All Rights Reserved.
This work has been summarised from the textbook Numbers, Hypotheses &
Conclusions: A course in Statistics for the Social Sciences by Colin Tredoux and
Kevin Durrheim
ISBN 9781485125440
It includes notes taken based on lecture slides from relevant topic lecturers, all of
whom are named in the appropriate section. These notes are elaborations based on
the author’s own understanding.
This document, including all content and materials contained within, is the
intellectual property of Arièlle Denis, with thanks to Kayla Paul and Ruby Webb
for their contributions on the textbook notes and further summaries.
No part of these notes may be reproduced, distributed, or transmitted in any form
or by any means, including photocopying*, recording, or other electronic or
mechanical methods, without the prior written permission of the author, except in
the case of brief quotations embodied in critical reviews and certain other
non-commercial uses permitted by the copyright law.
For permission requests, please contact the author at
© 2026 Arièlle Denis,
University of Cape Town. All rights reserved.
Thank you for your support, and good luck for the course! :]
*Note: If you are printing these notes for personal use, they cannot be photocopied.
, RESEARCH IN PSYCHOLOGY I
PSY2015F | Term 1
Statistics | Chapters 1-11 of Tredoux and Durrheim (2019) textbook
by Ella Mendelow
→ Research: A structured process of turning questions into evidence-based answers.
→ Psychological research: The systematic, scientific study of behaviour and mental processes
using experiments, surveys, observations, etc.
There are two types of research methods:
1. Quantitative (numerical): Using psychometrics, or how we get numbers, and statistics,
how we analyse those numbers.
2. Qualitative (non-numerical): Using meanings, experiences, etc.
→ Variable: A measurable representation of a concept, consisting of different values across
people, objects and time.
Types of variables:
1. Independent: Predictor (causes or factors manipulated)
2. Dependent: Outcome (effects measured to see the change)
e.g. We wanted to measure if giving students a free coffee (the independent variable) would
improve students’ attendance (the dependent variable) at 8AM classes.
Classes of variables which define the type of statistical analysis used (both quantitative):
● Categorical: Describes group membership according to categories
○ e.g. Left, right, ambidextrous
○ Nominal: No inherent order, e.g. gender, blood type, nationality, species
○ Ordinal: Meaningful order, e.g. education level, severity of pain
● Continuous: Numerical values, any within a range, including decimals
○ e.g. Distance or height
○ Interval: No true “zero” point, e.g. IQ, temperature, calendar - cannot have “0” IQ
○ Ratio: Meaningful “zero” point, e.g. distance, height, age, time - can have a
distance of 0m
A continuous ratio variable like age in years can be turned into a categorical ordinal variable like
an age range.
Central Tendency and Variability
→ Central tendency: A single value represents the center of data distribution.
, Measures of central tendency provide a summary of a collection of numbers and the midpoint of
a group of scores, NOT the way the scores are arranged around a midpoint.
MEAN
● The average of the data
● Used when data is continuous
● Misleading when outliers exist
● Mean = Sum of each score/Number of observations
MEDIAN
● The middle of the data when numbers are arranged largest to smallest
● Used when data has extreme outliers or is skew
● Orders the data from smallest to largest and finds the middle value
○ If data is even-numbered: Average of two middle values
○ If data is odd-numbered: Single middle value
● Median = Number of observations +1/2
MODE
● Finds the value that occurs most frequently
● Best for nominal and categorical data
● Unimodal: Datasets that have a single mode
● Bimodal: Two different scores/categories have the same highest frequency, which can
indicate two populations
→ Variability: Tells us how spread out a dataset is around the midpoint, how widely dispersed
scores are. Often reported with central tendency.
RANGE
● Crude range: Highest - lowest value
● Extended range: Crude +1
● Potential range: Highest value - 0
● Interquartile range: 75% of the data - 25% of the data
VARIANCE
● How far each score is from the mean
● Variance is the square of the standard deviation, θ.
● Variance = Sum of the (value minus population mean) squared divided by the number of
observations
STANDARD DEVIATION
This work has been summarised from the textbook Numbers, Hypotheses &
Conclusions: A course in Statistics for the Social Sciences by Colin Tredoux and
Kevin Durrheim
ISBN 9781485125440
It includes notes taken based on lecture slides from relevant topic lecturers, all of
whom are named in the appropriate section. These notes are elaborations based on
the author’s own understanding.
This document, including all content and materials contained within, is the
intellectual property of Arièlle Denis, with thanks to Kayla Paul and Ruby Webb
for their contributions on the textbook notes and further summaries.
No part of these notes may be reproduced, distributed, or transmitted in any form
or by any means, including photocopying*, recording, or other electronic or
mechanical methods, without the prior written permission of the author, except in
the case of brief quotations embodied in critical reviews and certain other
non-commercial uses permitted by the copyright law.
For permission requests, please contact the author at
© 2026 Arièlle Denis,
University of Cape Town. All rights reserved.
Thank you for your support, and good luck for the course! :]
*Note: If you are printing these notes for personal use, they cannot be photocopied.
, RESEARCH IN PSYCHOLOGY I
PSY2015F | Term 1
Statistics | Chapters 1-11 of Tredoux and Durrheim (2019) textbook
by Ella Mendelow
→ Research: A structured process of turning questions into evidence-based answers.
→ Psychological research: The systematic, scientific study of behaviour and mental processes
using experiments, surveys, observations, etc.
There are two types of research methods:
1. Quantitative (numerical): Using psychometrics, or how we get numbers, and statistics,
how we analyse those numbers.
2. Qualitative (non-numerical): Using meanings, experiences, etc.
→ Variable: A measurable representation of a concept, consisting of different values across
people, objects and time.
Types of variables:
1. Independent: Predictor (causes or factors manipulated)
2. Dependent: Outcome (effects measured to see the change)
e.g. We wanted to measure if giving students a free coffee (the independent variable) would
improve students’ attendance (the dependent variable) at 8AM classes.
Classes of variables which define the type of statistical analysis used (both quantitative):
● Categorical: Describes group membership according to categories
○ e.g. Left, right, ambidextrous
○ Nominal: No inherent order, e.g. gender, blood type, nationality, species
○ Ordinal: Meaningful order, e.g. education level, severity of pain
● Continuous: Numerical values, any within a range, including decimals
○ e.g. Distance or height
○ Interval: No true “zero” point, e.g. IQ, temperature, calendar - cannot have “0” IQ
○ Ratio: Meaningful “zero” point, e.g. distance, height, age, time - can have a
distance of 0m
A continuous ratio variable like age in years can be turned into a categorical ordinal variable like
an age range.
Central Tendency and Variability
→ Central tendency: A single value represents the center of data distribution.
, Measures of central tendency provide a summary of a collection of numbers and the midpoint of
a group of scores, NOT the way the scores are arranged around a midpoint.
MEAN
● The average of the data
● Used when data is continuous
● Misleading when outliers exist
● Mean = Sum of each score/Number of observations
MEDIAN
● The middle of the data when numbers are arranged largest to smallest
● Used when data has extreme outliers or is skew
● Orders the data from smallest to largest and finds the middle value
○ If data is even-numbered: Average of two middle values
○ If data is odd-numbered: Single middle value
● Median = Number of observations +1/2
MODE
● Finds the value that occurs most frequently
● Best for nominal and categorical data
● Unimodal: Datasets that have a single mode
● Bimodal: Two different scores/categories have the same highest frequency, which can
indicate two populations
→ Variability: Tells us how spread out a dataset is around the midpoint, how widely dispersed
scores are. Often reported with central tendency.
RANGE
● Crude range: Highest - lowest value
● Extended range: Crude +1
● Potential range: Highest value - 0
● Interquartile range: 75% of the data - 25% of the data
VARIANCE
● How far each score is from the mean
● Variance is the square of the standard deviation, θ.
● Variance = Sum of the (value minus population mean) squared divided by the number of
observations
STANDARD DEVIATION
