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Basic Statistics

Basic Statistics. Regression and Correlation. Regression. Finds the best linear equation to match the relationship between one variable and another. This is called simple regression ie the relationship between one independent variable (x) and a dependent variable (y).

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Basic Statistics

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  1. Basic Statistics Regression and Correlation

  2. Regression • Finds the best linear equation to match the relationship between one variable and another. • This is called simple regression ie the relationship between one independent variable (x) and a dependent variable (y). • Multiple regression examines the relationship between one dependent variable and multiple independent variables

  3. Correlation (r) • Measures the strength of the relationship between variables. • For example, how useful is the independent variable x in predicting values of y in a simple linear regression. • Correlation can be weak or strong and can be positive or negative (inverse).

  4. Correlation continued • The most common correlation formula is Pearson’s Product Moment Correlation – used for interval and ratio data. • Spearman’s rho, Kendall’s tau (and others) for ordinal measures. • Note the interpreting of Pearson r +1 to 0 to -1

  5. Significance • In addition to the strength of the correlation between pairs of variables, how significant is it? • Calculation of statistical significance ranges between 0 and 1. The closer to zero the better and is reported as the significance level. For example: .01 is one chance in 100 of being mistaken by the result.

  6. Population and Sample • Remember that your statistics are usually from a sample of the population covered by your research. • Each sample you take will very likely give different correlation and significance levels. • The extent to which your sample matches all other random samples is a measure of reliability

  7. Sampling If you are surveying a population, you will gather your data from a sub-set or sample of that population. Selecting your sample to be sure it matches the entire population is of prime importance. Sampling allows you to draw conclusions that apply to the whole population. That is to say, your sample should be representative of your population to enable you to generalise (draw conclusions).

  8. Probability Sampling Techniques • Simple Random Sampling: totally random selection • Systematic Sampling: eg choosing every 10th person from a list • Stratified Random Sampling: to ensure coverage of the population within subsets • Cluster Sampling: choosing a particular concentration within a population

  9. Non-probability Sampling Techniques • Convenience Sampling: because you have access to a sample of the population • Volunteer Sampling: eg you advertise for participants in your research, or you work with your friends and professional associates • Quota Sampling: You choose representatives within specified categories

  10. Sample Size • Not easy to answer – depends on several factors • Participation rate (response rate) within the sample is important • Larger random samples will display less sampling error • Large populations – larger sample? • 1%? 5%? 10%? • Expert opinion needed?

  11. t-tests • Used to find out if there are differences between two or more sub-groups that you have surveyed by comparing the means and SDs of the two groups. • If two sub-groups come from different samples, use an independent t-test. • Note: there are several variations of t-test depending on the research sample and the source of the data.

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