MEDIATED MOOCS Introduction to descriptive statistics San Jose State University (via Udacity) Prof Jenny Roberts Institute for Open and Distance Learning (IODL) University of South Africa (Unisa) buckjj@unisa.ac.za

Descriptive Statistics This course will teach you the basic terms and concepts in statistics as well as guide you through introductory probability. Statistics is an important field of math that is used to analyse, interpret, and predict outcomes from data. Descriptive statistics will teach you the basic concepts used to describe data. This is a great beginner course for those interested in Data Science, Economics, Psychology, Machine Learning, Sports analytics and just about any other field

Programme Lesson Topic Date of mediated support Content 1 Introduction to research methods 14 March Introduction to statistical study methods 2 Visualising data Create and interpret histograms, bar charts and frequency plots 3 Central tendency 10 May Mean, median and mode 4 Variability Range and standard deviations Interquartile range 5 Standardising 28 June Convert distributions into normal distributions using the z-score 6 Normal distribution Compute probabilities Use of Z-table 7 Sampling distributions Apply concepts of probability and normalisation to data sets

Instructions Log onto www.class-central.com/course/udacity-intro-to-descriptive-statistics-2309 Register – They require your email address, your full name as well as a password Click – GO TO CLASS to start Click – START FREE COURSE

Some common concepts Constructs Independent and dependant variables Population Sample Frequency tables Relative frequency Percentages Histogram Bar chart

CONSTRUCTS Objective measurement of a subjective phenomena Some attributes can be measured directly e.g. height, weight etc. In the behavioral and social sciences, we usually must use more indirect ways to measure constructs, so we develop a number of items to assess the construct e.g. Depression – use a scale which measure depression or a happiness scale to measure levels of happiness The personal characteristic to be assessed is called a construct. This personal attribute cannot be directly measure (as in height and weight) but can be assessed by using a number of indicators In this MOOC constructs are used with reference to the behavioral and social sciences

Independent and dependent variables A variable is anything that can be measured Dependent variable – value depends on the variables that are being manipulated e.g. exam results are dependent on time spent studying. In this case the dependent variable is exam results (which was are not manipulating at all) and time spend studying is the independent variable as this can be changed in order to test its outcome on the exam results Independent variable is also called the predictor variable Dependent variable also know as the outcome variable https://keydifferences.com/difference-between-independent-and-dependent-variable.html

Population and sample The POPULATION are all members of a defined group that we are studying. A sample is a part of the population The population is the broader group of people to whom you intend to generalise the results of your study. Your sample is a subset of your population

Frequency tables Frequency tells you how often something occurs. The frequency of an observation in statistics tells you the number of times the observation occurs in the data. For example, in the following list of numbers, the frequency of the number 9 is 5 (because it occurs 5 times): 1, 2, 3, 4, 6, 9, 9, 8, 5, 1, 1, 9, 9, 0, 6, 9. Number Count frequency Relative frequency Percentage 1 1/16=0.06 1/16*100=6.25 111 3 3/16=0.19 3/16*100=18.75 2 4 5 6 11 2/16=0.13 2/16*100=12.5 7 8 9 11111 5/16=0.32 5/16*100=31.25 Total ∑ 16 16/16=1 16/16*100=100

Visualising data Scatter charts/Bar charts/Histograms 1, 2, 3, 4, 6, 9, 9, 8, 5, 1, 1, 9, 9, 0, 6, 9.

Scatter plots score frequency Relative frequency 2 0.02 1 4 0.04 7 2 0.02 1 4 0.04 7 0.07 3 5 0.05 12 0.12 15 0.15 6 20 0.2 25 0.25 8 9 10 0.1 total 100 Data: Test scores out of 10 for 100 students 8 0 2 7 6 6 10 0 4 5 9 4 6 7 6 8 9 1 4 6 2 5 5 9 3 2 6 6 7 4 7 6 7 7 7 2 4 6 7 3 7 6 7 7 7 9 6 6 7 1 3 9 6 7 7 6 4 7 6 2 6 7 7 4 2 6 7 9 7 1 6 7 7 6 1 7 7 6 5 5 5 7 5 5 3 2 3 4 4 5 5 5 4 4 4 5 5 5 5 9

Bar Charts and Histograms Histogram refers to a graphical representation, that displays data by way of bars to show the frequency of numerical data – uses quantitative data (numerical) Bar graph is a pictorial representation of data that uses bars to compare different categories of data – use categorical data

Histogram – because each column represents a continuous quantitative variable X axis is your independent variable and y axis is your dependent variable Marks for test are dependent on hours spent studying – therefore marks are the dependent variable and hours spent studying is the independent variable