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Current list of tutorial topics includes:
- Introduction to Statistics for Research
- In this tutorial, a basic introduction is provided for those completely new
to statistics. Data types and measurement scales, types of variables (eg.
independent, dependent, covariates, confounders, etc.) and statistical tests
(eg. parametric vs non-parametric, comparison versus correlation, etc.) are
discussed.
- Descriptive Statistics and Measures of Variability
- This tutorial describes the very basic descriptive statistical analyses
used in research. Here we focus on describing distributions with frequency
tables and histogram plots, quantifying central tendency (mean, median,
mode, etc.) and variance (standard deviation, coefficient of variation, etc.).
We also discuss the properties of the normal distribution, which is central to
most parametric statistical tests.
- Inferential Statistics and Hypothesis Testing
- In this tutorial, we discuss the basic concepts behind inferential statistical
analyses. Specifically, sampling error and probabilities are discussed in terms of
how we make objective decisions with statistics. We will briefly explore the
Central Limit Theorum, and see how to make use of this theory (via the
standard error) to compute confidence intervals, and compare population samples.
Other topics include hypothesis testing, and different types of statistical
error (type I and type II).
- Comparing Means: The t-Test
- One of the most basic and popular tests in research is the Student t-test.
In this tutorial we examine the two main types of t-test applications: 1)
Comparing means between subjects (independent t-test), and 2) Comparing
means within subjects (paired t-test). Details of computing the t
statistic are provided, and the concept of homogeneity of variance is also
discussed (eg. Levene's test). Examples are provided and compared in terms of hand
calculations and the SPSS software package.
- One-Way ANOVA & Multiple Comparison Tests
- In this tutorial we extend the concepts of the two-sample t-test to the
more generalized and powerful Analysis of Variance (ANOVA) method, based on the
F-distribution. Concepts of the F-distribution are discussed in relation to
conducting between-subjects analyses (one-way ANOVA) when we have k
independent groups of subjects. This tutorial also explores in detail how we
develop and test specific hypotheses about the group differences we expect using
various multiple comparison tests (such as Bonferonni, Tukey's test, Neuman-Keuls,
and Scheffe comparison). Examples are provided and compared in terms of hand
calculations and the SPSS software package.
- Two-Way Analysis of Variance
- This tutorial further expands upon the concepts in the prior tutorial
to deal with research designs that have more than one independent grouping
variable (two-way ANOVA). Here we discuss the concepts of "main effects" and
"interaction effects" and see how their variances are partitioned in the
two-way model. Specific examples and details are provided for conducting simple main effects
analyses and simple paired comparisons when interactions are significant (using
the SPSS /Lmatrix command).
- Repeated Measures Analysis of Variance
- This tutorial explores the extension of the paired samples t-test to the more
general Repeated Measures ANOVA test. Here we see how to make statistical comparisons of
within-subjects means when subjects have multiple repeated measures. Post-hoc testing
is described in terms of multiple-comparisons tests, and the protection against
type I error using Bonferonni, and Holm's-Bonferonni alpha adjustments. Other topics,
such as mixed models designs, are discussed briefly. Examples are provided and compared in terms of hand
calculations and the SPSS software package.
- Bivariate and Partial Correlations
- This tutorial switches gears to the concept of testing for associations between
variables, rather than comparing means. We briefly discuss the concepts of the
r-distribution, and witness the development of one of the most common and powerful
statistical tests used in modern statistics: the correlation coefficient, r.
Pearson product-moment correlation is introduced, as well as non-parametric tests
such as Spearman correlation, rank-biserial and phi correlations. We then examine
the concepts of "partial" correlation analysis, whereby we control our comparisons
for one or more covariates or confounding variables. Examples are provided and compared in terms of hand
calculations and the SPSS software package.
- Linear Regression and ANCOVA
- In this tutorial we extend the concepts of correlation to equation modeling
using linear regression analysis. Here we discuss the basic structure of the
linear regression model, and how we can evaluate the statistical significance of
various aspects of our resulting linear equations (constant, slope, etc.). We
then return to the prior concepts of ANOVA, and see how we can combine linear
regression and ANOVA to control for covariates or confounding variables when
we are conducting between-subjects comparisons, using Analysis of Covariance
(ANCOVA). Examples are provided using the SPSS software package.
- Chi-Square Analysis of Frequencies
- While all the above tests have dealt with parametric statistics, and more
specifically, continuous type variables, in this tutorial we introduce a
class of statistics, called Chi-Square analysis, for testing categorical type
data, based on proportions. The chi-square distribution is discussed, and we will
see how to use this versatile technique to conduct "Goodness of fit" tests, and
"Contingency Table" analysis (Crosstabs), as well as repeated measures types tests,
such as the McNemar test. Examples are provided and compared in terms of hand
calculations and the SPSS software package.
- Non-Parametric Tests
- Last but not least are the class of comparison-type tests for ordinal or
non-normally distributed variables, known as non-parametric tests. Here we discuss
how tests are conducted based on ranks when we do not (or cannot) make assumptions
about the distribution of our measurements. We will examine the specific non-parametric
analog tests to the common parametric tests, such as the Mann-Whitney U-test, Wilcoxon
signed-rank test, the Kruskal-Wallis test, and the Friedman two-way test. Examples are
provided using the SPSS software package.
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