Statistics for EMCL students

Overview before final exam

Topics

1. Descriptive statistics (M&M 1.1 and 1.2, handout).
2. More variables: independence, correlation, regression (M&M 2).
3. Basics of inferential statistics: sampling distributions, confidence intervals, tests. Experiment design, ethical issues, etc. (M&M 3, 5.2, 6).
4. Statistical procedures (tests and confidence interval): z-test and confidence interval (one-sample), t-test (one-sample and two-sample; confidence interval with t-statistic), test for proportions, chi-square, ANOVA, nonparametric tests (esp. Wilcoxon rank sum test).

Test yourself:

Can you define in one sentence the following concepts?

• Informed consent (For those using earlier editions of M&M: check 3.4 in the newest version!).
• Variable: nominal, ordinal, numerical scales.
• Measures of center vs. measures of spread.
• Resistant measure (NB: resistancy is a relative and not an absolute property).
• Density curve vs. cumulative proportion.
• Sample vs. population. Statistic vs. parameter.
• Bias and variability of a statistic. How to avoid them?
• Confidence level, significance level, p-value, error margin (in a confidence interval), critical value (of a distribution for a priori set up significan level).
• Parametric vs. nonparametric statistical procedure.
• Histogram, boxplot, stemplot, normal quantile plot, scatterplot.
• Null hypothesis vs. alternative hypothesis.
• One-side vs. two-sided hypotheses.
• Error of type I vs. error of type II. Connection to p-value.
• Independent samples vs. paired (matched) data samples.
• A robust statistical procedure.
• The 68-95-99.7 rule. The 1.5 X IQR rule.
• The Central Limit Theorem.
• Explanatory variable vs. response variable. Lurking variable.
• Two variables are independent vs. associated. Positive association vs. negative association. Association vs. causation.
• Slope vs. intercept.
• Two-way table. Column variable vs. row variable. Joint distribution, marginal distribution, conditional distribution. Observed counts vs. expected counts.
• What is the goal of least-squares regression? What are the possible values of correlation r, and what is their meaning?
• For what purpose do we use... a Normal quantile plot, a scatterplot, a chi-square test, a matched pairs t-test, etc.?
• When do we use a "contrast" (cf. ANOVA)? Why do we use Bonferroni in multiple comparisons?
• Under what conditions may you use test ...?

Formulas etc. that you need to know:

1. How to compute: mean (a.k.a. average), median, mode, standard deviation, variance, IQR. Degree of freedom.
2. Conversion to standard z-scores.
3. Standard error for samples over n elements.
4. Use of tables for z, t, chi-square.
5. Interpret SPSS output for z, t, chi-square, ANOVA and Wilcoxon.

For all tests: pay attention to the guidelines for practical use! Be able to decide when is which test to be used (decision tree).

Type of questions in the test:

• Multiple choice.
• Open questions (answer with one sentence).
• Basic calculations by hand + use of table (provided).
• Interpret graphs and SPSS outputs ("write the magic sentence").

Further practice recommended before the final test:

Basic computations.

Paper-and-pen assignments that you should be able to solve during the final exam (by John Nerbonne):

Normal curve
Sample statistics
Confidence interval, statistical significance

You can expect very similar questions in the final test.

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