Unit 1 Exam Flashcards
Mantissa
What is its rule?
Number of digits after the decimal in a logarithm result.
the number after the log will have the same number of sig figs as numbers after the decimal in the answer.
X bar is…
Mean average
N
Sample size
Degrees of freedom
General Rule
N-1
You lose one degree of freedom whenever you take the average because you lose the ability to change one of the numbers
Accuracy
How close you can get to the accepted value
Precision
Reproducibility of the data
How does precision affect a histogram?
More precision the more narrow the histogram gets
Absolute Error
E
Margin of error within a particular measurement
xi-xt
Relative Error
Er
Percent of total error
xi-xt/xt *100
What are the Types of Error? Describe each.
Systematic- determinate, flaw, reproducible, can be eliminated
Random- indeterminate, always present, never can be eliminated, equal chance of being positive and negative
Gross- large, personal error, outliers
Precision is due to….error
Accuracy is due to….. error
Random
Systemic
What is the most common type of error and was causes it?
Systemic
Equipment and instrumentation, methods, personal
Standard deviation
s
Used to measure how closely the data are to the mean value, the smaller the SD the closer to the mean
Gaussian distribution results from…..errors and therefore represents the ….
Random
Precision
Population
Symbol for mean average
Symbol for standard deviation
All measurements that are possible, infinite
µ
σ
Sample
Symbol for mean average
Symbol for standard deviation
A subset of the population
x bar
s
How many data points are needed to assume that the sample and population are the same?
30
What does a negatively skewed graph tell you about the mean and median?
Mean< Median
What does a positively skewed graph tell you about the mean and median?
Mean>Median
What percent of data lies between +/- 1 standard deviations of the mean?
68%
What percent of data lies between +/- 2 standard deviations of the mean?
95%
What percent of data lies between +/- 3 standard deviations of the mean?
99%
Standard Error
sm
Used to convey a sense of precision. something is more likely to be more precise than something else
What are the 3 ways to convey error?
Standard deviation
Standard Error
95% confidence interval
What is the variance calculation?
Standard deviation squared
Relative standard error
RSD
Provides a simple perspective on the magnitude of the data sets deviation
Coefficient of variation
CV
Relative standard deviation as a percent
Confidence interval
the range of values within which the population mean is expected to lie with a certain probability
Central limit theorem
large data sets will tend toward a normal distribution, use principle of larger sets to justify smaller ones
T-test
equation
allows for the calculation of confidence intervals
Based on the degrees of freedom
µ= x bar (+/-) (ts/(square root (N))
What does the 95% confidence interval mean?
95 out of a 100 means with individually computed confidence intervals will overlap with the true mean
What do you compare your mean average to, in order to learn about its accuracy?
An acceptable mean from a population (known value)
A particular cutoff value (high or low)
A separate experimental mean
Null Hypothesis
H0
There is no difference between the quantities
Alternative Hypothesis
Ha
The opposite of the null hypothesis
What is first determined in hypothesis testing? What does that value provide?
Confidence level (1-a)
Significance level (a)
Type 1 error
When the null hypothesis is rejected even though it is true.
False negative
Type 2 error
When the null hypothesis is accepted even though it is false
False positive
F-test
F= (s1^2/s2^2)
Compares two means of two data sets, comparing variances
ANOVA
Compares between to within, internal variances are incorporated
What is the difference between ANOVA and a t-test
ANOVA includes internal variances where as t-tests assume equal or unequal variances
Q-test
Exposes outliers
Interquartile Range
Q3-Q1
What are the 3 calibration methods?
External standards-
ppm
1 µg/ 1 mL
(mass of substance/mass of sample)*10^6
ppb
1 ng/ 1 mL
(mass of substance/mass of sample) *10^9
