These tests analyse data presented in a contingency table, an example of which is given below
Observation X Observation Y Total
Group A 200 250 450
Group B 100 450 550
Total 300 700 1000
Table 2.7: Example of contingency table, with illustrative values
Chi2 testing and Fisher’s exact test measure the significance of association between the two classifications in the table (observation X and observation Y).
Both the chi2 test and Fisher’s exact test analyse categorical data (eg placental finding present - Group A, or absent - Group B) with numerical data (numbers in each group).
The counts are presented in a contingency table with analysis of counts in the context of predetermined level of significance and degrees of freedom (based on the numbers of
population, and so Fisher’s exact test (which becomes unbalanced with large populations) is used with smaller populations. By convention, Fisher’s exact test is used when a cell in the contingency table contains a value of 5 or less. Many statistics programmes provide both Fisher’s exact and mid P exact values. Fisher’s exact test is “conservative” – it requires more evidence than is necessary to reject a null hypothesis. Mid P is more
“powerful”, is better suited to larger populations, and delivers a p value that is closer to the p value for entirely uncorrected data. In this study, the possible conflict between small numbers (in individual subgroups) and large numbers (the whole study) is addressed by examining, where appropriate, both Fisher’s exact and mid P values.
The Mantel-Haenszel test is used in meta-analysis, providing a pooled odds ratio (qv) across independent studies, by analyzing data entered in multiple 4x4 contingency tables. It thus tests whether the overall degree of association is significant. When combined with a chi2 test, data can be assessed for equality as well as a pooled odds ratio.
D’Agostino-Pearson normality test
A completely normally distributed population is expressed graphically as a bell-shaped curve, symmetrically distributed about the mean. The spread depends on the variable under study, but ~ 68% of observations lie within 1 standard deviation of the mean, and 95% of observations lie within 2 standard deviations of the mean. A data set may be tested for
“skewdness” and deviation from normal distribution with a normality test formula, which calculates the variation of each value from the value expected with a Gaussian distribution, and computes a single p value from the sum of these discrepancies.
Mann-Whitney test
The Mann-Whitney test compares the median values of two groups – with a small p value, the null hypothesis that there is no difference between the median values of two groups can be rejected. A large p value does not imply that the medians are the same, but provides no statistical evidence that they differ. Gaussian distribution is not necessary for this analysis.
Odds ratio and 95% confidence interval
An odds ratio is commonly expressed as a statistical “best guess” as to the size and direction of the effect of an experimental intervention compared to a control intervention.
In this study, this concept is adapted in that the “intervention” takes the form of a specific
placental finding with the control group formed by those cases in the study group not showing this finding.
The odds ratio is presented as a single number – a point estimate. A positive odds ratio implies a positive association with a given clinical outcome, while a negative odds ration implies a negative (or protective) association with a given clinical outcome. The odds ratio is, however, expressed in the context of a 95% confidence interval. Very wide confidence intervals imply that the true effect is unclear, and a confidence interval which crosses zero implies that there is no clear evidence for a significant odds ratio in either direction.
One way ANOVA and Bartlett’s test
This statistical test assesses the equality of three or more means, with the null hypothesis that the population means are equal. This test assumes normal distribution, and will identify at least one mean which is different – although not where the difference lies. The ANOVA test also assumes equal variance (the spread of values from the mean) within each population, but this can be confirmed by applying Bartlett’s test to the data sets.
P values (one tailed and two tailed)
The p value is a numerical expression of the outcome of a null hypothesis (H0) test. For example, in this study, observed placental findings are analysed in the context of clinical outcome, generating the null hypothesis that placental finding A is not associated with clinical outcome B. Rejection of the null hypothesis requires a p value less than a specific value, conventionally < 0.05 – implying that there is a probability of 0.95 that rejection of the null hypothesis is the correct decision. In this study, given the large number of
calculations undertaken, p values around 0.05 are carefully reviewed.
The p value generated from the testing of any null hypothesis can be expressed as one-tailed or two-one-tailed. One-one-tailed p values are used in a context only where there is pre-existing statistical evidence for an effect that is unidirectional. In this project, a one-tailed p value would imply, for example, that placental finding A is already known (from pre-existing analysis of the project data) to be positively associated with clinical outcome B.
This does not apply to the data in this project and so two-tailed p values, which test for statistical significance in both directions, are used throughout.
Spearman’s rank correlation coefficient
Spearman’s rank correlation coefficient measures the strength of association between two ranked variables. This test applies to monotonic variables: where one variable increases, a second increases/decreases. The value generated, rs, lies between +1 (perfect association), 0 (no association) and -1 (perfect negative association). The data do not have to conform to a particular pattern of distribution for this analysis (non-parametric).
T test
The t test compares the means of two groups for statistical significance, while taking into account the spread of the data (standard deviation) and number of subjects in each group (degrees of freedom).
z scores
z scores standardize measurements from different groups, by transforming raw values to a score expressing the standard deviation from the mean for each data value. Initial
calculation of the mean and standard deviations for each data group are thus required. The resulting values are often thus more informative than comparison of means between groups, as each data value is indexed.
2.3 CONCLUSIONS
Recruitment protocols drawn up
Clinical data recorded on a password protected NHS Trust server1
Placentas examined in accordance with a standardized protocol1
Analysis of placental eccentricity (shape) and cord insertion undertaken1
Computer based analysis of photographs showing placental infarction undertaken
Tissue blocks from the prosected placentas processed to paraffin2
Haematoxylin and eosin2 and immunohistochemical staining3 of tissue sections undertaken
Diagnostic criteria for a range of placental lesions drawn up, with two rounds of reporting4: the first in accordance with current clinical reporting protocols, the second to identify all possible histological lesions
Computer based analysis and scoring of immunohistochemical slides undertaken
Systematic review methodology reviewed and adapted for histopathology-based research
Statistical tests selected for analysis of project data
1. Collection of clinical data, analysis of placental eccentricity and cord insertion site and approximately 50% of placental prosection was undertaken by Dr Sangeeta Pathak, Clinical Research Fellow, Department of Obstetrics and Gynaecology, Addenbrooke’s Hospital.
2. Tissue block processing, cutting and H&E staining were carried out by members of the biomedical science team, Addenbrooke’s Hospital.
3. Immunohistochemical micro-array tissue blocks and immunohistochemical staining was undertaken by Ms Rebecca West, biomedical scientist, Great Ormond Street Hospital.
4. The initial round of reporting was undertaken jointly between Dr F Jessop and Professor NJ Sebire.