Module 1.1 Basic Concepts in Inferential Statistics

Question 1

a branch of science consisting of theory and methods concerned with the collection, organization, presentation, analysis of the data and interpretation of the results of the analysis in order to answer the research questions at hand

Answer 1

statistics (singular)

Question 2

collection of numerical figures

Answer 2

statistics (plural)

Question 3

how can statistics be viewed?

bonus: differentiate your answers

Answer 3

statistics can be viewed in a singular and plural sense

bonus:

In a singular sense, statistics is a branch of science consisting of theory and methods concerned with the collection, organization, presentation, analysis of the data and interpretation of the results of the analysis in order to answer the research questions at hand

while in a plural sense, statistics is a collection of numerical figures

Question 4

give examples of statistics in a plural sense

Answer 4

• number of active COVID-19 cases
• unemployment rate
• proportion of Filipinos who are satisfied with government response to COVID-19
• basketball statistics
• etc.

Question 5

What are the two important things that you should know in order to make good decisions based on the data?

Answer 5

1. what questions you hope to answer with the data
2. how the data will be obtained

Question 6

definition of population

Answer 6

the entire collection of individuals or entities where information wanted is present, on which inferences are made

Question 7

definition of sample

Answer 7

subset of the population actually examined to gather examine information

Question 8

the entire collection of entities where information wanted is present, on which inferences are made

Answer 8

population

Question 9

What is the difference of population and sample?

Answer 9

population is the entire collection of individuals or entities whose characteristics are to be studied, on which inferences are made

while sample is a subset of the population actually examined to gather information

Question 10

When obtaining data, do you gather information on a population or sample?

bonus: why?

Answer 10

sample

because, often the population is very large hence it would be very costly and time-consuming to observe the population in its entirety

Question 11

Vocabulary:

sums up the features of a data sample; information that gives a quick and simple description of the data

bonus: It includes what? (examples)

Answer 11

summary measures [synonyms: summary statistics, descriptive statistics]

bonus:
1. statistical properties - mean, median, mode, min value, max value, range, standard deviation, etc.
2. graphical representations - histograms, box plots, etc.

Question 12

summary measures from a population

Answer 12

parameters

Question 13

summary measures based on a sample

Answer 13

statistics

Question 14

differentiate parameters from statistics

Answer 14

both are summary measures but

parameters - based on population

statistics - based on sample (hence the subject name)

Question 15

Modified True or False:

summary measures from a sample is called statistics

Answer 15

true

Question 16

why is the subject called statistics?

Answer 16

because we interpret data from a sample rather than a population and summary measures from a sample is called statistics hence the subject name

Question 17

______ are often denoted by Greek letters

Answer 17

parameters

Question 18

Modified True or False:

The size of a population is traditionally denoted by lower-case English alphabet letters

Answer 18

False

Possible Answers:

1. The size of a population is traditionally denoted by uppercase English alphabet letters
2. The size of a sample is traditionally denoted by lower-case English alphabet letters

Question 19

“N” can be a denotation for ________ while “n” can be a denotation for ___________

Answer 19

the size of the population; the size of the sample

Question 20

a characteristic or attribute that is measured for the unit under consideration

Answer 20

variable

Question 21

differerence between observation and data

Answer 21

observation - realized value of a variable that is measured and recorded for each unit

data - collection of observations on one or more variables

Question 22

realized value of a variable that is measured and recorded for each unit

bonus: What is a variable?

Answer 22

observation

bonus: a characteristic or attribute that is measured for the unit under consideration

Question 23

definiton of data

Answer 23

collection of observations on one or more variables

Question 24

What are the different categories of variables?

Bonus: definitions

Answer 24

qualitative and quantitative

Bonus:

1. qualitative variable - measures a characteristic that can be classified into one of a group of categories and cannot be measured on a natural numerical scale
2. quantitative variable - measures a characteristic that is recorded on a naturally occuring numeric scale

Question 25

observations made on qualitative variables are sometimes referred to as ________

Answer 25

categorical data

Question 26

**True or False:** qualitative variables could be represented in a database as numbers and we can perform any arithmetic operation on these variables

Answer 26

False, qualitative variables can be represented in a database a snumbers but performing any arithmetic operation on these variables does not convey meaning as these values do not express quantity, amount, or magnitude

Question 27

**Modified True or False:** quantitative variables measures a characteristic that is recorded on a naturally occuring numerical scale hence performing arithmetic operations on this type of variables has meaning

Answer 27

True

Question 28

Zipcode is an example of a _______ variable bonus: give another example

Answer 28

qualitative bonus: age, gender, blood type, etc.

Question 29

**True or False:** gender, for example, can be represented as 0 if female and 1 if male bonus: What type of variable is gender?

Answer 29

True qualitative variables could be represented in a database as numbers bonus: qualitative

Question 30

categories of quantitative variabales

Answer 30

discrete and continuous

Question 31

a quantitative variable is said to be _______ if it can only take a finite or countable number of values

Answer 31

discrete

Question 32

differentiate the two categories of quantitative variables

Answer 32

discrete - can only take a finite or countable number of values continuous - takes infinitely many values at any point on a given interval

Question 33

**Modified True of False:** Height is an example of a discrete variable bonus: what type of variable is a discrete variable?

Answer 33

False, height is an example of a continuous variable bonus: quantitative

Question 34

Why is height a continuous quantitative variable?

Answer 34

Because a height of a student can assume any value from the minimum possible height and the maximum height, hence a height measurement of a whole number (e.g. 174cm) does not imply that it is discrete as the height is just recorded to the nearest whole number but still, height can take any value within an interval

Question 35

What are the four levels of measurement?

Answer 35

arranged in a heirarchy (lowest to highest): 1. nominal level 2. ordinal level 3. interval level 4. ratio level

Question 36

Statistics is the science of decision-making in a world full of __________

Answer 36

uncertainties

Question 37

The student council at a university with 15,000 students is interested in the percentage of students who favor a change in the grading system from the numerical grade system (1.00, 1.25, 1.5, ...) to a letter grade system (A+, A, A-, ...). 200 students are interviewed to determine their attitude towards this proposed change What is the population of interest?

Answer 37

set of all 15,000 student in the college

Question 38

To examine the effect of exercise on body composition, healthy women aged 35 to 50 were classified as either active (>=9hrs of physical activity per week) or sedentary. For each group of participants, their body fat percentage was measured. Describe the population

Answer 38

set of all healthy women aged 35 to 50

Question 39

A researcher would like to conduct a study on the most popular video games (in terms of sales in the Philippines) by investigating the relationship between video game rating (for everyone, >= 13 years old, >=17 years old) and the number of violent interactions per minute of play Determine the population

Answer 39

set of all most popular video games (in terms of sales in the Philippines)

Question 40

Add "__________" when describing the population

Answer 40

set of all

Question 41

A consumer group conducts crash tests of new car models. To determine the severity of the damage to 2023 Geely Coolray cars resulting from 10mph crash into a concrete wall, the research group tests six cars of this type and assesses the amount of damage What is the population?

Answer 41

set of all 2023 Geely Coolray cars

Question 42

Quantitative or Qualitative: number of correct answers on a five-item multiple choice exam bonus: if quantitative, discrete or continuous?

Answer 42

quantitative bonus: discrete

Question 43

Quantitative or Qualitative: amount of water poured into a 250ml glass container (in mL) bonus: if quantitative, discrete or continuous?

Answer 43

quantitative bonus: continuous

Question 44

It is the lowest level of measurement

Answer 44

Nominal

Question 45

definition of nominal bonus: qualitative or quantitative?

Answer 45

gives names or labels to various categories without a sense of order bonus: qualitative

Question 46

**Modified True or False:** In a nominal level, categories are distinct, with no overlaps, and mutually exhaustive

Answer 46

True

Question 47

**Modified True or False:** In an ordinal level, categories are of equal importance

Answer 47

False Possible answers: In a nominal level, categories are of equal importane In an ordinal level, categories have implied ordering

Question 48

Examples of variables in a nominal level

Answer 48

name, age, sex, birth date, etc.

Question 49

Arithmetic operations are not done with variables at the _________ level and information that can be obtained from processing data on these variables is limited to frequency counts and percentages

Answer 49

nominal/ordinal *with ordinal, also limited to frequency counts and percentages but with additonal information on ordering

Question 50

define the ordinal level bonus: qualitative or quantitative?

Answer 50

contains the properties of the nominal level but the values of the variable have implied ordering bonus: qualitative

Question 51

**Modified True or False:** The ordinal level deals with qualitative variables with an inherent ordering. However, the difference between categories cannot be measured and has no meaning

Answer 51

True

Question 52

quantitative varibales with differences between two consecutive quantities being constant; has no absolute zero

Answer 52

interval

Question 53

what do we mean by "there is no absolute zero"? bonus: In what level is this characteristic present?

Answer 53

the value of zero does not imply the absence of the characteristic being measured bonus: interval

Question 54

what is a ratio?

Answer 54

contains the properties of the interval level but has an absolute/a true zero point

Question 55

**Modified True or False:** The highest level of measurement is the nominal level

Answer 55

False, Possible answers: The highest level of measurement is the ratio level The lowest level of measurement is the nominal level

Question 56

highest educational attainment (highschool graduate, bachelors, masters, etc.), satisfaction rating (dissatisfied, neutral, satisfied, etc.), and student classification (freshman, sophomore, junior, senior) can be classified at the _________ level

Answer 56

ordinal

Question 57

examples of variables in an interval level

Answer 57

temperature, IQ score

Question 58

a classroom having zero amount of students is a variable of what level?

Answer 58

ratio

Question 59

Interval and ratio levels of measurement deals with ___________ variables while nominal and ordinal levels deals with ___________ variables

Answer 59

quantitative; qualitative

Question 60

The level of measurement depends mainly on the _____________ and not on the property being measured

Answer 60

measuring process *given weight, if we measure it by kilograms, it can be classified as a quantitative variable in the ratio level; however, if we measure weight by [light, medium, heavy] then it becomes a qualitative variable at the ordinal level

Question 61

If I measure weight by kg, what type of variable is it and at what level?

Answer 61

quantitative variable at a ratio level

Question 62

If I measure weight by [light, medium, heavy] what type of variable is it and at what level?

Answer 62

qualitative variable at an ordinal level

Question 63

The student council at a university with 15,000 students is interested in the percentage of students who favor a change in the grading system from the numerical grade system (1.00, 1.25, 1.5, ...) to a letter grade system (A+, A, A-, ...). 200 students are interviewed to determine their attitude towards this proposed change. What type of variable is being measured and at what level?

Answer 63

Qualitative variable at the ordinal level

Question 64

To examine the effect of exercise on body composition, healthy women aged 35 to 50 were classified as either active (>=9hrs of physical activity per week) or sedentary. For each group of participants, their body fat percentage was measured. What type of variable is being measured and at what level?

Answer 64

Quantitative at a ratio level

Question 65

How to remember the definition of statistics? singular = science plural = p____________ clue: two words

Answer 65

processed data

Question 66

**True or False:** Some consider interval and ratio as the same

Answer 66

True, because there are only few examples of variables at an interval level but there is still a difference with the two, that being the presence of an absolute zero point

Question 67

Quantitative variable is also known as? bonus: how about qualitative variable?

Answer 67

numerical variable bonus: categorical variable

Question 68

**True or False:** Only people can be a population

Answer 68

False, a population is a collection of all inividuals AND ENTITIES whose characteristics are to be studied, on which inferences are made