Statistical Correlation Tests
Statistical correlation tests are performed with the aim of finding out whether a relationship exists between variables, and then determining the magnitude and action of that relationship. In other words, correlation is a statistical measure that expresses the extent to which two variables are linearly related. It’s commonly used for describing simple relationships without making a statement about cause and effect.
If two variables tend to move up or down together, they are considered to be positively correlated. However, if they tend to move in opposite directions, they are considered to be negatively correlated.
Parametric tests are based on an assumption that the data being analyzed follows a normal distribution. The more data points a distribution has, the more it can approach a normal distribution. Lack of data points would require the use of non-parametric tests.
Non-parametric tests a.k.a. distribution-free tests are methods of statistical analysis that do not require a distribution to meet the required assumptions to be analyzed, especially if the data is not normally distributed.
Student T-Test
UNPAIRED T-TEST – testing two means
The unpaired t-test a.k.a. independent t-test is a statistical test which aims to determine whether there is a difference between two unrelated groups. The unpaired t-test is used to make a statement about the population based on two independent samples. To make this statement, the mean value of the two samples is compared.
ANOVA – testing more than two means
ANOVA a.k.a. Analysis of Variance, is a statistical test used to investigate the difference between the means of more than two groups. A one-way ANOVA uses one independent variable, whereas a two-way ANOVA uses two independent variables.
CHI-SQUARED TEST – testing the association between two categorical variables
A chi-squared test is a statistical test that is used to compare observed and expected results. The main aim of the chi-squared test is to identify whether a disparity between actual and predicted data is due to chance or to a link between the variables under consideration.
Choosing the Right Test
Bias Potential Sources
Bias is the systematic deviation from the truth. Different sources of bias may include:
- selection or sampling bias – inadequate selection of study participants usually due to high non-response rate, inadequate follow-up, inadequate sampling method use, or inadequate controls or comparisons groups
- confounding bias – existing differences between comparison groups in one or more parameters which may be directly associated with the outcome and the candidate risk factor in question
- instrumental bias – faulty measurement instrumentation due to lack of calibration, inaccurate diagnostic tests, etc
- information bias – systematically incorrect measurements or responses, or from differential misclassification of disease or exposure status of participants eg. due to questionnaire ambiguity or insensitivity
- systematic bias – one observer may underestimate readings, leading to his respondents having lower readings than those observed by someone else
- respondent bias – misunderstandings, lack of interest, or recall issues in the unaffected group
- random bias – observer may underestimate or overestimate measurements, which mistakes tend to even out on averaging
Calculating Statistical Risk
In statistics, the risk for a particular group to develop a disease refers to the rate of disease in the group concerned.
RISK DIFFERENCE / ABSOLUTE RISK – the excess risk that exposed individuals have.
RISK RATIO – the measurement of the risk in the exposed group as a multiple of the risk in the unexposed group.
ODDS RATIO – odds refer to the chance of developing the disease rather than not developing the disease. Odds Ratio refers to the chances of developing the condition for an exposed individual relative to an unexposed individual.
The Relevance of Testing the Sensitivity & Specificity of a Screening Diagnostic Test
Screening programs need to provide diagnostic tests with the least disturbance possible for the individual, yet with enough sensitivity and specificity to detect the disease in question. Assessing the sensitivity and specificity of a test requires its outcome to be compared against a gold standard eg. comparing the Faecal Occult Blood Test sensitivity and specificity to a colonoscopy, in this case considered to be the gold standard.
Multi-Variate Analysis
Linear regression analysis is used to predict the value of a variable based on the value of another variable. The variable you want to predict is called the dependent variable, while the variable you are using to predict the other variable’s value is called the independent variable.
Logistic regression is a statistical analysis method to predict a binary outcome eg. yes or no, based on prior observations of a data set. A logistic regression model predicts a dependent data variable by analyzing the relationship between one or more existing independent variables. This technique results in an odds ratio rather than a rate of change per unit change in the independent variable.
Poisson Regression models are best used for modeling events where the outcomes are counts. Or, more specifically, count data: discrete data with non-negative integer values that count something, like the number of times an event occurs during a given time-frame or the number of people in line at the grocery store. This technique results in a risk ratio instead of a rate of change per unit change in the independent variable.
Survival Analysis is concerned with studying the time between entry to a study and a subsequent event. Originally the analysis was concerned with time from treatment until death, hence the name, but survival analysis is applicable to many areas as well as mortality.
Relative Survival is defined as the ratio of the proportion of observed survivors in a cohort of cancer patients to the proportion of expected survivors in a comparable set of cancer free individuals. The formulation is based on the assumption of independent competing causes of death.
Meta-analysis is a research process used to systematically synthesise or merge the findings of single, independent studies, using statistical methods to calculate an overall or ‘absolute’ effect. Meta-analysis does not simply pool data from smaller studies to achieve a larger sample size.
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