LEARN STATISTICS ONLINE
 understand data in your industry
 achieve your educational goals
 get a career in science or maths
 learn how to collect, compile and analyse statistics.
Strengthen your career with this course in Statistics. If you want to develop scientificallybased research studies, this is your starting point. Learn how to interpret data sets using established statistical analysis.This 100 hour course such as this provides the most essential knowledge and skills required by consultants and researchers in a wide variety of disciplines.
Lesson Structure
There are 10 lessons in this course:

Introduction

Key terms and concepts: data, variables

Measurements of scale: nominal, ordinal, interval,ratio

Data presentation

Probability

Rounding of data

Scientific notation

Significant figures

Functions

Equations

Inequalities

Experimental design

The normal curve

Data collection

Simple, systemic, stratified and cluster random sampling

Remaining motivated to learn statistics

Distributions

Scope and nature of distributions

Class intervals and limits

Class boundaries

Frequency Distribution

Histograms

Frequency polygons

Normal distributions

Other distributions

Frequency curves

Measures of central tendency

Range, percentiles, quartiles, mode, median, mean

Variance

Standard deviation

Degrees of freedom

Interquartile and semi interquartile deviations

The Normal curve and Percentiles and Standard Scores

Normal distribution characteristics

Percentiles

Standard scores

Z scores

T score

Converting standard scores to percentiles

Area under a curve

Tables of normal distribution

Correlation

Scope and nature of Correlation

Correlation coefficient

Coefficient of determination

Scatter plots

Product movement for linear correlation coefficient

Rank correlation

Multiple correlation

Regression

Calculating regression equation with correlation coefficient

Least squares method

Standard error of the estimate

Inferential Statistics

Hypothesis testing

Test for a mean

Errors in accepting or rejecting null hypothesis

Levels of significance

One and two tailed tests

Sampling theory

Confidence intervals

The t Test

Assessing statistical difference with the t test

t Test for independent samples

t Test for dependant (paired) samples

Analysis of variance

Scope and application of ANOVA

Factors and levels

Hypothesis

Calculate degrees of freedom

Calculate sum of squares within and between groups

Calculate mean square

Calculate F

Chi square test

Chi square goodness of fit test

Calculate degrees of freedom

Chi square test of independence

Calculate expected frequencies

Degrees of freedom

Contingency tables

Find expected frequencies

Calculate degrees of freedom
What You Will Do

To familiarise the student with different statistical terms and the elementary representation of statistical data.

To familiarize the student with distributions, and the application of distributions in processing data.

To apply measures of central tendency in solving research questions

Demonstrate and explain the normal curve, percentiles and standard scores.

To understand the methods of correlation that describes the relationship between two variables.

To make predictions, with regression equations and determine how much error to expect, when making the predictions.

To understand the basic concepts of underlying the use of statistics to make inferences.

To examine the difference between the means of two groups with the t Test.

Understand the use of ANOVA (Analysis of Variance) in analysing the difference between two or more groups.

To introduce and apply the concept of Non Parametric Statistics.
Statistics involves scientific techniques employed to gather, organise and analyse numerical data.
We are able to draw conclusions and make inferences on the basis of such analyses. Descriptive statistics describe a set of data, while inferential statistics make inferences about large groups based on data from a smaller subset of the group. To infer means to draw a conclusion based on facts or premises. Thus an inference is the end result; a proposition based on the act of inferring.
Measurements of Scale
Measurements are used to quantify any phenomenon and involve a comparison with a standard value. I.e.: we need to assign a number to a variable which we wish to measure. There are four types of measurements:
1. Nominal – the use of names to help measure variables. Variables measured on such a scale are known as categorical or qualitative variables. In this type of scale, variable may be assigned to descriptive categories, for example gender may be either male or female. Each category may then be assigned a number that does not denote importance, rank or size. The number is arbitrary. For example; blonde = 1, black = 2, grey = 3 and brown = 4.
2. Ordinal – the order in which things occur. Eg. 1,2,3,4…. Unlike the numbers assigned arbitrarily in nominal scales, in ordinal scales the numbers do imply rank on a continuous scale.
The scale used depends on the variable it is describing. Hence a race would rank accordingly from first place to last. The winner would be 1, second place 2 and so on. Note that the information here is only about rank and it does not describe the variability within placements. For example in a horse race we might know that racehorse 1 came first, and racehorse 2 came second, but we are not told about how close together these racehorses were.
3. Interval – the ‘distance’ between two or more values. eg. Differences in temperature. The distinguishing feature of interval scales is the lack of an absolute zero point. The characteristic cannot be not there, hence zero on the scale does not imply absence. The units used in such a scale are measured equally, but because zero does not imply absence, we cannot measure the ratio between values.
4. Ratio – the relationship between two or more values. eg. Differences in the height or weight of objects. The same as an interval scale with equal distances along the scale meaning the same thing no matter where on the scale you are except that zero on the scale does represent the absence of the variable being measured. Thus we can measure ratios, for example 4 apples is twice as much as 2 apples.
Data presentation
Statistical data can be represented in two main ways:
1. Tables – this is the presentation of data in rows and columns in a precise and unambiguous manner.
2. Graphs – these are visual representations of data to provide a clearer understanding than is possible with a table. Graphs commonly have the X axis (horizontal axis) and the Y axis (vertical axis). Common practice is to place the scores on the x axis and the frequency upon the y axis.
 Line graphs have vertical and horizontal axes that are useful for showing changing values.
 Bar graphs and pie charts are useful for comparing the relationship between different values.
 A Histogram displays the relationships between data in the same was as a graph except the bars are used instead of lines.
Tables and graphs must always be clearly labeled with all relevant information: units of measurement, dates, title, axis etc etc.
Samples
In most cases it is impossible to observe and record data for the entire group we are concerned with. Instead, we consider a sample of the population (entire group).
The population that we are concerned with may be finite or infinite.
If we are to make inferences about the population based on the statistical analysis, then the sample of the population must be representative.
Probability
Since inferences cannot be absolutely certain, they are referred to in terms of probability. Probability is the most likely or most reasonable explanation for a particular phenomenon. The level of probability will depend upon the type of statistical method used.
It is necessary to understand some basic mathematical principles in order to understand statistics…
Rounding of data
It is usual to round numbers to the nearest unit.
 4.6 would be rounded up to 5
 4.4 would be rounded down to 4
In rounding a number that ends in a 5, it is usual to round up:
 4.625 would be rounded to 4.63 (when rounding to the nearest hundredth)
Scientific Notation
Scientific notation is used to ease the writing of long figure with many numbers following a decimal point using powers of 10.
 If multiplying by 10x the decimal point moves x number of places to the left.
 If multiplying by 10x the decimal point moves x number of places to the right.
 103 = 10 x 10 x 10 = 1,000.00; 101 = 10
 103= 0.001; 101 = 0.1 or .1
 455,000 = 4.55 x105 by multiplying by 105 we move the decimal point 5 places to the right
 0.0000455 = 4.55 x 105 by multiplying by 105 we move the decimal point 5 places to the left