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Inferential Statistics
and t - tests
ScWk 242 – Session 9 Slides
Inferential Statistics
Ø Inferential statistics are used to test hypotheses
about the relationship between the independent
and the dependent variables.
Ø Inferential statistics allow you to test your
hypothesis
Ø When you get a statistically significant result
using inferential statistics, you can say that it is
unlikely (in social sciences this is 5%) that the
relationship between variables is due to chance.
Probability Theory Ø Probability theory: Allows us to calculate the exact probability that chance was the real reason for the relationship. Ø Probability theory allows us to produce test statistics (using mathematical formulas) Ø A test statistic is a number that is used to decide whether to accept or reject the null hypothesis. Ø The most common statistical tests include:
- Chi-‐square
- T-‐test
- ANOVA
- Correlation
- Linear Regression
Normal Distributions
- All test statistics that use a continuous dependent variable can be plotted on the normal distribution (chi-‐ square, for example, uses the chi-‐square distribution).
- A normal distribution is a theoretical bell shaped curve:
Two-‐Tailed Significance Tests
- Two-‐tailed statistical tests (most common) split the rejection region between the tails of the normal distribution so that each tail contains 2.5% of the distribution for a total of 5%.
- Two-‐tailed tests test non-‐directional hypotheses
- Example:
- It is hypothesized that there is a relationship between participation in Independent Living Programs while in foster care (the independent variable) and having been taught budgeting skills while in foster care (the dependent variable)
- We are not specifying whether the ILP group is more or less likely to have been taught budgeting skills while in foster care
- We are just saying that there is a difference in the dependent variable (budgeting skills) between the two groups (ILP vs. no ILP)
- Researchers usually choose two-‐tailed tests to allow for the possibility that the IV affects the DV in the opposite direction as expected
One-‐Tailed Tests One-‐tailed tests test directional hypotheses Example:
- It is hypothesized that youth who participated in Independent Living Programs while in foster care (the independent variable) will have a greater likelihood of having been taught budgeting skills while in foster care (the dependent variable)
- We are specifying the expectation that ILP youth will be more likely to have been taught budgeting skills while in foster care than non-‐ILP youth
- The possible risk with one-‐tailed tests of directional hypotheses is that if ILP youth have fewer budgeting skills, the test won’t pick it up and we would have missed a significant finding (in an unexpected direction).
t-‐ test Statistic
- The t statistic allows researchers to use sample data to test hypotheses about an unknown population mean.
- The t statistic is mostly used when a researcher wants to determine whether or not a treatment intervention causes a significant change from a population or untreated mean.
- The goal for a hypothesis test is to evaluate the significance of the observed discrepancy between a sample mean and the population mean.
- Therefore, the t statistic requires that you use the sample data to compute an estimated standard error of M.
- A large value for t (a large ratio) indicates that the obtained difference between the data and the hypothesis is greater than would be expected if the treatment has no effect.
Significance vs. Magnitude
- Degrees of Freedom (df) is computed by using n – 1
with larger sample sizes resulting in an increased
chance of finding significance.
- Because the significance of a treatment effect is
determined partially by the size of the effect and
partially by the size of the sample, you cannot
assume that a significant effect is also a large effect.
- Therefore, it is recommended that the measure of
effect size (differences of outcomes vs. expectations)
be computed along with the hypothesis test.
Happy Spring Break!