Flashcards
Categorical data calculations
Cards in this deck (24)
- 1How can categorical data be presented for analysis?Contingency tables are a common method. The variables are often nominal but they can be ordinal or binary too (e.g. Disease/No Disease).
Contingency tables are termed as r x c tables where r = rows and c = columns. The table above would therefore be a 2x2 table.
When there is a directional relationship, independent variables are presented as rows and dependent variables are presented as columns. - 2What is risk?A measure of the probability of an event occurring in a defined population within a given amount of time (e.g. the likelihood of migraines in MSc. TDB students between 22nd Nov - 10th Dec 2019)
- 3What is a risk difference?The proportional difference in risk between two groups (e.g. control and group of interest). Also known as the attributable risk due to the implication that the difference can be attributed to an exposure.
- 4What if the exposure is preventative and not a risk?The formula is instead:
PF = [Incidence (unexposed) - Incidence (exposed)] / Incidence (unexposed) - 5What is a risk ratio?The proportional difference between two groups' outcomes. No difference would equate to an RR = 1.
- 6What is a rate ratio?The same as a risk ratio but with a time frame considered.
- 7Why are risk and rate ratios used?They are easily understood and conveyed (e.g. MSc. TDB students are 40x more likely to develop a migraine if they study)
- 8When can you not use risk ratios?In studies where the sample statistic (e.g. Disease/No disease) does not estimate for the population parameter.
For example, in case control studies, the prevalence of a disease in the study would be pre-determined and the prevalence in the at-risk population would not be known. Instead, odds ratios are used. - 9What are odds ratios?They describe the difference in likelihood that an element with a particular outcome was/wasn't exposed. They are not risk ratios. You cannot infer causality with odds ratios.
They must be expressed in terms of "odds of x compared to the odds of y". - 10Calculate the odds ratio in this example(71/24) / (38/152) = 11.84
In the case group, the odds of exposure to the suspected risk is 12 times greater than in the asymptomatic group. - 11How do you calculate the confidence interval of a risk ratio?The RR is first converted into logarithmic form.
d1 = exposed group with the outcome
d0 = unexposed group with the outcome
n1 = total of exposed group
n0 = total of unexposed group
The result is +/- from the ln(RR) then converted out of the logarithmic form using the exponential function, e.
- 12How do you calculate the confidence interval of an odds ratio?The OR is first converted into logarithmic form.
a, b, c and d refer to the cells in the contingency table.
The result is +/- from the ln(OR) then converted out of the logarithmic form using the exponential function, e.
- 13How can you test whether a risk ratio or odds ratio is statistically significant?RRs and ORs are measures of the magnitude of the differences between groups. However, they do not determine whether an association is statistically significant, no matter how large the number.
The main tests for comparing differences in categorical variables are the Chi squared test and Fischer's exact test. - 14What is a Chi squared test?Also known as the Pearson's Chi squared test.
It tests hypotheses comparing two groups of categorical data.
They test if the variables are independent of one another.
They also always use frequencies and never proportions.
It can test for homogeneity, association and independence.
It can also be used to test the "goodness of fit" - 15How is a Chi squared value calculated?The formula for the expected values depend on what kind of test will be performed: homogeneity, association or independence.
- 16How is a Chi squared value calculated for a homogeneity test?The null hypothesis is that there is no difference (homogeneity) between the values in the contingency table. Therefore, the expected value is the mean of all the observed values.
A Chi squared distribution table is then assessed. - 17How is a Chi squared value calculated for an association test?The expected value is calculated for each cell:
(row total x column total) / population total
The degrees of freedom is then determined.
df = (# of row categories - 1) x (# of column categories - 1)
A Chi squared distribution table is then assessed.
- 18When is a Chi squared test not ideal?Chi squared tests are ideal for contingency tables with multiple variables. However, for 2x2 tables, it provides p values that are too small. This results in false positives (Type 1 errors).
To correct for this, the Yates' Continuity Correction is applied to the formula. - 19What is the Yates' Continuity Correction?It is a correction applied to artificially reduce the Chi squared value. This is done to increase the resultant p values thus reduce the likelihood of false positives (Type 1 errors).
The Yates' correction is simply reducing the (O-E) by 0.5.
- 20What is the Chi squared "goodness of fit" test?It is an application of the Chi squared test to determine how well the data set can be modeled against a theoretical distribution.
The method is the same as a normal Chi squared test but the expected values are each data point's corresponding value in the theoretical distribution.
- 21Why is it important to measure the magnitude of association?With large sample sizes, small associations are likely to be detected despite being very weak.
- 22How can the magnitude of associations be calculated?Either through risk ratios, odds ratios or Phi.
- 23How can Phi be calculated?When two variables are being compared, a Phi calculation can be performed.
X^2 = Chi squared
n = number of samples
The Phi value will be between 0 (no association) and 1 (perfect association)
- 24What is the relationship between odds ratios and Phi?This table shows the corresponding odds ratio to Phi values.
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- Public Health Flashcards on Categorical data calculations, created by Ralfh Pulmones on 10/11/2019.
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- Ralfh Pulmones · Nov 2019
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- Nov 10, 2019
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