Final Exam - Statistics

Different Levels of Measurement

Nominal, Ordinal, Interval, Ratio

Nominal Data

Used to name or classify data

Example of Nominal Data

Male or Female, Blue Eyes, Brown Eyes

Ordinal Data

Different instances of the variable can be rank-ordered

Interval Data

Measurement conveys information about the spacing between instances

Ratio Data

Measurement has a meaningful zero point, Relative comparisons can be made

Examples of Ratio Data

response time, response rate, number of responses

Discrete Variable

The variable can only take on certain values

Continuous Variable

The variable can take on an infinite number of values between any other two values

What type of procedure does Nominal and ordinal data require?

non-parametric

What type of procedure does Interval and ratio data allow?

Parametric

Descriptive statistics

summaries and numerical characterizations of sample data

Purpose of Descriptive Statistics

reduce a large set of data into a smaller set of numbers that can be more easily understood, while still characterizing the essential features of the larger data set

Inferential statistics

the procedures used to draw conclusions about the population from which a sample was obtained

statistics

summary numbers that describe sample data, and are represented by italicized Latin letter symbols

parameters

Summary numbers that describe population data, and are represented by lower case italicized Greek letter symbols

Mode

most frequently occurring score

Measures of central tendency

mean, median, mode

Z-Score/Standard Score

used to compare values of variables that are measured on different scales

The steps in hypothesis testing

State the hypothesis, pick the correct statistical procedure, set the decision rule, calculate the value of the test statistic, compare and interpret results

Null Hypothesis

Common form of statistical hypothesis testing, the assumption that there is no difference, no relationship, or no effect in a population

Alternative/Research Hypothesis

This is the prediction or statement that you will find sufficient evidence for the sought-after effect.

Nondirectional Hypothesis

does not specify whether the obtained value is greater or less than the expected value, just that it is different

What hypothesis is associated with a two tailed test?

nondirectional hypothesis

directional hypothesis

does specify the direction or sign of an effect

What hypothesis is associated with a one tailed test?

directional hypothesis

Type 1 Error

saying that the NULL is false, when it is true

Statistical power

the ability to reject the null hypothesis when the null hypothesis is false

Factors that influence power

effect size, sample size, measurement reliability, Alpha, Directionality of hypotheses

Parameter

is a number that describes some characteristic of the distribution of values in the population

Parametric statistical tests

assume underlying distributions of values of population parameters

Non-parametric statistical tests

make minimal or no assumptions about an underlying distribution of parameter values in the population, because they are inappropriate or entirely absent

Spearman’s Rho

Tests whether two ordinal level variables are related to one another

Chi-square test of independence

Tests whether two categorical variables are related to one another, Used when you only have frequency (nominal level) data

Chi-square goodness-of-fit test

Tests the hypothesis that observed frequencies in two or more categories are the same as expected frequencies, Used when you only have frequency (nominal level) data

Mann-Whitney U Test

Tests the null hypothesis that two distributions are identical, You would use this if you had only ordinal level data and 20 or fewer observations per condition, or if you couldn’t meet the assumptions for an independent groups t-test

Rank Sums Test

Tests the null hypothesis that two distributions are identical, should be used when you have more than 20 observations per group

McNemarTest

Tests whether two categorical variables are related to one another, repeated measures

Wilcoxon T test

Tests whether two distributions from dependent groups are identical, only ordinal level data or if you couldn’t meet the assumptions for a related samples t-test

Kruskal-Wallis H Test

Tests whether three or more independent groups are different, Used when you only have ordinal level data or when you cannot meet the assumptions of the one-way ANOVA

Cochran Q test

If you have three or more dependent groups, for nominal level data

Friedman Chi-square

3 or more dependent groups, ordinal level data, or when you cannot meet the assumptions of a repeated measures one-way ANOVA

What does ANOVA stand for?

One way Analysis of Variance