Chapter 2. Test for Significance

Question 1

the process by which we
determine the probability that there
is a significant difference between
two samples

Answer 1

Significance Testing (Hypothesis testing)

Question 2

Indeterminate error is sufficient to explain any
difference in the values
being compared.

• no significant difference hypothesis

Answer 2

Null Hypothesis

Question 2

The difference between the
values is too great to be explained by random error
and, therefore, must be real.

• have a significant difference

Answer 2

Alternative Hypothesis

Question 3

A null hypothesis is retained whenever the evidence is insufficient to prove it is incorrect. Because of the way in which significance tests are conducted, it is impossible to prove that a null hypothesis is true.

Question 4

the confidence level for retaining the null hypothesis (95%), or the probability that the null hypothesis will be incorrectly rejected

Answer 4

Significance Level

Question 5

Retain Null = statistically the same

Reject Null = significant difference

Question 6

If there is greater than a 5% chance of a result as extreme as the sample result when the null hypothesis is true, then the null hypothesis is retained. This does not necessarily mean that the researcher accepts the null hypothesis as true—only that there is not currently enough evidence to conclude that it is true.

Question 7

Rejecting the null hypothesis means that a relationship does exist between a set of variables and the effect is statistically significant (p > 0.05)

Question 8

The null hypothesis cannot be proven, although the hypothesis test begins with an assumption that the hypothesis is true, and the final result indicates the failure of the rejection of the null hypothesis. Thus, it is always advisable to state ‘fail to reject the null hypothesis’ instead of ‘accept the null hypothesis.

Question 9

Two-tailed test

Answer 9

• comparison
• key words: significant difference, same effect, generate the same…

Question 10

One-tailed test

Answer 10

• key words: greater than, lower than, more effective, less effective…

Question 11

Type I Error

Answer 11

• The risk of falsely rejecting
  the null hypothesis (𝛼)
• risk is always equivalent to α
• false positive

Example:
Ho: he likes you back
Truth: he likes you back
Decision: falsely rejected Ho (missed your chance)

Question 12

Type II Error

Answer 12

• The risk of falsely retaining
  the null hypothesis (β).
• (β) - depends on sample size and variance
• false negative

Example:
Ho: he likes you back
Truth: he doesn’t like you back
Decision: accepted Ho (wrongly invited him)

Question 13

Minimizing a type 1 error by
decreasing 𝛼, for example,
increases the likelihood of a type 2 error

Question 14

F-Test

Answer 14

a test designed to indicate
whether there is a significant
difference between two
methods based on their
standard deviations.

Question 15

Always write the formula Ysa!!!

Question 16

F-Test
- higher value is always on the numerator

Question 17

F is defined in terms of the
variances of the two methods, where the variance is the
square of the standard deviation

Question 18

If 𝑭𝒄𝒂𝒍𝒄 > 𝑭𝒕𝒂𝒃𝒍𝒆, then the
variances being compared are

Answer 18

Significantly different

Question 19

If 𝑭𝒄𝒂𝒍𝒄 < 𝑭𝒕𝒂𝒃𝒍𝒆, then the
variances being compared are

Answer 19

Statistically the same

Question 20

The purpose of significance testing is

Answer 20

provide evidence to reject the null hypothesis

Question 21

Null hypothesis

Answer 21

Something we believe/expect to be true; no difference hypothesis

have no significant difference

Question 22

Alternative hypothesis

Answer 22

have significant difference

Question 23

comparison is made between two
sets of replicate measurements
made by two different means

Answer 23

t-test

Question 24

If 𝒕𝒄𝒂𝒍𝒄 > 𝒕𝒕𝒂𝒃𝒍𝒆, then the data being compared have

Answer 24

Significant Difference

Question 25

If 𝒕𝒄𝒂𝒍𝒄 > 𝒕𝒕𝒂𝒃𝒍𝒆, then the data being compared have

Answer 25

significant difference

Question 26

Several ways and several situations in which t-test can be used:

Answer 26

▸ t- test when a reference value is known ▸ Comparison of the means of two methods ▸ Paired t-Test ▸ t-test to compare different samples

Question 27

➢ used to obtain an improved estimate of the precision of a method and for calculating the precision of the two sets of data ➢ provides a more reliable estimate of the precision of a method than is obtained from a single set ➢ if random error is assumed to be the same for each set, then the data of the different sets can be pooled

Answer 27

Pooled Standard deviation

Question 28

side = denominator top = numerator (0.05, numerator, denominator)

Question 29

➢ two methods are used to make single measurements on several different samples. ➢ No measurement has been duplicated

Answer 29

Paired t-Test

Question 30

▸ Analysis of Variance ▸ allows comparisons among more than two population means ▸ 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.

Answer 30

ANOVA

Question 31

𝐻0: 𝜇1 = 𝜇2 = 𝜇3 = ⋯ = 𝜇𝑖 𝐻𝐴 : at least two of the 𝜇𝑖’s are different

Question 32

Applications

Answer 32

1. Is there a difference in the results of five analysts determining calcium by a volumetric method? 2. Will four different solvent compositions have differing influences on the yield of a chemical synthesis? 3. Are the results of manganese determinations by three different analytical methods different? 4. Is there any difference in the fluorescence of a complex ion at six different values of pH?

Question 33

The basic principle of ANOVA is to compare the variations between the factor levels (groups) to that within factor levels

Question 34

When H0 is TRUE, the variation between the group MEANS IS CLOSE to the variation WITHIN groups.

Question 35

When H0 is FALSE, the variation between the group mean is LARGE compared to the variation within groups.

Question 36

Grand mean can be calculated as the weighted average of the individual group means,

Answer 36

Single Factor ANOVA

Question 37

A statistical t value is calculated and compared with a tabulated value for the given number of tests at the desired confidence level

Answer 37

t-test when a reference value is known

Question 38

use this when comparing two methods, that is, when analyzing a sample by two different methods

Answer 38

comparison of the means of two methods

Question 39

▸ use this when comparing two methods with individual differences (𝐷𝑖) ▸ average difference is calculated and the individual deviations of each from are used to compute a standard deviation, sd

Answer 39

paired t-test

Question 40

To calculate the variance ratio needed in the F test, it is necessary to obtain several other quantities– the sums of squares:.

Answer 40

1. The sum of the squares due to the factor SSF 2. The sum of the squares due to error SSE 3. The total sum of the squares SST is obtained as the sum of SSF and SSE: SST = SSF + SSE

Question 41

Assumptions: 1. equal variance (variances of the I populations are assumed to be identical-tested through Hartley test) - the largest s should not be much more than twice the smallest s for equal variances to be assumed. 2. each of the I populations is assumed to follow a Gaussian distribution

Question 42

If 𝑭𝒄𝒂𝒍𝒄 > 𝑭𝒕𝒂𝒃𝒍𝒆, then the variances being compared are

Answer 42

SIGNIFICANTLY DIFFERENT

Question 43

If 𝑭𝒄𝒂𝒍𝒄 < 𝑭𝒕𝒂𝒃𝒍𝒆, then the variances being compared are

Answer 43

STATISTICALLY THE SAME

Question 44

a statistical measure (expressed as a number) that describes the size and direction of a relationship between two or more variables.

Answer 44

correlation

Question 45

A correlation between variables does not automatically mean that the change in one variable is the cause of the change in the values of the other variable.

Question 46

indicates that one event is the result of the occurrence of the other event(i.e. there is a causal relationship between the two events) This is also referred to as cause and effect.

Answer 46

causation

Question 47

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