CHEM275 STATS LECTURE

What are the two main categories of errors?

1. Determinate 2. .indeterminate

What are the three tests of significance?

1. F tests 2. t tests 3. Q test

What are the two types of t tests?

1. when the accepted value is already known -- t test only applied to new method 2. when the t test is applied to two methods

There is a ___% chance that the true value is contained within the range of one standard deviation of the mean (IN NORMAL/Gaussian distribution)

68%

What is the equation for the mean error?

AVERAGE of measured value minus true value

During the F test, if calculated F is GREATER than tabulated F, then there is a significant difference between the ____ and the ____ of the two methods.

Calculated F greater than tabulated: significant difference between the variance and the precision

During the F test, if calculated F is LOWER than tabulated F, then there is no _____ ____ between the variances and the precision of the two methods

Calculated F lower than tabulated: no significant difference between variance and precision

For N (number of measurements) greater than _____, sample becomes "infinite"

N greater than 30 = infinite population

The number of degrees of freedom can be calculated by v =

N-1 (n = number of measurements)

Indeterminate errors follow a _____ distribution

Normal AKA gaussian

Q calculated less than Q tabulated, outlier ____ ____ rejected at that confidence level

Q calculated LESS THAN Q tabulated, outlier cannot be rejected.

If Q calculated is GREATER than Q tabulated, the outlier _____ _____ rejected at that confidence level

Q calculated greater than Q tabulated, outlier REJECTED (determinate error)

You want to express your relative error in terms of ppt (parts per thousand). How would the equation change?

Relative error = absolute error divided by true value For ppt, multiply by 1000

The equation for the *relative error* is

absolute error divided by true value (*100%) --NOTE absolute error = measured - true

Indeterminate errors are also called ____ errors

accidental or random errors

Accuracy is usually expressed in terms of _____ error, ____ error, and ______ error

accuracy expressed in terms of ABSOLUTE error MEAN. error RELATIVE error

The relative standard deviation of the mean is also known as the

coefficient of variation

too low a confidence level may _____ valid random numbers

may exclude (range too narrow)

THE EQUATION FOR *RELATIVE ACCURACY* is

mean divided by true value (*100%) Mean = average of all measured values

The equation for the *ABSOLUTE ERROR* is

measured minus true

For Gaussian distribution curves, the _____ standard deviations from the mean, the more certain we are the true value lies within the range of values

more standard deviations from the mean (ie, larger range of values considered) increases the likelihood that the true value is included in considered values.

an infinite set of data is also referred to a s a ________

population

F test compares _____ between two measurements

precision

Precision is usually expressed in terms of standard _____, v_______, standard deviation of _____, _____/RSD, and range

precision is described using: 1. standard deviations 2. variance 3. standard deviation of the mean 4. CV/RSD 5. range

If an outlier is determined by the Q test to be a determinate error, this outlier should be _____

rejected.

Reliability of the sample standard deviation (s) ______ with the number of measurements

reliability of s *increases* with greater number of measurements

Analyzing the precision of results using RANGE is only used for a (small/large) set of data

small (less than four measurements)

What is the equation for the CV/RSD?

standard deviation divided by MEAN (Times 100%)

how do you find the standard deviation of the mean?

standard deviation divided by squareroot of N (number of sample)

How do you find the variance?

standard deviation squared

The standard deviation of the mean is also called the

standard error

The t test is used to determine if the measured value is ____ _____ to the accepted value

statistically equal (equivalent to calibration)

The results of indeterminate errors can be evaluated using ______

statistics

Determinate errors are also called ____ errors

systematic errors

In the t test, comparisons are made between replicate measurements by ____ method and _____ method

t test measures the TEST method and the ACCEPTED method

The confidence ____ is the probability that the true value falls within the confidence interval range

the confidence LEVEL

The confidence ____ is the range that the true value might fall (with a given probability)

the confidence interval= range

the confidence ____ is the max/min values of the confidence interval range

the confidence limits

Tests if two procedures measured do the same thing

the t test

If t calculated is GREATER than t tabulated, there is _____ a significant difference between the two methods (at that confidence level)

there IS a significant difference when t calculated is GREATER than t tabulated

If t calculated is LESS THAN t tabulated, there is ____ significant difference between the two methods

there is NO significant difference when t calculated is LESS THAN t tabulated

The "t" test is used to determine if two sets of measurements obtained with ____procedures are statistically different

two sets of measurements obtained with DIFFERENT procedures.

The confidence limit is the

upper and lower limits of confidence interval range

Standard deviation squared is also known as the _____

variance

The calculation for the standard deviation of an infinite set is ____(different/the same) as the calculation for the standard deviation of a finite set

DIFFERENT

The test compares the precision of two methods

F test

This test used to test if there is a significant difference between two methods based on standard deviation.

F test

compares the result of a newly developed method with a standard method

F test

The Q test detects ____ errors or ____

detects gross errors or outliers

______ errors affect accuracy

determinate AKA systematic errors

The Q test is used to determine if an outlier is due to a ____ error

determinate error

systematic errors are also called _____ errors

determinate errors

Determinate errors affect ____, indeterminate errors affect ______

determinate: accuracy indeterminate: precision

_____ errors affect precision

indeterminate AKA random

random errors are also called ____ errors

indeterminate errors

Too high a confidence level may include ____ data

invalid data ( range too wide)