Quant Test#2

Accuracy

Refers to the agreement of a particular value with a true value

Precision

Refers to the degree of agreement among several elements of the same quantity

Variance:

STDev ^2

Method of least squares

Process of fitting a mathematical function to a set of measured points by minimizing the sum of the squares of the distances from the points to the curve.

Standard Solutions:

A solution whose composition is known by virtue of the way it was made from a reagent of known purity or by virtue of its reaction with a known quantity of standard reagent.

Student's t

A statistical tool used to express confidence intervals and to compare results from different experiments.

Gaussian Distribution

Theoretical bell‐ shaped distribution of measurements when all error is random. The center of the curve is the mean(micro), and the width is characterized by the standard deviation(sigma)

Sig figs in add. and sub. are limited by?

the least certain number ex. 9.8982 + 98.23= 110.39- therefore UNCERTAINTY begins in the hundredths place

Degrees of Freedom

the number of independent measurements. - In a standard deviation of an average there is one measurement needed to have any idea of the average. The remaining measurements are the degrees of freedom.

The number of digits in the antilog x=(10^x) is

the number of sig figs in the mantissa of x

Characteristic

the part of the logarithm to the left of the decimal point

ALt. HYp

the two data sets are different

Null Hypothesis:

the two sets of data are the same.

How do you round when doing a series of calculations?

wait to round the final result

When are zeros significant?

when they are located i n the middle of a number and when they are at the end of a number on the right hand side of a decimal point

What are the 4 steps in detecting a systematic error?

1. Analyze samples of unknown composition 2. Analyze 'blank' samples containing none of the analyte being sought 3. Use a diff. analytical methods to measure the same quantity 4. Round robin experiment: assign different people/labs to analyze identical samples

What are the 4 steps of the F test?

1. Are the standard deviation of two sets of measurements different? 2. Null Hypothesis, s1 = s2 3. Alt. Hyp: s1 ≠ s2 4. Compare a calculated F value to the F value in the table. If Fcalc > Ftable, the two are different, if not they are the same.

The Real rule for sig figs

1. The 1st uncertain figure is the last sigfig

What are 2 possible options for systematic error?

1. Uncertainty in Molar mass 2. Multi. deliveries from one pipet

what is the criteria for sig figs in rounding? If the digit/s are to be removed- list 3

1. is less than 5-the preceding digits stay the same 2. Is greater than 5 preceding digit is increased by 1 3. Is =5 -the preceding digits remains the same or increases by 1 depending on what number gives an even digit

what are relative uncertainties by function =list the amount from least- most uncertain

1. x and z have equal r UN 2. when multiplied it increases by a 1/4 3. if the r UN of x or z is squared alone the r UN is doubled

Calibration Curve:

a graph showing the value of some property versus concentration of analyte. When the same property of an unknown is measured, its concentration can be determined from the graph.

Blank Solution

a solution that does not contain analyte. - Is used to correct for interferences.

Linear Range

the analyte concentration range over which response is proportional to concentration.

Dynamic range

the analyte concentration range over which there is a measurable response to analyte.

Confidence intervals or standard deviations can be used as

the error term is error propagation

Degrees of Freedom:

#observations ‐ #estimates

CI of Slope: ±tsm

-Where t has (n‐2) degrees of freedom - Where sm is the standard error of the slope.

Relative Standard Deviation:

100 * std. dev. / avg

Percent Relative Uncertainty

100 x relative uncertainty

Propagation of Unc Multi. and Div

A= B*/C*/D %RUa=[(RU)^2b + (%RU)^2c + (%RU)^2d]^1/2 Use percent R unc.

The Propagation of UNc. from random Error Add. and SUb.

A=B C D Ua=(Ub^2+Uc^2+Ud^2)^1/2 - ABs UNc are used -can use STDev

Absolute Uncertainty

An expression of the margin of uncertainty ass. with measurement

Confidence Intervals

An expression stating that the true mean, , is likely to lie within a certain distance from the measured mean, . X

Confidence level

Analytical work usually 95% confidence.

Fcalculated =s1^2 /s2^2

Arrange so that Fcalculated is greater than 1.

use a graph to displace qualitative behavior of data- list an example

Calibration curve of a buret

Relative Uncertainty

Compares the size of the absolute uncertainty with the size of its ass. measurement - Rel UNc.= Abs UNc/ Mag. of Measurement

Comparing a Measured Result with a "Known" Value

Comparing an average,X, to a known value. • Null Hypothesis,X = known value. • Compare a calculated t value to the t value in the table. If tcalc > ttable, the two are different, if not they are the same.

F Test:

Comparison of Standard Deviations

Interpolation

Estimate all readings to the nearest tenth of the distance between scale divisions

The Real Rule for Bad Data

If you know that you have a bad data point. Lets say you dropped some of the sample. You can eliminate that point without performing a statistical test. • Beveryhesitanttothrowoutdatapointswhenyou are not certain that they are bad. • TheGrubbstestisnotveryreliable.

Method of least Squares

Involves such fun stuff as matrix algebra and calculus

Standard Deviation:

Is a measure of how closely the data are clustered to the mean (average).

What is a significant number?

NONZEROS

Sig figs are limited by what in Multiplication and div.?

Number of digits contained in the number w/ the fewest sig figs ex. 984.9879481 x 98.94= 9809

Systematic error aka determinate error

Occurs in the same direction each time (high or low), often resulting from poor technique

Significant Figures

The minimum number of digit needed to write a given value in scientific notation without the loss of accuracy

Mantissa

The part of the logarithm to the right of the decimal point

Student's t Test

Used to compare one set of data with another to decide whether or not they are "the same".

CI of intercept: ±tsb

Where sb is the standard error of the intercept.

n=10^a a= log n- means n is the antilog of a

log n =a

Random Error/ Indeterminate error

measurement has an equal probability of being high or low- Obeys the law of statistics

The number of digits in the mantissa of log x is equal to the

number of sig figs in x

G=

outlier-x/s

Comparing Replicate Measurements

• Are 2 labs getting the same answer, comparing two averages,X1 and X2 • Null Hypothesis, X1= X2 • Compare a calculated t value to the t value in the table. If tcalc > ttable, the two are different, if not they are the same.

list the 3 uses- Uses of Student's t Test

• Comparing a measured result with a "known" value. • Comparing replicate measurements. • Comparing individual differences.

Grubbs Test for an Outlier

• One measurement seems 'off' can it be thrown away? • Null Hypothesis, The data point is part of the data set • Alt. Hyp: The data point is not part of the data set • Compare a calculated G value to the G value in the table. If Gcalc > Gtable, the two are different, if not they are the same.

Propagation of Uncertainty with a Calibration Curve

• nu is the number of measurements of the unknown • n is the number of measurements in the calibration line • Y bar corresponds to the average of the calibration measurements • Yu bar is the average of the unknown readings.