IRM describing data

Question 1

Statistics help us to:

Answer 1

describe complex information in a simple manner

Question 2

Learning from data in 3 steps

Answer 2

Previous Steps
Form a hypothesis
Test: Does data support hypothesis?

Question 3

Aggregated data is

Answer 3

Summarised data relative to categories or levels

Question 4

Raw data

Answer 4

Is data that is not aggregated, basically just all the information accumulated but not organised

Question 5

Variables can be

Answer 5

Continuous or discreet and Independent or dependent

Question 6

An example of a discreet variable

Answer 6

discrete category such as male or female, on or the other, not both

Question 7

An example of a continuous variable

Answer 7

ie a score can lie anywhere on a continuum i.e 1-100

Question 8

4 levels of measurement properties in variables are

Answer 8

Nominal, Ordinal, Interval or Ratio

Question 9

Nominal variable

Answer 9

Arbitrary numerical value (this variable gives the least information) ie 1 for male 2 for female, arbitrary in the way the female is a greater number than the female, yet it means nothing

Question 10

Ordinal Variable

Answer 10

Rankings on a class test are an example of Ordinal value. can order from high to low, but may not give further information such as the difference between the highest and lowest

Question 11

Interval Variable

Answer 11

Interval variables have a consistent unit of measurement and the numerical difference between any two values is meaningful. In contrast to nominal and ordinal variables, interval variables allow for meaningful mathematical operations, such as addition and subtraction

Question 11

ratio Variable

Answer 11

A ratio variable is a type of quantitative variable in statistics that has a meaningful zero point and can be measured on a continuous scale. In other words, the values of a ratio variable can be expressed as a ratio of two numbers, where the denominator is not equal to zero. Examples of ratio variables include length, weight, age, height, income, and many others.

Unlike interval variables, ratio variables have a true zero point, which represents the absence of the measured attribute. This allows for meaningful comparisons between measurements using ratios and proportions. For example, if one person’s income is twice that of another person, it means they earn twice as much money, not just that they earn more.

Question 12

epistemic

Answer 12

things we don’t known because of a lack of data or experience

Question 13

aleatoric

Answer 13

things that are simply unknown, like what number a die will show on the next roll

Question 14

Uncertainty defined

Answer 14

Uncertainty relates to how the estimate might differ from the “true value” and these measures help users of ONS statistics to understand the degree of confidence in the outputs

Question 15

4 measures of uncertainty

Answer 15

standard error

confidence interval

coefficient of variation

statistical significance

Question 16

2 different types of samples

Answer 16

representative: proportionate
convenient sample: potential for bias

Question 18

whats some alternative words that are less likely to infer causation (ie rather than effect as that infers causality, we can say:)

Answer 18

association, relationship

Question 19

What makes a good measurement

Answer 19

Validity and Reliability

Question 20

What questions the measurement and it make sense on its face?

Answer 20

Face validity

Question 21

What validiity verifys if the measurement is related to other measurements in an appropriate way

Answer 21

Construct validity.

Question 22

different measurements are closely related to one another is known as

Answer 22

Convergent validity

( If my theory of personality says that extraversion and conscientiousness are two distinct constructs, then I should also see that my measurements of extraversion are unrelated to measurements of conscientiousness.)

Question 23

measurements thought to reflect different constructs should be unrelated, known as

Answer 23

divergent validity

( If my theory of personality says that extraversion and conscientiousness are two distinct constructs, then I should also see that my measurements of extraversion are unrelated to measurements of conscientiousness.)

Question 24

If our measurements are truly valid, then they should also be predictive of other outcomes

Answer 24

Predictive validity.

Question 25

All variables must take on at least two different possible values otherwise they would be a ….

Answer 25

constant rather than a variable)

Question 25

different values of the variable can relate to each other in different ways, which we refer to as:

Answer 25

scales of measurement.

Question 26

here are four ways in which the different values (features) of a variable can differ.

Answer 26

Identity:
Magnitude:
Equal intervals:
Absolute zero:

Question 26

Different values: Each value of the variable has a unique meaning.

Answer 26

Identity

Question 27

Different values:
The values of the variable reflect differently ——- and have an ordered relationship to one another – that is, some values are larger and some are smaller.

Answer 27

Magnitude(s)

Question 28

Different Values:
Units along the scale of measurement are equal to one another. This means, for example, that the difference between 1 and 2 would be equal in its magnitude to the difference between 19 and 20.

Answer 28

Equal intervals

Question 29

Different values:
The scale has a true meaningful zero point. For example, for many measurements of physical quantities such as height or weight, this is the complete absence of the thing being measured.

Answer 29

Absolute zero:

Question 30

There are four different scales of measurement that go along with these different ways that values of a variable can differ.
(4 ways to measure the variable)

Answer 30

Nominal scale.

Ordinal scale.

Interval scale.

Ratio scale.

Question 31

Values of a Variable: satisfies the criterion of identity, such that each value of the variable represents something different, but the numbers simply serve as qualitative labels as discussed above. For example, we might ask people for their political party affiliation, and then code those as numbers: 1 = “Republican”, 2 = “Democrat”, 3 = “Libertarian”, and so on. However, the different numbers do not have any ordered relationship with one another.

Answer 31

Nominal scale.

Question 32

Values of a variable

satisfies the criteria of identity and magnitude, such that the values can be ordered in terms of their magnitude. For example, we might ask a person with chronic pain to complete a form every day assessing how bad their pain is, using a 1-7 numeric scale. Note that while the person is presumably feeling more pain on a day when they report a 6 versus a day when they report a 3, it wouldn’t make sense to say that their pain is twice as bad on the former versus the latter day; the ordering gives us information about relative magnitude, but the differences between values are not necessarily equal in magnitude.

Answer 32

Ordinal scale.

Question 33

Values of a variable

has all of the features of an ordinal scale, but in addition the difference between units on the measurement scale can be treated as equal. A standard example is physical temperature measured in Celsius or Fahrenheit; the physical difference between 10 and 20 degrees is the same as the physical difference between 90 and 100 degrees, but each scale can also take on negative values.

Answer 33

Interval scale.

Question 34

Values of a variable

has all four of the features outlined above: identity, magnitude, equal intervals, and absolute zero. The difference between a —- scale variable and an interval scale variable is that the —– scale variable has a true zero point. Examples of —— scale variables include physical height and weight, along with temperature measured in Kelvin.

Answer 34

Ratio Scale

Question 35

What are the two primary reasons for paying attention to the scale of measurement of a variable in research and statistics?

Answer 35

The scale determines the types of mathematical operations applicable to the data.
It indicates the kinds of statistics that can be computed on each type of variable.

Question 36

What mathematical operations can be applied to nominal variables

Answer 36

Nominal variables can only be compared for equality, meaning whether two observations have the same numeric value. (since they don’t really function as numbers in a nominal variable, but rather as labels)

Question 37

What mathematical operations can be performed on ordinal variables?

Answer 37

Ordinal variables allow comparison for greater or lesser values, but arithmetic operations are not possible.

Question 38

What mathematical operations are permitted on interval and ratio variables

Answer 38

Interval variables allow addition and subtraction, while ratio variables also permit multiplication and division.

Question 39

Can you provide examples of variables for each scale of measurement?

Answer 39

Answer: Nominal examples include gender or ethnicity. Ordinal examples include rankings like socioeconomic status. Interval examples include temperature in Celsius or Fahrenheit. Ratio examples include height or weight.

Question 40

Question: What types of statistics are appropriate for nominal variabes

Answer 40

Answer: Nominal variables can have statistics like mode.

Question 41

What types of statistics are appropriate for ordinal variables?

Answer 41

. Ordinal variables can have median-based statistics.

Question 42

What types of statistics are appropriate for interval variables?

Answer 42

Interval (and ratio) variables can have mean-based statistics.

Question 43

Descriptive representations of information is known as what type of data

Answer 43

Qualitative (often interviews and focus groups)

Question 43

What types of statistics are appropriate for ratio variables?

Answer 43

Ratio (and interval) variables can have mean-based statistics.

Question 44

Qualitative data is collated and analysed to identify

Answer 44

Key Themes

Question 45

Numerical representations of information is know as what type of data?

Answer 45

Quantitative Data (often observational and experimental studies)

Question 46

Binary data can also be called…

Answer 46

discrete

Question 47

A variable may also be called a

Answer 47

factor

Question 48

a fundamental aspect of a variable is that it…..

Answer 48

varies

Question 49

if something is not a variable it is a

Answer 49

constant

Question 50

3 types of data

Answer 50

Binary, integer and Continuous

Question 51

What is a term to describe a limited or non diverse sample that may not be representative of the population

Answer 51

Highly selective (ie all marshmellow test participants went to stanford daycare)

Question 52

What is binary data?

Answer 52

Binary data consists of only two possible values, typically represented as 0s and 1s.

Question 53

What are integer numbers?

Answer 53

Integer numbers are whole numbers without any decimal or fractional parts.

Question 54

What are real numbers?

Answer 54

Real numbers include all rational and irrational numbers, encompassing integers, fractions, and decimals.

Question 55

What are the key characteristics of binary data?

Answer 55

Binary data is discrete, with only two possible values, and is commonly used in digital computing and communication systems.

Question 56

What are the key characteristics of real numbers?

Answer 56

Real numbers are continuous and infinite, covering all possible values on the number line, including integers and fractions.

Question 57

Name some key characteristics of integers?

Answer 57

Whole Numbers
No Fractional Parts
Infinite Set
Ordered
Closure Under Addition and Subtraction
Closure Under Multiplication (with Exceptions)
No Decimal or Fractional Representation

Question 58

——– measures the spread or dispersion of a set of data points around their mean. It quantifies how much the values in a dataset differ from the mean value.

Answer 58

variance

Question 59

How does variance contribute to our understanding of statistical data?

Answer 59

Variance provides insight into the variability or spread of data points within a dataset, helping to assess the consistency or volatility of the data around the mean.