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)