General Lab Practice Lecture 2

The complete set of all observations that might occur as a result of performing a particular procedure according to specified conditions: all possible values for a particular characteristic

• Impossible to study in their entirety

• Characteristics are described by parameters

• - Populations mean, median, population variance, population standard deviation

• Example: All fasting glucose levels of all hospitalized patients in the US

Population

A subgroup of observations taken from the population used to form conclusions about population characteristics

Example: all fasting glucose levels of the babies in the NICU at Saint Francis Hospital

Sample

Each member of the population has an equal chance of being selected

Characteristics are described by statistics

• sample mean, sample standard deviation, and coefficient of variation

Statistical analysis and interpretation depends on the assumption of a random sample from a fixed population

Random sample

A graphical device for displaying a large set of data: Histogram

• presents the number of times a given value occurs

• constructed by diving the measurement scale into cells of equal width counting the number of values (n_i) that fall within each cell and drawing a rectangle above each cell whose height is proportional to n_i

• Tends to form a normal, or Gaussian distribution

Frequency Distribution

Also known as normal distribution. Is a relative frequency distribution that forms a bell-shaped curve and is composed of an infinitely large number of values.

• During measurement it is assumed that values will follow a normal distribution with an equal number of measurements above and below the mean value.

• Statistical procedures are based on the assumption of a Gaussian distribution of values

• Mean, median, and mode are identical

• Tails of the curve are asymptomatic to the baseline (curve gets close to the x-axis without touching it)

Gaussian Distribution

Large populations tend to form this type of frequency distribution

A subset of large population by random sample draw will have a frequency distribution very close to normal

A constant relationship exists between the standard deviation and the probability of values occurring in a population sample

The probability of the same observation having a value between the mean and 1 standard deviation greater than the mean is 34.13%. The probability of a value between ±1SD of the mean is 68.2%. The probability of an observation having a value within ±2SD of the mean is 95.44%. The probability of an observation having a value within ±3SD of the mean is 99.27%

The relationship between the frequency distribution curve and the SD applies only to normal distribution and not all populations will form a normal distribution

Characteristics of a Normal/Gaussian Distribution

_________ of a normal curve depends on how the data points are concentrated around the center of and toward the tails of the curve.

There are four characteristics of a set of data that are illustrated by a distribution curve

Measure of central tendency is how data points fir around the center (or the highest point or points) of the distribution

One point = unimodal

Multiple points = mean, median, and mode

Line of central tendency is the area in the distribution pattern where most of the observation seem to accumulate (does not have to be the mean)

Variation

Measure of __________ is how widely the data points are scattered around the center of the distribution.

A curve that flattens out and extends widely to each side has data with a greater pattern of variation than the one with a sharp peak and narrow base

Range, variance, standard deviation, and coefficient of variation

Variability

_________ of the curve about the center is whether the data points are evenly arranged around the measure of central tendency or skewed with the tail to the right (positive) or to the left (negative)

Symmetry

_________ is how the data points are distributed along the base of the distribution diagram with regard to the relative frequency of data appearing at the center point and each flank, with thinning of data between the center and the tails.

Increases as the tails become heavier (negative)

Decreases as the tails become lighter (positive)

Kurtosis

__________ of a set of data is obtained by adding all the numbers in the set and diving the sum by the number of values in that set

Arithmetic Mean

_________ is the middle value of a body of data ranking variables in order of increasing magnitude; the 50th percentile

With an even number of observations, the average of the middle two values becomes the median value

Median

________ is the most frequently occurring variable in a mass of data; the value at the peak of the frequency distribution curve

Mode

________ is the percentage of scores in the whole distribution that fall below the score that is being compared

Percentile

_________ the spread of data around the mean

Range

____________ (s²) reflects dispersion around the mean and is the square of the standard deviation

Variance

__________ measures dispersion of the variable about the mean and is the square root of teh variance

The larger the spread of the distribution curve, the larger the standard deviation (large SD indicates the data is not very uniform)

The narrower and more pointed the distribution curve, the smaller the standard deviation (SD) (small SD indicates the data is more uniform)

Standard Deviation

The ratio of the standard deviation to the mean: Also known as relative standard deviation

Reflects random variation of analytical methods in units that are independent of methodology, because it is a percentage comparison

Relates the SD to concertation as a percentage

Used for comparing the dispersion of two similar sets of data. It is an index of precision

Coefficient of Variation

_____________(Ho) is a probability theory that states there is no difference between two sets of values which are being compared

Used to determine if a difference exists; based on the calculation of the mean and variance for each series of numbers

Statement is not rejected unless the sample data provides convincing evidence that it is false

Rejected when test statistic (F test or t test) is large

If the ________________ is not rejected we cannot say the statement is true, we have just failed to disprove Ho

It is almost impossible to prove something by statistical methods

Null hypothesis

____________ is a test statistic based on the comparison of the variance values from two or more series of numbers

Interpreted by comparing the calculated F value to a critical F value which is obtained from a statistical table

Null hypothesis is rejected when the observed F value is greater than the critical F value

F Test

_________ is a test statistic based on the comparison of mean values from two or more series of numbers or methods

Determines if the two means are significantly different

Interpreted by comparing the calculated t value with a critical t value which is obtained from a statistical table

Null hypothesis is rejected if the calculated t value is greater than the critical t value

T test

_________ an equation that expressed the linear relationship between two variables

Describes the graphical plot of test values versus reference values when comparing method experiments

A line is drawn through the data points using visual judgement (line of best fit)

Linear Regression

_________- is the technique to determine the best fit for the line by measuring the distance from each point to the line, squaring the distance, then totaling the squares

The line with the lowest total is called the least squares line and should be the best line

Least Squares Analysis

____________(r value) determines if two series of numbers are related positively, negatively, or not at all

r should be very near 1.000 when performing a calibration

values less than 1 are due to random error

Accuracy of method should not be judged based on r value

Systematic error has no effect on r

Only use of r in comparison of methods is to assess the reliability of the linear regression estimates of slope and y intercept

Correlation coefficient

What is the formula for arithmetic mean?

Sum of values/number of values

Given the following values: 100, 120, 150, 140, 130 what is the mean

128

The middle value of a data set is statistically known as the

Median

The most frequent value in a collection of data is known as

Mode

Which of the following is the formula for coefficient of variation

(SD x 100)/mean

The following 5 control values in unit (nEq/L) were obtained: 140, 135, 138, 140, 142)

Calculate SD

Calculate CV

SD=2.65

CV=1.9%