1. More on inferential statistics (hypothesis testing)
2. Comparison of means using the t-tests
3. Statistical significance
In the first module we reviewed descriptive (univariate) statistics by examining separate variables based on measures of central tendency (mean, median and mode) and measures of dispersion (standard deviation, variance, and range). In this module we will link two variables to form a hypothesis, which will be tested using inferential statistics (bivariate methods). We will focus on the t-test also referred to as the
student t-test (because it was developed by William S. Gossett, while he was a student/apprentice at the Guinness Brewery in Ireland). He was prohibited from using his name because of issues relating to trade secrets.
NOTE that an INFERENTIAL STATISTICAL TEST is used for testing a hypothesis about a population based on data from a representative sample of the population. In other words, this technique allows us to INFER (or generalize) from the sample to the population. This involves some “risk”, and therefore attention to STANDARD ERROR.
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Sit back and relax!!
Review of the t-test
The t-test is used for comparing two means in order to determine if the difference is statistically significant (explained below). There are three types of t-test, as follows:
Comparing a sample mean to a known population mean refers to a one-sample t-test.
An independent samples t-test is applied when the same variable (numerical) has been measured in two independent groups/populations, and the researcher wants to know whether the difference between the group means is statistically significant. "Independent" indicates that the groups are different, that is, contain different subjects.
A dependent, related or paired samples t-test is the appropriate test when the same subjects have been measured (twice) under two different conditions. It is also referred to as a repeated measures t-test (note two measurements, as in a pre-test, post-test design).
Assumptions underlying the t-test
1. The t-test is a parametric test (assumes a normal distribution). The variable being measured must be normally distributed in the population.
2. The observations within each sample must be independent of each other. That is, each observation/value/score must come from a different subject/unit.
3. The two populations from which the samples were selected must have equal variances (referred to as homogeneity of variances). This applies to the independent samples t-test.
NOTES ON STATISTICAL SIGNIFICANCE
What does "statistical significance" mean?
A statistically significant finding (usually, p < .05), means that the finding was unlikely to have occurred by chance only, and can therefore be considered “true” and repeatable (reliable).
Significance is indicated by a probability level (p), which practically speaking is a measure of the probability (p) of error. Hence we want this probability (level of significance) to be low - less than .05 (the alpha level).
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Alpha refers to the maximum level of error (usually .05, but can also be set at .01) we are prepared to tolerate in order to conclude that a finding is statistically significant.
Note that a statistically significant finding must be assessed for practical significance, that is, its value or importance to the field or discipline.
Note also that large samples can render small differences statistically significant (with little or no practical significance). This is usually referred to as an artifact of statistics.
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