Preventive Medicine: Biostatistics 2

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Questions and Answers

What can cause variation in clinical medicine?

Only genetic differences

Techniques and conditions of measurement, errors in measurement, and random variation (correct)

Only the presence or absence of disease

Only biologic differences

What is the term for variation that distorts data systematically in one direction?

Biologic variation

Measurement bias

Systematic error (correct)

Random error

What is the effect of random error on data?

It increases the noise and makes it harder to detect a signal (correct)

It has no effect on data

It introduces bias and distorts the truth

It eliminates variation in data

What is an example of biologic differences that can affect blood pressure?

All of the above Signup and view all the answers

Why do tall parents usually have tall children?

Because of genetic differences Signup and view all the answers

What can polluted water cause in children?

Intestinal infections that can retard growth Signup and view all the answers

What is the result of starvation on growth?

Stopped growth altogether Signup and view all the answers

What allows the full genetic growth potential to be achieved?

Good nutrition Signup and view all the answers

What is the term for the presence of multiple diseases in a patient?

Comorbidity Signup and view all the answers

Why is it important to standardize the conditions under which medical data is obtained?

To avoid variation attributable to measurement errors Signup and view all the answers

What can cause variation in blood pressure measurements?

All of the above Signup and view all the answers

Why do different techniques of measurement produce different results?

All of the above Signup and view all the answers

What is the primary role of statistics in clinical medicine and research?

To interpret data despite biologic variation Signup and view all the answers

What is the first step in understanding variation in medical data?

To describe it Signup and view all the answers

Why is it important to understand the different types of variables in medicine?

To choose the correct statistical tool Signup and view all the answers

What is the term for the difference in measurement results due to differences in measurement technique or instrument?

Measurement error Signup and view all the answers

What is the purpose of standardizing the conditions under which medical data is obtained?

To avoid variation attributable to measurement errors Signup and view all the answers

What can cause variation in the interpretation of medical data?

All of the above Signup and view all the answers

What is the primary characteristic of a quantitative variable?

It is characterized using a rigid, continuous measurement scale. Signup and view all the answers

What is the main difference between a qualitative and a quantitative variable?

Qualitative variables are described using words, while quantitative variables are described using numbers. Signup and view all the answers

Which of the following is an example of a qualitative variable?

Skin color Signup and view all the answers

What is the purpose of assigning a number to a nominal variable?

To facilitate data entry into a computer system Signup and view all the answers

What is the main limitation of a dichotomous variable?

It is often inadequate by itself to fully describe a characteristic Signup and view all the answers

Which of the following is an example of a dichotomous variable?

Normal/abnormal skin color Signup and view all the answers

What is the difference between a dichotomous variable and a nominal variable?

A dichotomous variable has two levels, while a nominal variable has more than two levels. Signup and view all the answers

Why is it important to know the direction of a dichotomous variable?

To interpret the results of the data analysis Signup and view all the answers

What is the purpose of creating a variable with multiple levels?

To fully describe a characteristic Signup and view all the answers

What is the main difference between a continuous variable and a ratio variable?

A continuous variable has a measurement scale with a true zero point, while a ratio variable does not. Signup and view all the answers

What is the definition of a risk in medicine?

The conditional probability of an event in a defined population in a defined period Signup and view all the answers

What is a characteristic of risks and proportions in medicine?

They share characteristics of both discrete and continuous variables Signup and view all the answers

What is an example of a unit of observation in medical research?

A person Signup and view all the answers

How can a continuous variable be converted?

By categorizing units with similar values together Signup and view all the answers

What type of table is used to display counts of characteristics?

Frequency table Signup and view all the answers

What can be used to analyze observed counts in tables?

Statistical methods for discrete data Signup and view all the answers

What is an example of converting a continuous variable to an ordinal variable?

Converting birth weights to ranges of birth weights Signup and view all the answers

What type of variable is 'satisfaction with care' that can take on the values of 'very satisfied', 'fairly satisfied', or 'not satisfied'?

Ordinal variable Signup and view all the answers

What is the main difference between nominal and ordinal variables?

Ordinal variables have a clear direction from better to worse Signup and view all the answers

What type of data is measured on a scale from 0 to 10, with 0 being no pain and 10 being the worst imaginable pain?

Ordinal data Signup and view all the answers

What is an advantage of using continuous variables in research?

They enable investigators to make more detailed inferences than ordinal or nominal data Signup and view all the answers

What is a characteristic of ratio variables?

They have a true 0 point Signup and view all the answers

What is the difference between the centigrade and Kelvin temperature scales?

The Kelvin scale is a ratio scale, while the centigrade scale is not Signup and view all the answers

What type of analysis is often required for ordinal variables?

Special techniques of analysis Signup and view all the answers

What is an example of a nominal variable in medical data?

Location of a heart murmur Signup and view all the answers

What type of data would be used to measure the amount of swelling in a patient's legs?

Ordinal data Signup and view all the answers

What is the main advantage of using ordinal variables over nominal variables?

They provide more information and enable more informative conclusions to be drawn Signup and view all the answers

What is a characteristic of the mean of a random sample?

It is an unbiased estimator of the mean of the population from which it came. Signup and view all the answers

What is the median?

The 50th percentile. Signup and view all the answers

What is the interquartile range?

The distance between the 25th and 75th percentiles. Signup and view all the answers

What is an advantage of using percentiles?

They can be applied to any set of continuous data. Signup and view all the answers

What is a property of the mean?

The sum of the squared deviations from the mean is smaller than from any other number. Signup and view all the answers

What is the range?

The distance between the highest and lowest values. Signup and view all the answers

What is a characteristic of the sum of the squared deviations from the mean?

It is fixed for a given set of observations. Signup and view all the answers

What is the purpose of percentiles?

To describe the distribution of a set of data. Signup and view all the answers

What is the primary advantage of using the mean as a measure of central tendency?

It has many mathematical properties. Signup and view all the answers

What is the sum of the squared deviations from the mean called?

Sum of squares. Signup and view all the answers

Why is the standard deviation used to describe the amount of spread in a frequency distribution?

Because it is a more intuitive measure of spread than the variance. Signup and view all the answers

What is the relationship between the variance of the sum of two independently sampled variables?

The variance of the sum is equal to the sum of the variances. Signup and view all the answers

What is the purpose of the mean deviation?

To define the concept of dispersion. Signup and view all the answers

What is the symbol for the sample variance?

s² Signup and view all the answers

What is the effect of squaring the deviations from the mean in the formula for variance?

It solves the problem of the sum of the deviations being zero. Signup and view all the answers

What is the difference between the variance and the standard deviation?

The standard deviation is the square root of the variance. Signup and view all the answers

What is the concept that is measured by the variance?

Dispersion. Signup and view all the answers

What is the primary purpose of checking the original source of data?

To ensure the data is accurate Signup and view all the answers

What is the main advantage of using histograms and line graphs to illustrate frequency distributions?

They provide a visual representation of the data Signup and view all the answers

What is the purpose of the stem and leaf diagram?

To visualize the frequency distribution Signup and view all the answers

What does the modified boxplot show?

The interquartile range and outliers Signup and view all the answers

What is the purpose of the whiskers in a boxplot?

To show the range where most values would be expected Signup and view all the answers

What is the benefit of displaying data visually?

It makes the data easier to understand Signup and view all the answers

What happens to the binomial distribution when the probability of heads is not equal to 0.5?

It becomes skewed. Signup and view all the answers

What type of test is used to analyze nominal and ordinal variables?

Nonparametric test Signup and view all the answers

What is the distribution used to describe uncommon events occurring in time or space?

Poisson distribution Signup and view all the answers

What is the primary role of statistics in clinical medicine and research?

To describe and understand variation Signup and view all the answers

What can be calculated for the binomial distribution?

Mean and standard deviation Signup and view all the answers

What is the term for the analysis of counts in frequency tables?

Chi-square analysis Signup and view all the answers

What type of data is usually analyzed using tests based on the normal distribution?

Continuous data Signup and view all the answers

Why are nonparametric tests used for nominal and ordinal variables?

Because they make no assumptions about an underlying frequency distribution Signup and view all the answers

What is a characteristic of the normal distribution?

The mean and median coincide Signup and view all the answers

What is the purpose of understanding the types of variables in medicine?

To understand and describe variation Signup and view all the answers

What is the result of subtracting the mean from each value and dividing by the standard deviation?

Normalizing the data Signup and view all the answers

What type of distribution is used to describe rare events?

Poisson distribution Signup and view all the answers

What is the purpose of creating z values?

To express the value of each observation as the number of standard deviations from the mean Signup and view all the answers

What type of statistics can be used when the normal distribution cannot be assumed?

Non-parametric statistics Signup and view all the answers

What is the result of the probability of success and failure being the same, and the number of trials being large?

The binomial distribution approximates the normal distribution Signup and view all the answers

What does a boxplot effectively convey about a distribution?

All of the above Signup and view all the answers

Why is normalizing data useful?

To eliminate the effects of unit choice on statistical values Signup and view all the answers

What is the formula for calculating individual z-values?

zi = (xi - x) / s Signup and view all the answers

What is the characteristic of a distribution of z-values?

Mean of 0 and standard deviation of 1 Signup and view all the answers

What is the purpose of calculating z-values in clinical medicine?

To determine how extreme an observed test result is Signup and view all the answers

What is the concept that describes the probability of outcomes in a coin flip experiment?

Binomial formula Signup and view all the answers

What is the sum of all probabilities in a probability distribution?

1.0 Signup and view all the answers

What is the purpose of standardizing data in medical research?

To eliminate the effects of unit choice on statistical values Signup and view all the answers

What is the advantage of using z-values in statistical analysis?

They allow for comparison across different units Signup and view all the answers

What is the purpose of flipping a coin in probability theory?

To demonstrate the concept of probability distribution Signup and view all the answers

What is the term for a horizontal stretching of a frequency distribution to one side, resulting in a longer tail of observations?

Skewness Signup and view all the answers

What is the purpose of comparing the mean and median in a distribution?

To detect skewness Signup and view all the answers

What is the term for a vertical stretching or flattening of a frequency distribution?

Kurtosis Signup and view all the answers

What is the problem posed by a value that is abnormally far above or below the mean?

Outliers Signup and view all the answers

Why are statistical tests not valid if used to compare extremely abnormal distributions?

Because they assume normality Signup and view all the answers

What is the formula commonly used in clinical studies to show the extent of variation in clinical data?

x ± 1.96 standard deviations Signup and view all the answers

What is the term for the problem of treating a value that is abnormally far above or below the mean?

Extreme values Signup and view all the answers

Study Notes

Sources of Variation in Medicine

Variation in clinical medicine can arise from:
- Biologic differences (e.g., genetic differences, nutrition, environmental exposures, age, gender, race)
- Presence or absence of disease (e.g., cancer, comorbidity)
- Techniques and conditions of measurement (e.g., time of day, ambient temperature, fatigue or anxiety in the patient)
- Errors in measurement (e.g., defective blood pressure cuffs, differences in laboratory instruments)
- Random variation (e.g., slight inaccuracies in obtaining measurements)

Types of Variables

Nominal variables:
- Categorical variables with no measurement scale and no rank order (e.g., blood groups, occupations, food groups, skin color)
- Examples: blood groups (O, A, B, AB), occupations
Dichotomous (Binary) variables:
- Variables with only two levels (e.g., normal/abnormal skin color, well/sick, living/dead)
- Often inadequate by themselves to fully describe a phenomenon
Ordinal (Ranked) variables:
- Variables with three or more qualitative values that have a clearly implied direction from better to worse (e.g., satisfaction with care, amount of swelling in a patient's legs)
- Examples: respiratory distress (absent, mild, moderate, or severe), pain intensity (0-10 scale)
Continuous (Dimensional) variables:
- Variables measured on a continuous scale (e.g., patients' heights, weights, systolic and diastolic blood pressures, serum glucose levels)
- Examples: birth weight and probability of survival of newborns
Ratio variables:
- Continuous scales with a true 0 point (e.g., Kelvin temperature scale)
Risks and proportions as variables:
- Conditional probability of an event (e.g., death or disease) in a defined population in a defined period
- Share characteristics of both discrete and continuous variables

Statistics and Variables

Statistics help clinicians and investigators understand and explain variation in medical data
The first step in understanding variation is to describe it
Types of variables are important to understand in order to choose the correct statistical tools for analysis

Properties of the Mean

The mean of a random sample is an unbiased estimator of the population mean.
The mean is the mathematical expectation and is different from the mode, which is the value observed most often.
The sum of squared deviations from the mean is smaller than the sum of squared deviations from any other number.
The sum of squared deviations from the mean is fixed for a given set of observations.

Measures of Dispersion Based on Percentiles

Percentiles are the percentage of observations below a certain point in a ranked dataset.
The median is the 50th percentile, the 75th percentile is the point below which 75% of observations lie, and the 25th percentile is the point below which 25% of observations lie.
The interquartile range (IQR) is the distance between the 75th and 25th percentiles.

Measures of Dispersion Based on the Mean

Mean deviation is the average of the absolute values of the deviations from the mean, but it's not widely used.
Variance is the sum of squared deviations from the mean divided by the number of observations minus one.
Standard deviation is the square root of variance and is a measure of spread.

Properties of Variance

The variance of a random sample is an unbiased estimator of the population variance.
The variance of the sum of two independently sampled variables is equal to the sum of their variances.
The variance of the difference between two independently sampled variables is equal to the sum of their variances.

Standard Deviation

The standard deviation is a measure of spread that is easy to interpret.
One standard deviation above and below the mean includes 68% of the data, and two standard deviations above and below the mean include 95.4% of the data.

Problems in Analyzing a Frequency Distribution

Skewness occurs when the data is not symmetrical and the mean is not equal to the median.
Kurtosis occurs when the data is more or less peaked than a normal distribution.
Extreme values (outliers) can affect the mean and should be checked for plausibility.

Methods of Depicting a Frequency Distribution

Histograms and line graphs are commonly used to display frequency distributions.
Stem and leaf diagrams, quantiles, and boxplots are other methods of visualizing data.

Unit-Free (Normalized) Data

Data can be normalized by subtracting the mean and dividing by the standard deviation to create z-values.
Z-values have a mean of 0 and a standard deviation of 1.
Normalizing data eliminates the effect of units of measurement.

Frequency Distributions of Dichotomous Data and Proportions

Dichotomous data can be analyzed using the binomial distribution.
The binomial distribution approaches the normal distribution as the number of trials increases.

Frequency Distributions of Other Types of Data

Nominal and ordinal data require nonparametric tests that do not assume a specific distribution.
The chi-square distribution is used to analyze counts in frequency tables.
Ordinal data can be analyzed using nonparametric tests such as the Wilcoxon test and the Mann-Whitney U test.### Understanding Variation in Clinical Medicine
Variation in clinical medicine can be caused by biologic differences, presence or absence of disease, differences in measurement techniques, errors in measurement, and random variation.
Statistics helps in describing and understanding variation, but it cannot correct for measurement errors or bias.

Types of Variables or Data

Nominal data: categorical data with no inherent order or ranking
Dichotomous data: binary data with two distinct categories
Ordinal data: categorical data with inherent order or ranking
Continuous data: measured data with a range of values
Ratio data: continuous data with a true zero point
Risks, rates, and proportions: special types of data used to describe events or outcomes

Continuous Data and Frequency Distribution

Frequency distribution can be described by two parameters: measure of central tendency and measure of dispersion
Measure of central tendency: median and mean are the most important
Measure of dispersion: variance and standard deviation are the most important
Normal (Gaussian) distribution: a common distribution type where mean and median coincide, and 95% of observations are within 1.96 standard deviations above and below the mean

Skewed Distribution and Normalization

Skewed distribution: a distribution where the mean is farther in the direction of the long tail than the median
Normalization: making data unit-free by creating z-values, which express the value of each observation as the number of standard deviations above or below the mean

Probability Distributions

Binomial distribution: describes probability of dichotomous data, where the probability of success and failure are 0.5 each, and the number of trials is large
Poisson distribution: used to describe rare events, and has the convenient property that the mean equals the variance

Non-Parametric Statistics

Used when the normal distribution cannot be assumed, to study differences and associations among variables

Studying That Suits You

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This quiz covers the sources of variation in clinical medicine, including biological differences, measurement errors, and random variation. It also explores how systematic error and bias can affect data.

Preventive Medicine: Biostatistics 2

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Podcast

Questions and Answers

What can cause variation in clinical medicine?

What is the term for variation that distorts data systematically in one direction?

What is the effect of random error on data?

What is an example of biologic differences that can affect blood pressure?

Why do tall parents usually have tall children?

What can polluted water cause in children?

What is the result of starvation on growth?

What allows the full genetic growth potential to be achieved?

What is the term for the presence of multiple diseases in a patient?

Why is it important to standardize the conditions under which medical data is obtained?

What can cause variation in blood pressure measurements?

Why do different techniques of measurement produce different results?

What is the primary role of statistics in clinical medicine and research?

What is the first step in understanding variation in medical data?

Why is it important to understand the different types of variables in medicine?

What is the term for the difference in measurement results due to differences in measurement technique or instrument?

What is the purpose of standardizing the conditions under which medical data is obtained?

What can cause variation in the interpretation of medical data?

What is the primary characteristic of a quantitative variable?

What is the main difference between a qualitative and a quantitative variable?

Which of the following is an example of a qualitative variable?

What is the purpose of assigning a number to a nominal variable?

What is the main limitation of a dichotomous variable?

Which of the following is an example of a dichotomous variable?

What is the difference between a dichotomous variable and a nominal variable?

Why is it important to know the direction of a dichotomous variable?

What is the purpose of creating a variable with multiple levels?

What is the main difference between a continuous variable and a ratio variable?

What is the definition of a risk in medicine?

What is a characteristic of risks and proportions in medicine?

What is an example of a unit of observation in medical research?

How can a continuous variable be converted?

What type of table is used to display counts of characteristics?

What can be used to analyze observed counts in tables?

What is an example of converting a continuous variable to an ordinal variable?

What type of variable is 'satisfaction with care' that can take on the values of 'very satisfied', 'fairly satisfied', or 'not satisfied'?

What is the main difference between nominal and ordinal variables?

What type of data is measured on a scale from 0 to 10, with 0 being no pain and 10 being the worst imaginable pain?

What is an advantage of using continuous variables in research?

What is a characteristic of ratio variables?

What is the difference between the centigrade and Kelvin temperature scales?

What type of analysis is often required for ordinal variables?

What is an example of a nominal variable in medical data?

What type of data would be used to measure the amount of swelling in a patient's legs?

What is the main advantage of using ordinal variables over nominal variables?

What is a characteristic of the mean of a random sample?

What is the median?

What is the interquartile range?

What is an advantage of using percentiles?

What is a property of the mean?

What is the range?

What is a characteristic of the sum of the squared deviations from the mean?

What is the purpose of percentiles?

What is the primary advantage of using the mean as a measure of central tendency?

What is the sum of the squared deviations from the mean called?

Why is the standard deviation used to describe the amount of spread in a frequency distribution?

What is the relationship between the variance of the sum of two independently sampled variables?

What is the purpose of the mean deviation?

What is the symbol for the sample variance?

What is the effect of squaring the deviations from the mean in the formula for variance?

What is the difference between the variance and the standard deviation?

What is the concept that is measured by the variance?

What is the primary purpose of checking the original source of data?

What is the main advantage of using histograms and line graphs to illustrate frequency distributions?

What is the purpose of the stem and leaf diagram?

What does the modified boxplot show?

What is the purpose of the whiskers in a boxplot?

What is the benefit of displaying data visually?

What happens to the binomial distribution when the probability of heads is not equal to 0.5?

What type of test is used to analyze nominal and ordinal variables?

What is the distribution used to describe uncommon events occurring in time or space?

What is the primary role of statistics in clinical medicine and research?

What can be calculated for the binomial distribution?

What is the term for the analysis of counts in frequency tables?

What type of data is usually analyzed using tests based on the normal distribution?

Why are nonparametric tests used for nominal and ordinal variables?