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ScWk 242 – Session 9 Slides, Study notes of Statistics

Inferential statistics are used to test hypotheses about the relationship between the independent and the dependent variables.

Typology: Study notes

2021/2022

Uploaded on 09/27/2022

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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!