the table given for a Mann Whitney test
If the sample is less than 20 (small)
What to report when reporting Mann Whitney test results (4)
U-value
p-value
Z score
Medians
Effect size (R) = …
Z / square root N
Difference between N and n
N = number of all observations n = number of observations in the sample
Requirement for a dependent t-test (3)
Related groups
Parametric assumptions met
interval or ratio data
What do dependent t-tests typically measure
A sample doing the same thing twice (before and after doing something else)
Can also be matched pairs of similar units
Example of dependent t-test
Amount of pull-ups done before and after participants train in a bootcamp
Conclusion if p < 0.05 in a dependent t-test
Significant, H0 rejected, a significant difference between samples before and after
Degrees of freedom = …
(N.1 - 1) + (N.2 - 1)
What to do with results if we have a one-tailed hypothesis
divide the p-value by 2 and then see if its significant
When are effect sizes used a lot for comparisons
In medicine and forensics to compare with (eg) results of other drugs
Effect size is…
a way to quantify between two groups, it emphasises the size of difference without confounding with the sample
The difference between two sample means
How effect size can be measured (2) and when should each of these be used
Pearson’s r - for non parametric tests
Cohen’s d - for parametric tests
Small medium and large for Pearson’s r
Small: > 0.1
Medium: > 0.3
Large: > 0.5
How to calculate Cohen’s d
Difference between means divided by the ‘pooled’ standard deviation for the means
Small, medium and large for Cohen’s d
Small: 0.2
Medium: 0.5
Large: 0.8
(it can be over 1)
What would a small Cohen’s d likely mean
A larger sample is needed
Wilcoxon signed rank (matched pairs) test
Non-parametric equivalent to repeated measures t-test, it tests the difference of medians for repeated samples
Requirements for Wilcoxon signed rank (matched pairs) test (3)
Non parametric
Ordinal data or above
Repeated samples
Conclusion if p < 0.05 for Wilcoxon signed rank (matched pairs) test
Significant difference between the samples medians, accepts H1. They are from different populations
What to report for a Wilcoxon signed rank (matched pairs) test (3)
Z value
P-value
Medians
What does N equal for repeated measures design
Still means both samples, so is participants x 2
Df =… for chi squared tests
(Number of Rows - 1) x (number of columns - 1)
Limitation of a p value
Only gives statistical significance, not real life significance
Other name for One sample Wilcoxon signed rank test
Wilcoxon rank sum test
z score = …
x - mean / SD
What does a z score mean
The number of standard deviations that the score is away from the mean
How to report Chi-squared
X^2(df) = Value, p = p-value
How to report a Wilcoxon signed rank / rank sum test
T = T-value, p = p-value… (state medians before)
Slides say only p-value essential for APA format
How to report a Mann-Whitney U test
U = U-value, Z = Z-value, p = p-value… state medians before
How to report a Wilcoxon signed rank (matched pairs) test?
Z = Z-value, p = p-value… state medians before
Different null hypothesis’ for Chi-squared test of independence
No relationship between categories
Proportions are the same for the categories
Hypothesis for Mann-Whitney test
Probability of observation from one population exceeding the other is more than 0.5
Null hypothesis for Mann-Whitney test
Equal distribution of both groups, probability of observation from one group exceeding the other equals the probability of the reverse
