Statistics

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 scientifically-based 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:

1. 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
2. Distributions
   • Scope and nature of distributions
   • Class intervals and limits
   • Class boundaries
   • Frequency Distribution
   • Histograms
   • Frequency polygons
   • Normal distributions
   • Other distributions
   • Frequency curves
3. Measures of central tendency
   • Range, percentiles, quartiles, mode, median, mean
   • Variance
   • Standard deviation
   • Degrees of freedom
   • Interquartile and semi interquartile deviations
4. 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
5. Correlation
   • Scope and nature of Correlation
   • Correlation coefficient
   • Coefficient of determination
   • Scatter plots
   • Product movement for linear correlation coefficient
   • Rank correlation
   • Multiple correlation
6. Regression
   • Calculating regression equation with correlation coefficient
   • Least squares method
   • Standard error of the estimate
7. 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
8. The t Test
   • Assessing statistical difference with the t test
   • t Test for independent samples
   • t Test for dependant (paired) samples
9. 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
10. 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 10-x 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
• 10-3= 0.001; 10-1 = 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 10-5 by multiplying by 10-5 we move the decimal point 5 places to the left