# Statistics

Course Code BSC304 S3 100 hours Statement of Attainment

## 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

## Aims

• Discuss different statistical terms and the elementary representation of statistical data.
• Discuss distributions, and the application of distributions in processing data.
• Use measures of central tendency for solving research questions
• Demonstrate and explain the normal curve, percentiles and standard scores.
• Explain methods of correlation that describes the relationship between two variables.
• Predict, with regression equations and determine how much error to expect
• Explain basic concepts of underlying the use of statistics to make inferences.
• Explain the difference between the means of two groups with the t Test.
• Explain the use of ANOVA (Analysis of Variance) in analysing the difference between two or more groups.
• Describe and apply the concept of Non Parametric Statistics.

### STATISTICS ARE THE KEY TO MAKING MISTAKES

If you want a reason for studying statistics, like it or not; they are the key to greater efficiency with everything we do.

Through this course, you will learn to understand and apply a knowledge of statistics to gather, analyse and interpret numerical information in the context of any industry or workplace. By doing so, you better understand the failures and successes in that context. This gives you a foundation for making better informed decisions, reducing risks and increasing success rates.

Statistics (singular) is the science of data analysis. That is, statistics is concerned with scientific methods for collecting data, organising, summarising, presenting, and analysing sample data, as well as drawing valid conclusions and making reasonable decisions based on such analysis.

Statistics are an integral part of the scientific method. There is need of statistical data in every walk of life. No field of study is complete without the supporting quantitative information about that field. Study material in Economics, Commerce, Accountancy, Geography, Physics, Chemistry, Biology etc., are all flooded with quantitative information. No government department can function well without the support of statistical data.

Statistics consists of a set of methods and rules for organising and interpreting observations.

### Quantitative vs. Qualitative Data

Data is typically defined as ‘quantitative’ if it is in numerical form and ‘qualitative’ if it is not. Qualitative data can be more than just words or texts. Photographs, videos, sound recordings, diary entries, comments from open ended questions etc., can be considered as qualitative data. All quantitative data is based upon qualitative judgements; and all qualitative data can be described and manipulated numerically.

All qualitative data can be easily converted into quantitative, and there are many instances when doing so has added considerable value to research projects. The simplest way to do this is to divide the qualitative data into units and number them. This enables you to organise and process the qualitative data more efficiently. For example, you could take text information (say, excerpts from transcripts) and pile these excerpts into piles of similar statements. When we do something as easy as this simple grouping, we can describe the results quantitatively.
For example, if we had ten statements and we grouped these into five piles, we could describe the piles using a 10 x 10 table of 0’s and 1’s. If two statements were placed together in the same pile, we would put a 1 in their row/column juncture. If two statements were placed in different piles, we would use a 0.  The resulting matrix would or table would describe the grouping of the ten statements in terms of their similarity.
Even though the data in this example consists of qualitative statements, the result of this simple qualitative procedure (that is, grouping similar excerpts into the same piles) is quantitative in nature.

Statistics (plural) are numbers, usually used as estimates of summary measures of larger sets of data.