Measures of Central Tendency: Mean and Median

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40 Questions

What is the method of calculating the mean?

Summing each value of the continuous variable and dividing it by the sample size

What is a disadvantage of the mean?

It is sensitive to extreme values

What is the middle value in a dataset when the values are sorted in ascending order?

Median

What happens to the median when the number of patients is even?

The median will be the average of the middle two values

What is the mode of the dataset 80, 90, 95, 110, 120?

There is no mode

What is the purpose of measures of dispersion?

To provide an index of how much there is dispersion or variability in the values of a continuous variable

What is the range of the dataset 80, 90, 95, 110, 120?

40

What is a disadvantage of the range?

It ignores all the values and takes only the lowest and the highest

What is the main purpose of inferential statistics in clinical research?

To generalize the results from the sample to the population

What is a confidence interval?

A range of values that estimates a parameter with a specified degree of confidence

Why is it important to ensure that the sample represents the target population?

To ensure that the results are generalizable

What is the main difference between descriptive statistics and inferential statistics?

Descriptive statistics summarizes data, while inferential statistics makes conclusions about the population

What is the ultimate goal of using inferential statistics in clinical research?

To generalize the results to the target population

What is hypothesis testing used for in inferential statistics?

To test a hypothesis about the population

What is the purpose of estimating a parameter using a confidence interval?

To provide a range of values within which the parameter is likely to lie

Why is it important to understand the concept of inferential statistics in clinical research?

To generalize the results to the population

What type of statistics will be used to summarize the data in EXAMPLE 1?

Both descriptive and inferential statistics

What statistical test will be used to compare means between groups in EXAMPLE 1?

t-test

What software will be used to perform statistical analyses in EXAMPLE 1?

SPSS software version 25

What is the significance level set for all statistical tests in EXAMPLE 1?

0.05

What type of statistical analysis will be used to explore relationships between variables in EXAMPLE 2?

Correlation and regression analyses

What software will be used to perform statistical analyses in EXAMPLE 2?

R software version 4.0

What is the purpose of checking assumptions of normality, homoscedasticity, and multicollinearity in EXAMPLE 2?

To conduct regression analyses

How many stages of data analysis will be performed in EXAMPLE 3?

3

What is the primary outcome measure in the diabetes management program?

Glycated Hemoglobin (HbA1c) Levels

What is the rationale for measuring Body Weight in the diabetes management program?

Weight management is crucial in diabetes control and can influence glycemic levels

What is the primary outcome measure in the smoking cessation intervention?

Smoking Abstinence Rate

How is smoking abstinence verified in the smoking cessation intervention?

By carbon monoxide (CO) breath tests

What is the purpose of measuring Fasting Blood Glucose Levels in the diabetes management program?

To provide additional information on daily glucose control

What is the measurement of Medication Adherence in the diabetes management program?

Proportion of days covered (PDC) by prescribed medications over 12 months

What is the rationale for measuring the incidence of hypoglycemic events in the diabetes management program?

Important safety outcome to assess potential risks associated with the program

What is the duration of the smoking cessation intervention?

6 months

What does a large variance indicate?

Values are far away from each other

What is the formula for Standard Deviation (SD)?

$$\sqrt{\frac{\sum(Xi - \bar{x})^2}{n}}$$

What is the main difference between a histogram and a bar chart?

The bars in a histogram are connected to reflect continuity

What is a primary outcome in a study?

The main result that a study is designed to assess

What is the purpose of secondary outcomes in a study?

To understand the broader effects of the intervention

What is a characteristic of primary outcomes?

Singular

What do secondary outcomes provide in a study?

Context and additional data to explain the primary outcome

When are primary outcomes defined?

Before the study begins

Study Notes

Measures of Central Tendency

  • Three measures of central tendency: Mean, Median, and Mode
  • Mean: calculated by summing up each value and dividing by sample size
  • Disadvantage of mean: sensitive to extreme values
  • Median: middle value that divides data into two halves
  • To calculate median: sort values in ascending or descending order and choose middle value
  • If number of patients is even, median is the average of middle two values
  • Mode: most frequently occurring number

Measures of Dispersion

  • Three measures of dispersion: Range, Variance, and Standard Deviation (SD)
  • Range: difference between highest and lowest values
  • Disadvantage of range: ignores all values except highest and lowest
  • Variance: measure of how much values are away from the mean
  • Small variance: values are close to each other
  • Large variance: values are far away from each other
  • Standard Deviation (SD): square root of variance; most frequently used measure of dispersion
  • Formula for SD: √((Σ(Xi - x̄)^2) / (n - 1))

Graphical Representation

  • Histogram: most frequently used graph for continuous variables
  • Box and Whisker Plot (Box Plot): another type of graph used to represent continuous variables

Determining Primary and Secondary Research Outcomes

  • Primary outcomes: main results of a study; pre-specified and critical to determining sample size and power calculations
  • Secondary outcomes: additional results that provide more information on the intervention's effects

Inferential Statistics

  • Used to draw conclusions on a population based on a sample
  • Crucial step in generalizing results from a study to the target population
  • Types of inferential statistics: confidence interval and hypothesis testing (p-value)
  • Confidence Interval (CI): range of values that includes the parameter being estimated with a specified degree of confidence

Examples of Statistical Analysis Sections in Research Proposals

  • Example 1: Simple statistical analysis section
  • Example 2: Intermediate statistical analysis section
  • Example 3: Advanced statistical analysis section

Quiz on measures of central tendency, including the mean and median, with examples and calculations. Learn about the advantages and disadvantages of each measure.

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