Understanding Descriptive and Inferential Statistics

Statistics

• Statistics involves the collection, organization, analysis, and interpretation of data.
• Descriptive statistics present study results without generalizing to a larger group.
• The goal of descriptive statistics is to present data characteristics and summarize them using averages, as well as the amount of variation in the data.
• Descriptive statistics include range, central tendency, and standard deviations.
• Inferential statistics draw conclusions about differences between groups and whether findings can be applied to larger populations (statistical significance).
• Statistical significance indicates if results are meaningful or likely due to chance, gauging the strength of associations between variables.
• A p-value less than or equal to 0.05 is often considered statistically significant.
• The type of statistical test used depends on the data involved.
• Analysis of Variance (ANOVA) measures statistical significance and the strength of associations.
• ANOVA examines relationships between exposures/procedures/independent variables and their impact on outcome measures/dependent variables.
• Multiple Analysis of Variance or MANOVA can be used when multiple outcomes are measured.
• Analysis of Covariance (ANCOVA) is used where demographic variables are unequally distributed between groups to make groups comparable.
• Power analysis determines the number of participants/subjects needed to reach 80% chance of obtaining statistical significance.
• Power analysis is done in planning stages to prepare sample size and subject groups.
• Aim for at least 10 subjects per outcome measure.
• Statistical significance estimates how much of an outcome is due to the treatment(s) being measured.
• Important to note whether a study performed any tests of statistical significance and whether authors provided rationale for the statistical tests they've used.

Descriptive Statistics: Deep Dive

• Central tendency represents the "middle" or "expected" value of a dataset, a central value for a probability distribution.
• Mean is the sum of all values divided by the number of people in the sample (the average).
• Median divides the higher half of a list of values from the lower half of that list, found listing data numerically and the number in the exact middle.
• If the data set is an even number, take the mean of the two central numbers.
• Mode is the most frequent value in a random variable.
• The mode is often a different number than the median and mean, particularly in skewed distributions.
• Mode may not be unique, hence bimodal or trimodal distributions.
• Dispersion measures the statistical variability of how data spreads or is distributed.
• Standard Deviation measures how spread out numbers are in a dataset
• If data points are close to the mean, the standard deviation is small.
• If data points are far from the mean, the standard deviation is large.
• A low standard deviation (e.g. +/- 1) means there is little variability.
• A high standard deviation means there is a lot of variability.
• Standard deviation can measure uncertainty.
• If the datapoint falls in the tail ends of standard deviation, it is an outlier and atypical.
• Range is the difference between the highest and lowest values.

Internal and External Validity

• External validity is the extent to which research findings can be applied beyond the study context or whether the results can be generalizable to a larger group or population.
• Internal validity is the capacity of a study to link cause and effect within the study itself.
• A method to improve internal validity is to exclude other hypotheses as possible explanations, ensuring direct connection between cause and effect
• I.e. correlation vs. causation.

Threats to Internal Validity

• Threats can include confounding variables or sources of bias.
• A confounding variable blurs or masks the impact of another variable.
• An example: students' reactions to coffee may be confounded by how much sleep they had the previous night.
• Bias: is a systematic error such as a tendency to underestimate the placebo effect.
• Selection: can be a threat such as choosing specific groups to survey/study.
• Example is that a study asking Facebook users how technology impacts their lives vs. asking non-computer-literate citizens.
• Selecting samples such as this can be limited by randomizing and including generalizable sample populations

Statistical Validity

• Statistical validity is a potential threat to the internal validity because statistics can be misrepresentative or have errors
• Type I error: A "false positive" where a true null hypothesis is rejected, indicating the research hypothesis is wrong
• Type II error: A "false negative" where a false null hypothesis is not rejected, meaning the research hypothesis is right.
• Errors can occur when the sample size is too small to make significant observations.
• The more participants complete a questionnaire and the fewer measured outcomes, the greater the power.
• If power is low (small sample, many treatment outcomes), a Type II error may occur.
• A true treatment may not be seen in the data if the sample is too small or there are too many treatment outcomes.

Reliability

• Reliability is dependability, consistency, and reproducibility of information.
• Reliability is the probability that different subjects will obtain the same results
• Three common methods to test reliability are test-retest, equivalent-forms method, and internal consistency method.
• Test-retest Reliability ensures the same test is administered twice to the same group.
• Equivalent Form ensures therapies to the same group at the same time are valid
• Internal-consistency ensures different researchers are consistent in matching the same data and constructs.

Validity vs. Reliability

• Validity = accuracy; reliability = consistency.
• Validity measures what it is supposed to measure.
• Reliability measures the same way each time it is used under the same conditions.

Peer Review Process

• A process by which experts in a field evaluate the quality of a scholarly work.
• Scientists write about their results, the journal editors receive an article and send it out for peer review, peer reviewers read the article and provide feedback to the editor.
• The transparency in the peer review process means that there should be details about peer review policy and guidelines, as well as journal names of editors.

Ethics Review

• Ethics committees act to safeguard human rights and protect people who participate in health care research.
• Governed by Panel on Research Ethics Government of Canada saying "Ethical principals and guidelines play an important role in advancing the pursuit of knowledge while protecting and respecting research participants.”
• Ethics violations have happened throughout the history of medical research
• Respect for persons recognizes the intrinsic value of human beings and the respect and consideration that they are due.
• Ethical research should have concern for welfare regarding the quality of a person's experience of life.
• Ethical research should have justice: an obligation to treat fairly and equitably.