Statistics is a very useful thing to learn. Statistical data is used in many professions; more than what you might think. A knowledge of statistics not only helps you collect and compile statistics; but it also enables you to better understand their relevance and application whether in business, research or day to day situations ranging from predicting the weather to determining what you should invest your money in.
Study statistics to be better at research, more effective as a planner or more profitable in business.
Measures of central tendency
The Normal curve and Percentiles and Standard Scores
The t Test
Analysis of variance
Chi square test
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.
What is Statistics?
Statistics are part of every day life. Every time you do something that can be described by a number, you are creating a statistic. When a group of related numbers are put together you have a collection of statistics or statistical data.
Consider if you drink two cups of coffee in a day; and a friend drinks four cups of coffee in a day; you can put your numbers together to say that two people together drank six cups of coffee in a day. This is a very simple example of using statistics.
Quite obviously, statistics can become increasingly complicated when you quantify more things and process the data collected in more sophisticated way.
Some people love statistics, and find it easy and exciting to deal with numbers; while others find the subject a difficult area of study.
Statistics are something that you cannot really escape though. If you want to be in business, undertake any sort of research or follow any type of academic pursuit, you will need to learn statistics to realise your full potential, and this is a course that gives you the fundamental grounding in the subject which is required.
Distribution of Statistical Data
One of the more important probability distributions in statistics is the "normal" distribution. It is also known as Gaussian Distribution. It was first described by de Moivre in 1733, this was built upon by Laplace in 1812 when Laplace examined experimental error. Gauss justified it 1809.
The normal distribution is depicted below. It is used to describe any population that clusters around a mean or average. Remember though, that the normal distribution is a mathematical model, an ideal symmetric distribution. Many real life distributions do approximate the normal curve, so we can use it to interpret data.
Many Different Concepts
Statistical concepts and applications are many and varied. Here are a few examples.
This is a graph of the frequency distribution. Statistical analysis would start with the raw data, create a frequency table, and then use that information to create a frequency polygon. The graphical format would allow observers to more easily understand the distribution of data. Usually the frequencies are placed on the Y-axis (vertical) and the scores, or data, placed along the X-axis (horizontal). The frequency data is marked on the graph and then a smooth, continuous line drawn through the marks. The shape of the ‘polygon’, or graph line, clearly shows the most common scores as well as the total range of the scores.
A normal probability curve on a frequency graph resembles a ‘bell-shaped’ curve. A normal distribution has a distinct peak in the middle of the data range that slopes down evenly on each side. Usually measurements of people’s physical characteristics follow a ‘normal’ curve e.g. height, weight. IQ etc.
Correlations, essentially, numerically show the relationship between two variables, or two sets of variables. The correlation value will tell us if there is a relationship between the two variables. For example, we might think that violent TV causes violence in children. A correlation might shows that there is a relationship between TV violence and violence in children, but it will not tell us that one causes the other, so we might think watching TV does cause violence in children OR violent children tend to watch more violent TV.
In the context of statistical analysis, predictions are based on data that has been previously accumulated and interpreted. The result of this analysis is firmly based on statistical methodology and principles. That gives us confidence that when we analysis data gathered under similar conditions looking at the same variables we can make useful predictions. These statistical predictions serve as a useful guide to the expected results of a new, but similar, test. The reliability of predictions is enhanced over time as larger volumes of data are collected and analysed.
Normal Distribution Characteristics
- It is a symmetrical distribution, meaning that the left half of the normal distribution is a mirror image of the right half.
- Most of the scores in a normal distribution tend to occur near the center, while more extreme scores on either side of the center become increasingly rare. As the distance from the center increases, the frequency of scores decreases.
- The mean (is the value at very centre of the curve), median, and mode of the normal distribution are the same.
- All normal curves are uni-modal, this is why the mean, median and the mode are the same.
- Scores on a normal distribution fall rapidly from the center outwards, however they never actually touch the horizontal axis. This is referred to as being asymptotic to the horizontal axis of distribution. This is because normal distributions describe an infinity of results on a continuous scale.
- The mean and standard deviation are the two features that may differ between normal distributions. They control how wide and the height of the normal distribution.