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ANALYTICAL CHEMISTRY C3 > Chapter 5: Statistical Data Treatment and Evaluation > Flashcards

Chapter 5: Statistical Data Treatment and Evaluation Flashcards

1
Q

this interval defines a numerical interval around the mean of a set of replicate results within which the population mean can be expected to lie with a certain probability

A

confidence interval

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2
Q

the limits of the interval are called

A

confidence limits

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3
Q

the probability that the true mean lies
within a certain interval and is often
expressed as a percentage.

A

confidence level

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4
Q

The probability that a
result is outside the confidence interval is often called the

A

significance level

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5
Q

90% confidence interval , z=

A

1.64

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6
Q

95% confidence interval , z=

A

1.96

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7
Q

99% confidence interval , z=

A

2.58

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8
Q

formula for finding confidence interval when standard deviation population is known or s is a good estimate of the standard deviation population

A

CI for u=x+- z(sigma)
CI for u= mean +- z(sigma)/square root of N

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9
Q

TRUE or FALSE
It is essential to keep in mind at all times that confidence intervals based on CI for u= mean +- z(sigma)/square root of N apply only in the absence of bias and only if we can assume that s is a good approximation of s.

A

TRUE

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10
Q

studied the limits of the Poisson and binomial distributions,
the sampling distribution of the mean and standard deviation, and several
other topics.

A

W. S. Gossett

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11
Q

His most important work on the t test was developed to determine how closely the yeast and alcohol content of various batches of Guinness matched the standard amounts established by the brewery

A

W. S. Gossett

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12
Q

is the basis for many decisions made in science and engineering.

A

Hypothesis testing

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13
Q

postulates that two or more observed quantities are the same.

A

null hypothesis

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14
Q

Specific examples of hypothesis tests that scientists often use include the comparison
of

A

1) the mean of an experimental data set with what is believed to be the true
value,
2) the mean to a predicted or cutoff (threshold) value, and
3) the means or
the standard deviations from two or more sets of data.

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15
Q

TRUE or FALSE
The first, the null hypothesis H0, states that m population is equal to true value of mean population. The second, the alternative hypothesis Ha can be stated in several ways.

A

TRUE

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16
Q

it does not matter whether the mean is larger or smaller than the known value

A

two-tailed test

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17
Q

other alternative hypotheses are mean population > true mean population or vice versa, which indicated the direction of the difference matters and is called

A

one-tailed test

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18
Q

TRUE or FALSE
The crucial elements of a test procedure are the formation of an appropriate test statistic
and the calculation of a probability value—p-value

A

TRUE

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19
Q

TRUE or FALSE
The smaller the value of p, the stronger the evidence against H0. Conversely, if the p value is large, there is good evidence that H0 is true, and therefore, it should be accepted

A

TRUE

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20
Q

For tests concerning one or two means, the test statistic might be the ________ if we have a large number of measurements or if we know s

A

z statistic

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21
Q

used for a small number of measurements with unknown s. Also, when in doubt, it is also should be used.

A

t statistic

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22
Q

TRUE or FALSE
If the probability p of obtaining
the z (or t) value is very low when assuming H0 is true, reject H0.

A

TRUE

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23
Q

TRUE or FALSE
using the rejection region approach, if z (or t) lies within the rejection region, reject H0.

A

TRUE

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24
Q

TRUE or FALSE
The rejection region approach has fallen
out of favor because the region holds only the chosen significance level

A

TRUE

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25
what test is applicable If a large number of results are available so that s is a good estimate of s
large sample z test
26
rejection can occur for results in either tail of the distribution.
two-tailed test
27
For a small number of results, use a similar procedure to the z test except that the test statistic is the t statistic and the test is called the
small sample t test
28
TRUE or FALSE In testing for bias, we do not know initially whether the difference between the experimental mean and the accepted value is due to random error or to an actual systematic error. The t test is used to determine the significance of the difference.
TRUE
29
TRUE or FALSE If the analytical method had no systematic error, or bias, random errors would give the frequency distribution
TRUE
30
TRUE or FALSE t test is used to determine the significance of the difference of experimental mean and the accepted value
TRUE
31
If it were confirmed by further experiments that the method always gave low results, we would say that the method had a
negative bias
32
TRUE or FALSE If the absolute value of the test statistic is less than the critical value, the null hypothesis is accepted, and no significant difference between the means has been demonstrated
TRUE
33
TRUE or FALSE A test value of t greater than the critical value indicates a significant difference between the means
TRUE
34
TRUE or FALSE Since t is less than or equal to the tcrit, you can conclude that there is a significant difference at % confidence level.
TRUE
35
TRUE or FALSE When t is greater than the tcrit value, accept the null hypothesis at % confidence level and conclude that there is no significant difference between the experimental and the accepted value.
TRUE
36
TRUE or FALSE The number of degrees of freeon for binding the critical value of t is N1+N2-2
TRUE
37
If there is good reason to believe that the standard deviations of the two data sets differ, the___________ must be used.1 However, the significance level for this t test is only approximate, and the number of degrees of freedom is more difficult to calculate.
two-sample t test
38
What statistical test should be used by scientists and engineers who often make use of pair measurements on the same sample in order to minimize sources of variability that are not of interest?
t test analyzing paired data
39
What statistical test should be used when two methods for determining glucose in blood serum are to be compared
t test analyzing paired data
40
occurs when H0 is rejected although it is actually true.
type I error
41
In some sciences, a type I error is called a
false negative
42
occurs when H0 is accepted and it is actually false.
type II error
43
type II error is sometimes termed as a
false positive
44
The probability of a type II error is given by the symbol
beta (B)
45
Making alpha (a) smaller such that 0.01 instead of 0.05 appears to make sense in order to minimize what type of error
type I error
46
TRUE or FALSE decreasing the type I error rate increases the type II error rate because they are inversely related to each other.
TRUE
47
TRUE or FALSE an a value of 0.05 (95% confidence level) provides an acceptable compromise.
TRUE
48
TRUE or FALSE If a type I error is much more likely to have serious consequences than a type II error, it is reasonable to choose a small value of a.
TRUE
49
TRUE or FALSE a type II error would be quite serious, and so a larger value of a is used to keep the type II error rate under control.
TRUE
50
TRUE or FALSE As a general rule of thumb, the largest a that is tolerable for the situation should be used. This ensures the smallest type II error while keeping the type I error within acceptable limits.
TRUE
51
What statistical analysis requires that the standard deviations of the data sets being compared are equal.
t test
52
can be used to test this assumption under the provision that the populations follow the normal (Gaussian) distribution. It is also used in comparing more than two means and in linear regression analysis
F test
53
is based on the null hypothesis that the two population variances under consideration are equal
f test
54
TRUE or FALSE t and z test is based on the null hypothesis that the two population mean under consideration are equal
TRUE
55
is defined as the ratio of the two sample variances is calculated and compared with the critical value of F at the desired significance level
test statistic F
56
TRUE or FALSE For a one-tailed test, we test the alternative hypothesis that one variance is greater than the other. Hence, the variance of the supposedly more precise procedure is placed in the denominator and that of the less precise procedure is placed in the numerator
TRUE
57
TRUE or FALSE If F1 is less than fcrit and p> actual value, we accept the null hypothesis
TRUE
58
TRUE or FALSE If F2 is greater than fcrit and p> actual value, we reject the null hypothesis
TRUE
59
Analysis of Variance also stands for
ANOVA
60
These methods use a single test to determine whether there is or is not a difference among the population means rather than pairwise comparisons as is done with the t test
ANOVA
61
take advantage of ANOVA in planning and performing experiments.
Experimental design methods
62
Common characteristics in a comparison are ________. The values of the factors are ________. Experimental results are ________
factors; levels; responses
63
the populations have differing values of a common characteristic called
factor or treatment
64
The different values of the factor of interest are called
levels
65
The comparisons among the various populations are made by measuring a
response
66
Often, several factors may be involved, such as in an experiment to determine whether pH and temperature influence the rate of a chemical reaction. In such a case, the type of ANOVA is known as a
two-way ANOVA
67
The basic principle of ________ is to compare the variations between the different factor levels (groups) to that within factor levels.
ANOVA
68
In ANOVA, the factor levels are often called
groups
69
TRUE or FALSE The basic principle of ANOVA is to compare the between-groups variation to the within-groups variation.
TRUE
70
The basic statistical test used for ANOVA is the
F test
71
detect difference in several population means by comparing the variances
ANOVA
72
it is the average of all the data
grand average
73
TRUE or FALSE The error sum of the squares is related to the individual group variances
TRUE
74
TRUE or FALSE As a rough rule of thumb, the largest s should not be much more than twice the smallest s for equal variances to be assumed
TRUE
75
By dividing the sums of squares by their corresponding degrees of freedom, you can obtain quantities that are estimates of the between-groups and within-groups variations. These quantities are called
mean square values
76
are sums of squares divided by degrees of freedom.
mean square values
77
is an estimate of the variance due to error
mean square due to errors
78
is an estimate of the error variance plus the between-groups variance
MSF/ mean square due to factor levels
79
TRUE or FALSE If the factor effect is significant, MSF is greater than MSE.
TRUE
80
There are several methods to determine which means are significantly different. One of the simplest is the
least significant difference method
81
In this method, a difference is calculated that is judged to be the smallest difference that is significant. The difference between each pair of means is then compared to the least significant difference to determine which means are different
least significant difference method
82
is a result that is quite different from the others in the data set and might be due to a gross error.
outliers
83
is a simple, widely used statistical test for deciding whether a suspected result should be retained or rejected
Q test
84
the absolute value of the difference between the questionable result xq and its nearest neighbor xn is divided by the spread w of the entire set to give the quantity Q:
Q test
85
TRUE or FALSE If Q is greater than Qcrit, the questionable result can be rejected with the indicated degree of confidence
TRUE
86
TRUE or FALSE the only valid reason for rejecting a result from a small set of data is the sure knowledge that a mistake was made in the measurement process. Without this knowledge, a cautious approach to rejection of an outlier is wise.
TRUE
87
is used to compare more than two means and to determine whether any differences are real or the result of random errors.
ANOVA
88
can be used to minimize sources of variability that influence both members of a pair of measurements.
paired t test
89
computes the t statistic and the probability of t assuming that H0 is true. If p is small compared to the significance level a, H0 is rejected. Alternatively, a rejection region is calculated from critical values of t.
t test
90
asserts that the mean is equal to the accepted value
null hypothesis
91
We can compare an experimental mean to a known value or an accepted level by a hypothesis test, the ____________, if the population standard deviation is known.
z test
92
is the interval within which the population mean is expected to lie with a certain probability.
confidence interval
93

ANALYTICAL CHEMISTRY C3 (21 decks)

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