Biostatistics Exam 1

box and whisker plot

A graph that displays the highest and lowest limits of data as whiskers, the middle two quarters of the data as a box, and the median

Percentile

Assume that the elements in a data set are rank ordered from smallest to largest. The values that divide a rank-ordered set of elements into 100 equal parts.

Quartiles

Values that divide a data set into four equal parts

Location parameter

Descriptive measures (Mean and Median) that can be used to designate certain positions on the horizontal axis when the distribution of a variable is graphed.

ordered array

An ordered list of data from largest to smallest or vice versa

frequency distribution

an arrangement of data that indicates how often a particular score or observation occurs

relative frequency distribution

The proportion of values falling within a class interval. Frequency/ total # of values.

statistic

a number that describes a sample

Parameter

a number that describes a population

frequency polygon

special kind of line graph that can portray a frequency distribution.

Histogram

A graph of vertical bars representing the frequency distribution of a set of data.

arithmetic mean (average)

The sum of all the values in the population/ sample divided by the number of values.

Properties of the Mean

1) Uniqueness: for a given set of data there is one and only one mean.

2) Simplicity: The arithmetic mean is easily understood and calculated.

3) Affected by each value: since each value in a set of data enters into the computation of the mean. extreme values, therefore, have an influence on the mean in some cases can so distort it that it becomes as a measure of central tendency.

Median

the middle score in a distribution; half the scores are above it and half are below it

Properties of a median

1) Uniqueness: there is only one median for a given set of data.

2) Simplicity: easy to calculate.

3) Not affected by extreme values.

Variance

compares how each value is with respect to the mean.

standard deviation

the square root of the variance.

how much members of a group can vary from the mean.

Skewness

a measure of the degree to which a distribution is asymmetrical

degrees of freedom

The number of individual scores that can vary without changing the sample mean. Statistically written as 'N-1' where N represents the number of subjects.

coefficient of variation

- Good for comparing the variation of 2 data sets.

- independent of the unit of measurement.

- useful for comparing the variability of 2 or more variable measures on different scales.

What are the advantages and limitations of the range as a measure of dispersion?

advantage: calculation is simple.

disadvantage: poor measure of dispersion.

Explain the rationale for using n-1 to compute the sample variance.

the usage of n-1 when calculating the sample variance is an unbiased and reliable calculation. When taking a sample from a population with a population mean of u(miu)= x, the sample will have a different mean compared to the population. subtracting 1 will allow the values to be more accurate when calculating the sample variance. n-1 is the degree of freedom of the variance.

we are eliminating 1 d.o.f from the sample mean in order to accurately represent the population mean u.

What is the purpose of the coefficient of variation?

it's useful for comparing the variability of 2 or more variable measures on different scales.

What is the purpose of Sturges's rule?

used for guidance in the matter of deciding how many class intervals to employ

What is another name for the 50th percentile (second or middle quartile)?

median

Statistic

-Statistics is about collecting, classifying, analyzing and interpreting data.

- we use is to simplify the world around us in order to understand it better . helps in decision making and assess risks.

Descriptive stat: organize and summarize data

Inferential stat: reach decisions about a large body of data by examining only a small part of it.

Biostatistics

Application of statistics to the analysis of biological and medical data.

Variable

Observed characteristic has different values in different people, places or things. ( height, age,...)

quantitative variable

measured by counting or measuring in the usual sense ( height, weight, age).

Convey info regarding amount. Can be divided in interval and ratios.

qualitative variable

no measurement can be made but the variable can rather be categorized.

Nominal: cannot be ordered ( male female)

Ordinal: can be arranged by pattern or size (age, level of intelligence)

random variable

A variable whose value arise as a chance factor and cannot be exactly predicted in advance. (attained adult height of a new born)

-Discrete random varaible: characterized by gaps in the values that it can assume ( whole numbers never decimals)

-Continuous Random variable: does not posses the gaps or interruptions characteristics of discrete random variable. ( height, weight... )

Population

A group of individuals that belong to the same species and live in the same area

Finite population

A population in which each individual member can be given a number

Infinite population

A population in which it is impossible to number each member

Sample

a subset of the population

simple random sample

every member of the population has a known and equal chance of selection

sampling with replacement

a selected individual is placed back into the population and could be chosen a second time

sampling without replacement

When selected individual from a population cannot be selected more than once

Measurement

the assignment of numbers to objects or events according to a set of rules

List, describe, and compare the four measurement scales.

1) Nominal Scale: "naming" or classisfying observations (male/ female)

2) Ordinal Scale: Categories can be ordered. Patients can be categorized as unimporoved, improved, much improved.

Interval Scale:

a scale of measurement in which the intervals between numbers on the scale are all equal in size

Ratio Scale

Highest level of precision. They are used to gather quantitative values. Fundamental to the ratio scale is a true zero point. When a scale consists not only of equidistant points but also has a meaningful zero point.

They incorporate all the characteristics of a nominal, ordinal and interval scale.

For each of the following variables, indicate whether it is quantitative or qualitative and specify the measurement scale that is employed when taking measurements on each:

(a) Class standing of the members of this class relative to each other

(b) Admitting diagnosis of patients admitted to a mental health clinic

(c) Weights of babies born in a hospital during a year (d) Gender of babies born in a hospital during a year

(e) Range of motion of elbow joint of students enrolled in a university health sciences curriculum

(f) Under-arm temperature of day-old infants born in a hospital

a) quantitative, ordinal

b)Qualitative, nominal

c)Quantitative, ratio

d)qualitative, nominal

e)quantitative, interval ("zero degrees" of motion varies by instrumentation)

f)quantitative, interval

For each of the following situations, answer questions a through e:

(a) What is the sample in the study?

(b) What is the population?

(c) What is the variable of interest?

(d) How many measurements were used in calculating the reported results?

(e) What measurement scale was used?

Situation A. A study of 300 households in a small southern town revealed that 20 percent had at least one school-age child present.

Situation B. A study of 250 patients admitted to a hospital during the past year revealed that, on the average, the patients lived 15 miles from the hospital.

Situation A

a)300 households

b)all households in the small southern town

c)number of school-- aged children present

d)number of households that reported one

or more children

e) nominal (categories: 0 children, 1 child, and so on)

Situation B

a)250 patients

b) total number of patients admitted

c) distance that patients lived away from the hospital

d) 250 distances

e)ratio

Probability

likelihood that a particular event will occur

mutually exclusive events

events that cannot happen at the same time

independence

the probability of A is the same regardless of whether or not B occurs.

P(A union B)= P(A) P(B)

P(A| B) = P(A)

P (B|A) = P(B)

if values are equal--> independent

if values are not equal--> dependent

Marginal Probability

depends only on totals found in the margins of the table

Joint Probability

the probability of two events occurring together (the intersection)

Conditional Probability

the probability that one event happens given that another event is already known to have happened

Addition Rule of Probability

Used to determine the probability that at least one of two independent events will occur.

P(A or B) = P(A) + P(B) - P(AB)

Multiplication Rule of Probability

the probability of two outcomes occurring simultaneously is the product of their individual probabilities

complementary events

Two or more mutually exclusive events that together cover all possible outcomes. The sum of the probabilities of complementary events is 1.

Partition Rule

there are different ways an event can happen, and to calculate the probability of the event one needs to add up the probabilities associated with each of the different ways it can happen.

Bayes' Theorem

The probability of an event occurring based upon other event probabilities.

Screening tests

In the health sciences field, a widely used application of probability laws and concepts is found in the evaluation of screening tests and diagnostic criteria. (i.e. presence/absence of disease,...)

A false positive (Type I error )

test indicates a positive status when the true status is negative.

A false negative (Type II error)

test indicates a negative status when the true status is positive.

Sensitivity

probability of a positive test result given the presence of the disease

P(T|D) = a/(a+c)

specificity

probability of a negative test result given the absence of the disease

P(Tc|Dc) = d/(b+d)

predictive value positive (precision)

probability that a subject has the disease given that the subject has a positive screening test result.

P(D|T) = a/(a+b)

predictive value negative

the probability that a subject does not have the disease, given that the subject has a negative screening test result.

Accuracy

proportion of true results (both true positives and true negatives) in the population.

= (sensitivity)(prevalence) + (specificity)(1-prevalence)