Statistical considerations for research should include careful statistical planning and use of the right statistical tests for data analysis to ensure a successful research project.
Central Tendency – Mean, Median & Mode
Central Tendency
The phrase ‘Central Tendency’ refers to a single value which aims to describe a set of data through the identification of the central position within the same set of data. The mean, which at times is referred to as the average, is most commonly considered to be the measure of central tendency, however, there are also the median and the mode which can be considered as measures of central tendency. Which measure is valid depends on the conditions under which they are being evaluated.
The Mean
The mean is the average, where all values are added together and then divided by the number of values.
The Median
The median is the middle value found within the list of values. To find the median you need to list all values in numerical order from smallest to largest, and then identify the value within the middle.
The Mode
The mode is the value occurring most often. This means that if in a particular list of values no number is repeated, there would be no mode for that particular list.
The Variance & Standard Deviation
The variance is a calculation of the normal distribution spread in a set of variables, in other words, a measure of dispersion. The standard deviation is the square root of its variance.
Hypothesis Testing Statistical Considerations
- Define the Null Hypothesis – no difference between the groups being compared
- Define an Alternative Hypothesis – existing difference between the groups being compared; defined difference should be clinically significant
- Calculate a p value – the probability of obtaining the results observed if the null hypothesis is true
- Based on the p value, accept or reject the Null Hypothesis
- If the Null Hypothesis is rejected, accept the Alternative Hypothesis
NOTE: the size of an expected difference (priori) should be defined prior to the data collection period.
The Null Hypothesis
Studies always start out with the assumption that the difference between the groups being compared will be non-existent a.k.a. null, hence why this is called the Null Hypothesis. Studies aim to have enough evidence to accept or reject this null hypothesis.
Unfortunately, errors may be made in accepting or rejecting the null hypothesis. To prevent such errors, the researcher should aim to have a sample size which is large enough.
The Confidence Interval & P-Value
The phrase confidence interval refers to the range of values which a specific statistic, most commonly being a mean or proportion of the population, can have in the reference population with a specific probability. Confidence intervals help in clinical trial data interpretation by determining upper and lower bounds on the likely size of any true effect.
The p-value determines whether trial results could have occurred by chance.
Confidence intervals are usually preferred to p-values since they provide a range of possible effect sizes in relation to the data, whilst p-values provide a cut-off beyond which we assert that the findings are statistically significant.
A confidence interval which embraces the value of no difference between treatments shows that treatment being investigated is not significantly different from the control.
The cut-off point for rejecting the null hypothesis is arbitrary, a typically being equivalent to 0.05
If p = 0.01, the chance of obtaining the same results as the experiment is 1%, meaning that it is very unlikely, thus we reject the null hypothesis.
If p = 0.7, then the chance of obtaining the same results as the experiment is 70%, thus, we accept the null hypothesis.
NOTE: bias must be assessed before confidence intervals are interpreted, since biased studies can be misleading even when very large samples and very narrow confidence intervals were involved.
(Davies and Crombie, 2003)
Errors & Power Statistical Considerations
Type 1 (Alpha) & Type 2 (Beta) Errors in Statistics
Power statistical considerations
Power is determined by sample size, magnitude of difference sought, and by the arbitrary. For example, a pilot study with a small sample size would have low power. Power desired is usually 0.80
Reference
Davies, H.T.O. & Crombie, I.K. (2003). What are confidence intervals and p-values? What is…? Series. Edition 2009. Hayward Communications Ltd. Hayward Group Ltd. Retrieved from http://www.bandolier.org.uk/painres/download/whatis/What_are_Conf_Inter.pdf on 12th February 2023
Kirkwood, Betty R. (2003). essential medical statistics. Blackwell Science, Inc., 350 Main Street, Malden, Massachusetts 02148–5020, USA: Blackwell. ISBN978-0-86542-871-3.
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Claire is keen about public education on health-related subjects as well as holistic patient-centered care. She is also passionate about spreading awareness on the negative effects that domestic abuse leaves on its victims’ mental, emotional, social and physical wellbeing.
Claire aspires to continue studying following completion of her Nursing Degree, because she truly believes in lifelong education.
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