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Statistical Considerations Central Tendency Null Hypothesis & More

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.

medical statistics — Retrieved from https://danielmiessler.com/blog/difference-median-mean/ on 23rd November 2022

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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Introduction to Medical Statistics

Statistics VS Medical Statistics

Statistics are quantities or sets of quantities which one can calculate from observed data. Thus, unless they are ratios, statistics should be reported in units. Medical statistics is a subdiscipline of statistics. Medical statistics can assist researchers in answering healthcare-related challenging questions.

“It is the science of summarizing, collecting, presenting and interpreting data in medical practice, and using them to estimate the magnitude of associations and test hypotheses. It has a central role in medical investigations. It not only provides a way of organizing information on a wider and more formal basis than relying on the exchange of anecdotes and personal experience, but also takes into account the intrinsic variation inherent in most biological processes.”
Kirkwood, 2003.

Population VS Sample

In relation to statistics, the term population refers to a well defined group of subjects that a researcher chooses to investigate about a particular issue. The size of such a population may be known or unknown, but when the study population is too big to be investigated fully, sampling becomes needed.

A sample is a feasible number of subjects chosen to represent a population, thus, the sample involved in the study needs to be as representative as possible to the target population. This can be achieved by:

selecting an adequate sampling population
using randomly selected participants rather than convenience sampling

Simple Random Sampling

Simple random sampling is a sampling method in which all members of a population have an equal chance of being chosen to participate in the study sample.

Retrieved from https://www.shsu.edu/~mgt_ves/mgt481/lesson9/sld014.htm on 20th November 2022

Stratified Random Sampling

In stratified random sampling, the population is stratified into defining blocks eg. gender and age.

Weighted Sampling

In weighted random sampling the subjects are weighted and the probability of each item to be selected is determined by its relative weight. This allows the sample to be more representative of the population.

Retrieved from https://www.geopoll.com/blog/weighting-survey-data-raking-cell-weighting/ on 20th November 2022

Cluster Sampling

In cluster sampling, random groups of individuals are recruited for the study sample.

Convenience Sampling a.k.a. Opportunity Sampling

In this type of sampling, no consideration is taken with regards to representation. Thus, all members of a population that a researcher can access have the opportunity to be recruited.

Snowball Sampling

When recruiting members into a sample population becomes difficult, researchers revert to snowball sampling, where recruits are asked to suggest friends who may be willing to participate in the study.

Sampling Used in Qualitative Studies

Sampling used in qualitative studies is usually either purposeful sampling or theoretical sampling:

PURPOSEFUL SAMPLING – the researcher seeks individuals who can provide the required data
THEORETICAL SAMPLING – the researcher uses a sampling method which, although similar to purposeful sampling, also includes changing and/or adapting the participants’ selection throughout the study based on results obtained from previous participants

NOTE: sample size does not matter in qualitative studies, since the aim is to acquire in-depth understanding of a phenomena.

Data Collection Variables in Medical Statistics

Variables are characteristics, numbers, or quantities which can be measured or counted. Some examples of variables include age, sex, blood pressure results, oxygen saturation levels etc.

Categorical Variables a.k.a. Qualitative Variables

Data collection in qualitative studies typically takes place during in-depth interviews such as one-to-one interviews or focus group interviews, and in some cases, non-structured observation may also be involved.

Categorical variables give qualitative information about the subject being investigated. Thus, possible responses in this variable are not numerical in nature, but instead are different categories related to the subject.

Categorical variables can also be divided into two:

Nominal Variable – a variable with a number of categories eg. occupation
Binary Variable – a variable with only two possible responses eg. yes or no

Continuous variables a.k.a. Quantitative Variables

Continuous variables give quantitative information about the subject in question. Thus, continuous variable responses can be any quantities within a set interval of values. Some examples would be age and BMI.

Data collection in quantitative studies may include:

readily available data such as data related to hospital activity, registers, prevalence and determinants
self-administered questionnaires which may include numerical scales
structured interviews through phone, electronic media, or face to face interviews, all of which allow an element of explanation and feedback between the researcher and the participant
structured observation which typically happen during observation schedules within a particular setting

Ordinal Variables a.k.a. Discrete Variables

Ordinal variables give limited quantitative information because responses achieved are numerically related to each other, yet have to be one within a limited number of values.

Data Analysis

Descriptive Statistics

Descriptive statistics feature a summary of data in a clear, concise and easy-to-understand way, usually through a numerical approach.

Inferential Statistics

Inferential statistics are statistics which, after being calculated from a sample, inferences are made on the original population using the same statistics.

Reference

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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