preFinals Math In Modern World

Question 1

are raw information or facts that become useful information when organized in a meaningful way. It could be of qualitative and quantitative nature.

Answer 1

Data

Question 2

is concerned with “looking after” and processing data

Answer 2

Data Management

Question 3

Data management involves the following: (there are 4 items)

Answer 3

• Looking after field data sheets
• Checking and correcting the raw data
• Preparing data for analysis
• Documenting and archiving the data and meta-data

Question 4

Importance of Data Management
(there are 3 items)

Answer 4

•Ensures that data for analysis are of high quality so that conclusions are correct
• Good data management allows further use of the data in the future and enables efficient integration of
results with other studies.
• Good data management leads to improved processing efficiency, improved data quality, and improved meaningfulness of the data.

Question 5

Methods of Data Collection
(4 items)

Answer 5

Census
Sample survey
Experiment
Observation study

Question 6

this is the procedure of systematically acquiring and recording information about all members of a given population. Researchers rarely survey the entire population for two (2) reasons: the cost is too high and the population is dynamic in that the individuals making up the population may change over time.

Answer 6

Census

Question 7

sampling is a selection of a subset within a population, to yield some knowledge about
the population of concern. The three main advantages of sampling are that (i) the cost is lower, (ii) data
collection is faster, and (iii) since the data set is smaller, it is possible to improve the accuracy and quality
of the data.

Answer 7

Sample survey

Question 8

this is performed when there are some controlled variables (like certain treatment in medicine) and the intention is to study their effect on other observed variables (like health of patients). One of the main requirements to experiments is the possibility of replication.

Answer 8

Experiment

Question 9

this is appropriate when there are no controlled variables and replication is impossible. This type of study typically uses a survey. An example is one that explores the correlation
between smoking and lung cancer. In this case, the researchers would collect observations of both smokers and non-smokers and then look for the number of cases of lung cancer in each group.

Answer 9

Observation study

Question 10

Planning and Conducting Surveys
1. Characteristics of a well-designed and well-conducted survey
a. ?
b. ?
c. ?
d. ?

Answer 10

1. A good survey must be representative of the population.
2. To use the probabilistic results, it always incorporates a chance, such as a random number generator.
   Often we don’t have a complete listing of the population, so we have to be careful about exactly how
   we are applying “chance”. Even when the frame is correctly specified, the subjects may choose not to
   respond or may not be able to respond.
3. The wording of the question must be neutral; subjects give different answers depending on the phrasing.
4. Possible sources of errors and biases should be controlled. The population of concern as a whole may not be available for a survey. Its subset of items possible to measure is called a sampling frame (from
   which the sample will be selected). The plan of the survey should specify a sampling method, determine
   the sample size and steps for implementing the sampling plan, and sampling and data collecting.

Question 11

2 types of sampling method

Answer 11

Non-probability sampling
Probability sampling

Question 12

is any sampling method where some elements of the population have no
chance of selection or where the probability of selection can’t be accurately determined.

Answer 12

Non-probability sampling

Question 13

it is possible to both determine which sampling units belong to which sample and the probability that each sample will be selected.

Answer 13

Probability sampling

Question 14

One example of nonprobability sampling is** 1. ___________ **sampling (customers in a supermarket are
asked questions). Another is 2. _____ sampling, when judgment is used to select the subjects based on
specified proportions.

Answer 14

1. convenience sampling
2. quota sampling

Question 15

The following sampling methods are example of probability sampling:

(There are 5 of them)

Answer 15

Simple Random Sampling (SRS)
Systematic sampling
Stratified sampling
Cluster sampling
Matched random sampling

Question 16

all samples of a given size have an equal probability of being
selected and selections are independent. The frame is not subdivided or partitioned. The sample variance is a good indicator of the population variance, which makes it relatively easy to estimate
the accuracy of results.

Answer 16

Simple Random Sampling (SRS)

Question 17

relies on dividing the target population into strata (subpopulations) of equal
size and then selecting randomly one element from the first stratum and corresponding elements
from all other strata.

Answer 17

Systematic sampling

Question 18

when the population embraces a number of distinct categories, the frame can be organized by these categories into separate “strata”.

Answer 18

Stratified sampling

Question 19

is an example
of two-stage random sampling: in the first stage a random sample of areas is chosen; in the second
stage a random sample of respondents within those areas is selected.

Answer 19

Cluster sampling

Question 20

in this method, there are two (2) samples in which the members are
clearly paired, or are matched explicitly by the researcher (for example, IQ measurements or pairs
of identical twins). Alternatively, the same attribute, or variable, may be measured twice on each
subject, under different circumstances (e.g. the milk yields of cows before and after being fed a
particular diet).

Answer 20

Matched random sampling

Question 21

C. Planning and conducting experiments:
1. Characteristics of a well-designed and well-conducted experiment

A good statistical experiment includes: (4 items)

Answer 21

a. Stating the purpose of research, including estimates regarding the size of treatment effects,
alternative hypotheses, and the estimated experimental variability. Experiments must compare the
new treatment with at least one (1) standard treatment, to allow an unbiased estimates of the
difference in treatment effects.
b. **Design of experiments, **using blocking (to reduce the influence of confounding variables) and
randomized assignment of treatments to subjects
c. **Examining the data set in secondary analyses, **to suggest new hypotheses for future study
d. Documenting and presenting the results of the study

Question 22

2. Treatment, control groups, experimental units, random assignments and replication
   (3 items)

Answer 22

a. Control groups and experimental units
- To be able to compare effects and make inference about associations or predictions, one typically has to subject different groups to different conditions. Usually, an experimental unit is subjected to treatment and a control group is not.
b. Random Assignments
- The second fundamental design principle is randomization of allocation of (controlled variables)
treatments to units. The treatment effects, if present, will be similar within each group.
**c. Replication **
- All measurements, observations or data collected are subject to variation, as there are no
completely deterministic processes. To reduce variability, in the experiment the measurements
must be repeated. The experiment itself should allow for replication itself should allow for
replication, to be checked by other researchers.

Question 23

To be able to compare effects and make inference about associations or predictions, one typically
has to subject different groups to different conditions. Usually, an experimental unit is subjected to
treatment and a control group is not.

Answer 23

Control groups & experimental units

Question 24

The second fundamental design principle is randomization of allocation of (controlled variables)
treatments to units. The treatment effects, if present, will be similar within each group.
c. Replication

Answer 24

Random Assignments

Question 25

All measurements, observations or data collected are subject to variation, as there are no
completely deterministic processes. To reduce variability, in the experiment the measurements
must be repeated. The experiment itself should allow for replication itself should allow for
replication, to be checked by other researchers.

Answer 25

Replication

Question 26

A stratified sampling approach is most effective when three conditions are met:
(3 items)

Answer 26

a. Variability within strata are minimized
b. Variability between strata are maximized
c. The variables upon which the population is stratified are strongly correlated with the desired
dependent variable (beer consumption is strongly correlated with gender).

Question 27

3. Sources of bias and confounding, including placebo effect and blinding
   (3 items)

Answer 27

Confounding
Placebo and blinding
Blocking

Question 28

is an extraneous variable in a statistical model that correlates
(positively or negatively) with both the dependent variable and the independent variable. The
methodologies of scientific studies therefore need to control for these factors to avoid a false positive
(Type I) error (an erroneous conclusion that the dependent variables are in a causal relationship with the independent variable).

Answer 28

Confounding

Question 29

is an imitation pill identical to the actual treatment pill, but without
the treatment ingredients.

Answer 29

Placebo and blinding

Question 30

is the arranging of experimental units in groups (blocks) that are similar to one another.

Answer 30

Blocking

Question 31

4. Completely randomized design, randomized block design and matched pairs

_____ are for studying the effects of one primary factor without the
need to take other nuisance variables into account. The experiment compares the values of a
response variable (like health improvement) based on the different levels of that primary factor (e.g.,
different amounts of medication).

Answer 31

Completely randomized designs

Question 32

4. Completely randomized design, randomized block design and matched pairs

____ is a collection of completely randomized experiments, each run within one of the blocks of the total experiment.

Answer 32

Randomized block design

Question 33

is used to determine whether there is significant difference between the expected value
frequencies and the observed frequencies in one or more categories.

Answer 33

Chi-square

Question 34

There are two (2) types of chi-square tests. Both use the chi-square statistic and distribution for different purposes:

Answer 34

chi-square goodness of fit test
chi-square test for independence

Question 35

determines if a sample data matches a population.

Answer 35

chi-square goodness of fit test

Question 36

compares two (2) variables in a contingency table to see if they
are related. It tests to see whether the distributions of categorical variables differ from each other.
- A very small chi-square test statistic means that your observed data fits your expected data well. In other words, there is a relationship.
- A very large chi-square test statistic means that the data does not fit very well. In other words, there
is no relationship.

Answer 36

chi-square test for independence

Question 37

Assumptions of the Chi-Square Test
The assumptions of the chi-square test are the same whether we are using the goodness-of-fit or the test-of independence. The standard assumptions are:
(3 items)

Answer 37

• Random sample
• Independent observations for the sample (one observation per subject)
• No expected counts less than five (5)

Question 38

is used to test whether a frequency distribution obtained experimentally fits an “expected” frequency distribution that is based on the theoretical or previously known probability of each outcome.

Answer 38

chi-square goodness-of-fit test

Question 39

is used to assess if two (2) factors are related. This test is often used in
social science research to determine if factors are independent of each other. For example, we would use this test to determine relationships between voting patterns and race, income and gender, and behavior and education.

Answer 39

chi-square test of independence