School of Communication, Information and Library Studies

STATISTICS

Methods of Inquiry Syllabus:514

Gustav W. Friedrich

The science of reducing masses of data to a few descriptive terms and drawing inferences from them.

Descriptive Statistics: reducing quantities of data to a few descriptive terms.
1. Organizing Data and Graphical Representation
a. Organizing Data:
1) Simple frequency distribution
2) Grouped frequency distribution
b. Graphical Representation
1) Nominal data: Bar Graphs; Pie Charts; Line Graphs
2) Continuous data:
a) Histograms
b) Frequency polygon
1) Symmetrical: rectangular, bell-shaped (lepto- & platy-kurtic), U shaped
2) Asymmetrical (skewed): positively, negatively, J shaped
3) Model: unimodal, bimodal, multimodal
2. Measures of Central Tendency
a. Mean
b. Median
c. Mode
3. Measures of Variability
a. Range-type Measures (R = L - S + 1)
b. Deviation-type Measures (Variance and Standard Deviation)
4. Standard Scores
a. Linear transformations: z, where Mean = 0; SD = 1
b. Area transformations: stanines

Inferential Statistics: comparing obtained results with chance expectations. Two forms:

1. Estimation Theory: using a statistic of a sample to estimate a parameter of a population (confidence level & confidence interval)

2. Hypothesis Testing: six steps; two forms.
1) State the null hypothesis
2) Choose a statistical test
3) Specify a significance level (alpha) (critical value)
4) Define the region of rejection (critical region)
5) Compute the value of the statistical test (calculated value)
6) Reject or don't reject (retain)
Type I error (a): rejecting null when you should not.
Type II error (b): not rejecting null when you should.

A. Assessing Differences
1. Parametric versus Nonparametric Statistics: size of sample; normality of distribution of population; homogeneity of variance; level of measurement.
2. One independent variable (IV)
a) Nominal level Dependent Variable (DV): chi square
b) Continuous level DV
1) Two levels of IV = t test (independent or dependent)
2) Three + levels of IV = one-way ANOVA (t2 = F)
3. Two + IVs
a) One DV
1) Nominal level: chi square (contingency table)
2) Continuous level: two-way ANOVA
b) Two + DVs
1) Nominal level: chi square
2) Continuous level: two-way MANOVA

B. Assessing Relationships
1. Two variables: correlation
a. Nominal level: point biserial or Cramer's V
b. Ordinal: Spearman rho
c. Continuous: Pearson r
2. Three + variables
a. Multiple regression
b. Factor analysis
c. Discriminant Analysis
d. Canonical Correlation

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