If you are seeking to summarise, catagorise or simply describe what the data is showing in its most basic form then you will need to use methods that allow for the description of data. Listed here are some of the key statistical methods of analysis used to provide this basic descriptive function.

Descriptive Statistics

This describes the mathematical processes used to summarise any given set of data. It describes the process from collection, to classification, to summarising through to the presenting of basic data. Data can then be presented in either table form or graph form and is used to describe the basic results of research.

Some methods used within descriptive statistics include:

• Frequency displays and distributions - This is a means of collating total responses to a particular question, or frequency of a certain variable. For example, a frequency display may show that a survey result showed 20 respondents identified themselves as 'fluent in Te Reo'.
• Measures of central tendency - This describes a group of formulas used to asses the mean, median, mode or averages within data sets.
• Variability - This describes the statistical dispersion or spread of data.

Click on the link below for more information on Descriptive Statistics

http://www.socialresearchmethods.net/kb/statdesc.htm

Inferential Statistics

If during the data collection phase you obtained a representative sample , you may wish to use frequency displays to make inferences on a wider population from which the sample was selected. In this case you would use inferential statistics.

There are two main methods used in inferential statistics, estimation and hypothesis testing. The purpose of estimation is to use the sample data to estimate a parameter, and then from this estimation draw a confidence interval. Hypothesis testing involves using data to test the accuracy of hypothesis against the data.

Some methods used in inferential statistics are:

• Chi Square Goodness of Fit Test - This is a probability test used to determine if the data sourced from a specific sample are comparable to theoretical values, and to determine whether deviation from an expected event occurred by chance.
• The T-Test - This test is used to compare the average performance between two groups.
• Analysis of Variance - A method used to measure the difference among means from two or more samples.
• Analysis of Co-variance - A method used to measure the difference among means from two or more samples, while taking into account the variation caused by one variable.
• Regression Analysis - This is a method used to determine relationships between variables.

Click on the link below for information on Inferential Statistics

http://www.socialresearchmethods.net/kb/statinf.htm

Chiang, Chin Long (2003) Statistical Methods of Analysis, World Scientific, New Jersey.

Diamond, Ian (2001) Beginning Statistics: An Introduction for Social Scientists, Sage, London.

"Elaboration enables you to statistically control variables that may contribute to (elaborate on) the basic relationship identified in the initial data analysis" (Dane, 1990, p. 141)

Once you have completed the analysis of data, you may need to begin the process of exploring and interpreting relationships among variables. This process is called elaboration, and allows for the examination of possible reasons 'why' the data is showing what it is showing.

This involves cross checking other variables against the two primary variables identified as having a correlating relationship. These other variables could be viewed as 'alternative hypothesis', and how they impact on the two primary variables could lead to possible causal relationships.

For example, if a survey found a correlation between 'fluency in Te Reo Maori' and 'Urban Dwelling', you may wish to test this against age, level of income, and level of education. If these variables are tested against fluency in Te Reo and no change occurs across the data, then you can eliminate them as possible causes on the relationship between the two primary variables.

Elaboration is similar to a process of elimination whereby variables are tested one by one to see how they impact on observed relationships. Some methods that can be used during elaboration analysis are:

• Pearons Product Moment Correlation Coefficient – This measures the tendency of two variables on the one object to increase or decrease together.
• Multiple Regression – This is a technique used for the estimating of simultaneous correlations among any number of predictor variables and a single response variable.
• Discriminant analysis – This is a technique used to estimate the relationship between predictor variables and catagorical responses.

When conducting exploratory analysis it is easy to make the mistake of making conclusions that have not been fully tested. These untested conclusions are called Ex post facto explanations. Be cautious in your research, and ensure that your analysis is thorough and clear. Steer clear from Ex post facto explanations.