Lesson Structure: Statistics BSC304

There are 10 lessons:

I  Introduction

• Data
• Variables
• Measurements of Scale
• Data presentation
• Samples
• Probability
• Rounding of data
• Scientific Notation
• Significant figures
• Functions
• Equations
• Inequalities
• The Normal Curve
• Data Collection: Simple random sampling, Systematic Random Sampling, Stratified Random Sample, Cluster Random Sampling
• A Word of Encouragement

2  Distributions

• Introduction
• Class Intervals and Limits
• Class Boundaries
• General Rules for creating a Frequency Distribution
• Histograms
• Frequency Polygon
• Cumulative Frequency Polygon
• Normal Distributions
• Other Distributions
• Frequency Curves

3  Measures of Central Tendency

• Mesures of Central Tendency
• Deviation or Variance
• Standard Deviation
• Degrees of Freedom
• Interquartile and Semi-interquartile Deviations
• Example

4  The Normal Curve, Percentiles and Standard Scores

• Normal Distribution
• Normal Distribution Characteristics
• Worked Example
• Percentiles
• Standard Scores (Z Scores and T Scores)
• Z Score
• T Score
• Converting Standard Scores to Percentiles
• Area under a curve
• Table of Normal Distribution
• Worked Example

5  Correlation

• Introduction
• Some Points about Correlation
• Scatterplots
• Product Moment For Linear Correlation Coefficient (Product Moment Formala)
• Rank Correlation (Spearman’s Formula For Rank Correlation)
• Multiple Correlation

6  Simple Linear Regression

• Regression
• Calculating Regression Equation With The Correlation Coefficient
• Worked Example
• Least Squares Method
• Worked Example
• Standard Error of the Estimate

7  Inferential Statistics

• Introduction
• Hypothesis Testing
• Test for a Mean
• Errors in accepting or rejecting null hypothesis
• Levels of significance
• One and Two tailed tests
• Sampling Theory
• Sampling distribution of the mean
• Central Limit Theorem
• Confidence Intervals
• Confidence Intervals for the Mean

8  The t Test

• Assessing Statistical Difference With the t Test
• t Test for Independent Samples
• Worked Example
• t Test for Dependent (Paired) Samples
• Worked Example
• Student t Test Probabilities

9  Analysis of Variance (ANOVA)

• Introduction
• Factors & Levels
• Worked Example: Hypothesis, Calculate the Degrees of Freedom, Calculate the Sum of Squares for within and between Groups, Calculate Mean Square

10 Chi-Square

• Introduction
• Chi-Square Goodness-of-Fitness Test
• Worked Example: Calculate Chi Squared, Calculate Degrees of Freedom
• Chi-Square Test of Independence (Pearson’s Chi-Square)
• 2 x 2 Contingency Tables: Calculate the Expected Frequencies, Degrees of Freedom
• H x K Contingency Tables (With H Rows and K Columns): Finding the Expected Frequencies, Degrees of Freedom

Learning Goals: Statistics BSC304

• Understand different statistical terms and the elementary representation of statistical data.
• Understand the important aspects of designing a reliable experiment or test
• Understand distributions, and the application of distributions in processing data
• Apply measures of central tendency in solving research questions
• Demonstrate and explain the normal curve, percentiles and standard scores
• Explain the method of correlation that describes the relationship between two variables
• Understand how to make predictions with regression equations, and determine how much error to
• expect
• Understand the basic concepts of underlying the use of statistics to make inferences
• 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
• Apply the concept of Non Parametric Statistics

The Importance of  Correlation 

A very important part of statistics is describing the relationship between two (or more) variables. One of the most fundamental concepts in research is the concept of correlation.

If two variables are correlated, this means that you can use information about one variable to predict the values of the other variable. Correlation is used to denote the direction and strength of a linear relationship.

Despite the apparently ever-changing view of the environment, when you look a little deeper, there are some things that do not change that much or change in a systematic and predictable way (sometimes referred to as invariant relationships).

In some areas of science, we can predict things quite accurately indeed. The movements of the planets, and the moons around the planets, can be predicted quite accurately centuries into the future from our current knowledge of orbits and physics. In the behavioural sciences things are not quite as predictable.

We can only talk about an increased likelihood or a decreased likelihood of something happening. We try to make predictions in a much more uncertain environment. But we can still discover relationships and predict an increased likelihood or a decreased likelihood of something happening, given that something else has happened.

If we were to gather data on hair colour and income, we would not expect to find that hair colour had an influence on income. Most likely we would not be able to find any relationship at all, regardless of how hard we looked.

We would say that there is zero correlation between the two variables (hair colour and income). However, if we found that every time we increased the processing speed of the chip in our computer, the speed of our computer increased proportionally, we would have found a perfect positive correlation (+1).

We can also have a perfect negative correlation (-1). For example, if we tested a class of students at mathematics and found that the ranking of each student was reversed for sport, we would have found a perfect negative correlation.

To find a measure of these relationships we find the correlation coefficient. The correlation data is expressed as the relationship of the dependent data (y) to the independent data (x) with a measure of how reliable the correlation is giving us a correlation coefficient (rxy).

As discussed before, the correlation coefficient is a number between -1 and 1. The strength of the correlation is relative to the purposes for the calculations. The closer the coefficient is to 1 the stronger the positive relationship; the closer the value is to -1 the stronger is the negative relationship.

The closer to 0 the weaker the relationship or the absence of any relationship is indicated. About the definitive value for determining whether a relationship exists, it is dependent upon the context. For example, what may be regarded as a high correlation in one discipline such as psychology may be regarded as only moderate in another such as physics.

Caution needs to be used when interpreting results. It is possible to get ‘junk’ or ‘trivial’ results which give a perfect correlation of +1 or -1 but which have no real value.

For example, finding a correlation between the height of a building and the number of bricks used in a vertical row.

It is important to understand that correlation does not imply causation. Just because you may find a correlation, this does not mean that you are seeing cause and effect.

The coefficient of determination is simply the correlation coefficient squared and is stated as r2.

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