Introduction to
Statistics
this summary is based on the book Statistics for the Behavioral Sciences by Gravetter, F. J., & Wallnau, L. B. ,
knowledge clips and explanations from the class and seminars
P a g e 1 | 77
Laura C./ Intro to Statistics/ 2022/2023
,Chapter 1- Intro to statistics
- statistics- methods for organising, summarizing, and interpreting data
- most research is conducted with samples as it’s impossible to examine every individual in
a population; a sample is a group of individuals selected from a population, usually to
represent the population in a research study
- a characteristic that describes a sample is called a statistic; a characteristic that describes
a population is called a parameter
usually, there are differences between a statistic and a parameter; the naturally
occurring difference between a statistic and a parameter is called sampling error
- there are two types of statistical methods:
o descriptive statistics- which organises and summarises data
o inferential statistics- which uses sample data to draw inferences about the
population of interest (it allows us to make generalisations about the population
from which we selected the sample)
- types of studies:
• in the correlational method, two different variables are observed to determine whether
there is a relationship between them; this method cannot, however, produce a cause-and-
effect explanation for the relationship
• in the experimental method, one variable is manipulated while another variable is
observed and measured; to establish a cause-and-effect relationship between the two
variables, an experiment tries to control all other variables to prevent them from
influencing the results
• nonexperimental studies (non-equivalent groups and pre-post studies) also attempt to
examine relationships between variables, but they lack the rigour of true experiments and
cannot produce cause-and-effect explanations; the ‘independent variable’ that is used to
create the different groups of scores in a nonexperimental study is called quasi-
independent variable
Measurement scales
- a measurement scale consists of a set of categories that are used to classify individuals;
there are four measurement scales:
o nominal scale
o ordinal scale
o interval scale
o ration scale
• nominal scale- consists of a set of categories that have different names; measurements on a
nominal scale label and categorise observations but do not make any quantitative distinctions
between observations
examples of nominal scales include classifying people by race, gender, or occupation
the measurements from a nominal scale allow us to determine whether two
individuals are different, but they do not identify either the direction or the size of the
difference
• ordinal scale- consists of a set of categories that are organised in an ordered sequence;
measurements on an ordinal scale rank observations in terms of size or magnitude
e.g., an ordinal scale consists of a series of ranks (first, second, third, and so on) like the
order of finish in a car race
P a g e 2 | 77
Laura C./ Intro to Statistics/ 2022/2023
, with measurements from an ordinal scale, you can determine whether two individuals
are different, and you can determine the direction of difference; however, ordinal
measurements do not allow you to determine the size of the difference between two
individuals
e.g.,: in a NASCAR race, the first-place car finished faster than the second-place car,
but the ranks don’t tell you how much faster
• interval scale- a scale that consists of ordered categories that are all intervals of precisely the
same size; equal differences between numbers on the scale reflect equal differences in
magnitude; the zero point on a scale is arbitrary and does not indicate a zero amount of the
variable being measured
e.g., temperature and IQ scores (a temperature of 0º Fahrenheit does not mean that there
is no temperature, and it does not prohibit the temperature from going even lower; an IQ
score of 0 does not mean one has no intelligence)
• ratio scale- it is an interval scale with the additional feature of an absolute zero point; the
existence of an absolute, non-arbitrary zero point means that we can measure the absolute
amount of the variable; that is, we can measure the distance from 0
e.g., weight, income
Continuous vs discrete variables
- a discrete variable consists of separate, indivisible categories, often whole numbers that vary
in countable steps; no values can exist between two neighbouring categories
o e.g., the number of children a family has, how many students attend a class each day,
classifying people by gender or occupation, etc.
- for a continuous variable, there are an infinite number of possible values that fall between
any two observed values; a continuous variable can be divisible into an infinite number of
fractional parts
e.g., when measuring weight, it’s unlikely that a group of people weighs 80 kg. One
person might weigh 80,1 kg, some 80,50kg, some 80,65 kg, etc.
- two factors apply to continuous variables:
1. when measuring a continuous variable, it should be very rare to obtain identical
measurements for two different individuals; because a continuous variable has an infinite
number of possible values, it should be almost impossible for two people to have exactly
the same score
2. when measuring a continuous variable, each measurement category is actually an interval
that must be defined by boundaries;
e.g., two people who both claim to weigh 150 pounds are probably not exactly the same
weight; however, they are both around 150 pounds
- continuous variables can be pictures on continuous lines; real limits are the boundaries of
intervals for scores that are represented on a continuous number line; the real limit separating
two adjacent scores is located exactly halfway between the scores; each score has two real
limits: the real upper limit is at the top of the interval, and the lower real limit is at the
bottom
P a g e 3 | 77
Laura C./ Intro to Statistics/ 2022/2023
, Statistical notation
- the letter X is used to represent scores for a
variable
- if a second variable is used, Y represents its scores
- the letter N is used as the symbol for the number of
scores in a population
- n is the symbol for the number of scores in a
sample
- ∑ (sigma) is used to stand for summation => ∑X means ‘the sum of all the scores’
Order of Mathematical Operations
1. any calculation contained within parentheses is done first.
2. squaring (or raising to other exponents) is done second.
3. multiplying and/or dividing is done third; a series of multiplication and/or division
operations should be done in order from left to right.
4. summation using the Σ notation is done next.
5. finally, any other addition and/or subtraction is done
P a g e 4 | 77
Laura C./ Intro to Statistics/ 2022/2023
Statistics
this summary is based on the book Statistics for the Behavioral Sciences by Gravetter, F. J., & Wallnau, L. B. ,
knowledge clips and explanations from the class and seminars
P a g e 1 | 77
Laura C./ Intro to Statistics/ 2022/2023
,Chapter 1- Intro to statistics
- statistics- methods for organising, summarizing, and interpreting data
- most research is conducted with samples as it’s impossible to examine every individual in
a population; a sample is a group of individuals selected from a population, usually to
represent the population in a research study
- a characteristic that describes a sample is called a statistic; a characteristic that describes
a population is called a parameter
usually, there are differences between a statistic and a parameter; the naturally
occurring difference between a statistic and a parameter is called sampling error
- there are two types of statistical methods:
o descriptive statistics- which organises and summarises data
o inferential statistics- which uses sample data to draw inferences about the
population of interest (it allows us to make generalisations about the population
from which we selected the sample)
- types of studies:
• in the correlational method, two different variables are observed to determine whether
there is a relationship between them; this method cannot, however, produce a cause-and-
effect explanation for the relationship
• in the experimental method, one variable is manipulated while another variable is
observed and measured; to establish a cause-and-effect relationship between the two
variables, an experiment tries to control all other variables to prevent them from
influencing the results
• nonexperimental studies (non-equivalent groups and pre-post studies) also attempt to
examine relationships between variables, but they lack the rigour of true experiments and
cannot produce cause-and-effect explanations; the ‘independent variable’ that is used to
create the different groups of scores in a nonexperimental study is called quasi-
independent variable
Measurement scales
- a measurement scale consists of a set of categories that are used to classify individuals;
there are four measurement scales:
o nominal scale
o ordinal scale
o interval scale
o ration scale
• nominal scale- consists of a set of categories that have different names; measurements on a
nominal scale label and categorise observations but do not make any quantitative distinctions
between observations
examples of nominal scales include classifying people by race, gender, or occupation
the measurements from a nominal scale allow us to determine whether two
individuals are different, but they do not identify either the direction or the size of the
difference
• ordinal scale- consists of a set of categories that are organised in an ordered sequence;
measurements on an ordinal scale rank observations in terms of size or magnitude
e.g., an ordinal scale consists of a series of ranks (first, second, third, and so on) like the
order of finish in a car race
P a g e 2 | 77
Laura C./ Intro to Statistics/ 2022/2023
, with measurements from an ordinal scale, you can determine whether two individuals
are different, and you can determine the direction of difference; however, ordinal
measurements do not allow you to determine the size of the difference between two
individuals
e.g.,: in a NASCAR race, the first-place car finished faster than the second-place car,
but the ranks don’t tell you how much faster
• interval scale- a scale that consists of ordered categories that are all intervals of precisely the
same size; equal differences between numbers on the scale reflect equal differences in
magnitude; the zero point on a scale is arbitrary and does not indicate a zero amount of the
variable being measured
e.g., temperature and IQ scores (a temperature of 0º Fahrenheit does not mean that there
is no temperature, and it does not prohibit the temperature from going even lower; an IQ
score of 0 does not mean one has no intelligence)
• ratio scale- it is an interval scale with the additional feature of an absolute zero point; the
existence of an absolute, non-arbitrary zero point means that we can measure the absolute
amount of the variable; that is, we can measure the distance from 0
e.g., weight, income
Continuous vs discrete variables
- a discrete variable consists of separate, indivisible categories, often whole numbers that vary
in countable steps; no values can exist between two neighbouring categories
o e.g., the number of children a family has, how many students attend a class each day,
classifying people by gender or occupation, etc.
- for a continuous variable, there are an infinite number of possible values that fall between
any two observed values; a continuous variable can be divisible into an infinite number of
fractional parts
e.g., when measuring weight, it’s unlikely that a group of people weighs 80 kg. One
person might weigh 80,1 kg, some 80,50kg, some 80,65 kg, etc.
- two factors apply to continuous variables:
1. when measuring a continuous variable, it should be very rare to obtain identical
measurements for two different individuals; because a continuous variable has an infinite
number of possible values, it should be almost impossible for two people to have exactly
the same score
2. when measuring a continuous variable, each measurement category is actually an interval
that must be defined by boundaries;
e.g., two people who both claim to weigh 150 pounds are probably not exactly the same
weight; however, they are both around 150 pounds
- continuous variables can be pictures on continuous lines; real limits are the boundaries of
intervals for scores that are represented on a continuous number line; the real limit separating
two adjacent scores is located exactly halfway between the scores; each score has two real
limits: the real upper limit is at the top of the interval, and the lower real limit is at the
bottom
P a g e 3 | 77
Laura C./ Intro to Statistics/ 2022/2023
, Statistical notation
- the letter X is used to represent scores for a
variable
- if a second variable is used, Y represents its scores
- the letter N is used as the symbol for the number of
scores in a population
- n is the symbol for the number of scores in a
sample
- ∑ (sigma) is used to stand for summation => ∑X means ‘the sum of all the scores’
Order of Mathematical Operations
1. any calculation contained within parentheses is done first.
2. squaring (or raising to other exponents) is done second.
3. multiplying and/or dividing is done third; a series of multiplication and/or division
operations should be done in order from left to right.
4. summation using the Σ notation is done next.
5. finally, any other addition and/or subtraction is done
P a g e 4 | 77
Laura C./ Intro to Statistics/ 2022/2023
