Docsity
Docsity

Prepare for your exams
Prepare for your exams

Study with the several resources on Docsity


Earn points to download
Earn points to download

Earn points by helping other students or get them with a premium plan


Guidelines and tips
Guidelines and tips

Choosing the Right Statistical Test: UQ Student Services Guide, Exercises of Data Analysis & Statistical Methods

This document from the university of queensland student services outlines the process of selecting the appropriate elementary statistical test based on the type of research question and the nature of the data. It covers tests for degree of relationship or dependence among variables, significance of group differences, and assumptions for each. Examples of statistical tests include t-test for correlations, goodness-of-fit test, z-test, t-test for independent samples, mann-whitney u test, anova, and kruskal-wallis test.

Typology: Exercises

2021/2022

Uploaded on 02/11/2022

lumidee
lumidee 🇺🇸

4.4

(47)

364 documents

1 / 2

Toggle sidebar

This page cannot be seen from the preview

Don't miss anything!

bg1
Student Services, The University of Queensland
CHOOSING THE RIGHT ELEMENTARY STATISTICAL TEST
The first step in determining what statistical test to use is to determine the type of research question to be answered by the statistical analysis. In
elementary courses, the two basic types of questions are:
1. the degree of relationship or dependence among variables (H0 = there is no relationship or dependence, and the statistical test answers the question
as to whether any relationship or dependence found is sufficiently different from zero that it can be considered “statistically significant”.)
2. the significance of group differences (H0 = there is no difference between groups. The statistical test answers the question as to whether an
observed difference is probably due just to random factors, or is large enough to be considered “statistically significant” and due to the treatment
factor.)
The next step is to determine the nature(s) of the variables under discussion, and whether they meet the assumptions of a particular test (e.g. the data are
normally distributed).
Types/levels of data:
nominal = unordered categories (e.g. religion; country of birth; etc.)
ordinal = ordered categories (e.g. level of agreement on an opinion survey; proficiency level at a martial art as measured by the colour of one‟s belt)
For nominal and ordinal data, what is usually recorded is the number of occurrences of a particular result (e.g. number of Christians, number of
Buddhists etc. but these numbers are not the values of the variable. In this case, variable = religion, values = Christian, Buddhist, …and the
numbers are the number of occurrences of a particular value.)
interval = ordinal + distance between values is of constant size (e.g. temperature)
ratio = interval + (i) there is a meaningful zero and (ii) the ratio between two numbers is meaningful (e.g. weight, distance, number of children)
ratio and interval data can be either discrete (i.e. there are gaps between values, e.g. number of children) or continuous (i.e. there are no gaps
between values (e.g. weight, height).
Type of Question
Level of Data /
Assumptions
Examples
Statistical Test
Degree of relationship or
dependence among variables
Is there a relationship between one trait
and another? (I.e. does the observed
frequency of one trait depend on the
frequency of another?)
Both nominal or one
nominal and one ordinal
(i) Is eye colour independent of hair colour?
(ii) Is opinion about a government policy independent of political
affiliation?
Contingency table
Is there a relationship between two
continuous variables?
interval, ratio
(i) Does GPA depend on IQ?
(ii) Does weight depend on height?
t-test for correlations
using Pearson‟s
correlation coefficient
Is there a relationship between two ordinal
variables?
ordinal
(i) How strong is the relationship between the starting grid position
of a race driver and their finishing position?
t-test for correlations
using Spearman‟s rs
pf2

Partial preview of the text

Download Choosing the Right Statistical Test: UQ Student Services Guide and more Exercises Data Analysis & Statistical Methods in PDF only on Docsity!

Student Services, The University of Queensland

CHOOSING THE RIGHT ELEMENTARY STATISTICAL TEST

The first step in determining what statistical test to use is to determine the type of research question to be answered by the statistical analysis. In

elementary courses, the two basic types of questions are:

1. the degree of relationship or dependence among variables (H 0 = there is no relationship or dependence, and the statistical test answers the question

as to whether any relationship or dependence found is sufficiently different from zero that it can be considered “statistically significant”.)

2. the significance of group differences (H 0 = there is no difference between groups. The statistical test answers the question as to whether an

observed difference is probably due just to random factors, or is large enough to be considered “statistically significant” and due to the treatment

factor.)

The next step is to determine the nature(s) of the variables under discussion, and whether they meet the assumptions of a particular test (e.g. the data are

normally distributed).

Types/levels of data:

nominal = unordered categories (e.g. religion; country of birth; etc.)

ordinal = ordered categories (e.g. level of agreement on an opinion survey; proficiency level at a martial art as measured by the colour of one‟s belt)

 For nominal and ordinal data, what is usually recorded is the number of occurrences of a particular result (e.g. number of Christians, number of

Buddhists etc. but these numbers are not the values of the variable. In this case, variable = religion, values = Christian, Buddhist, …and the

numbers are the number of occurrences of a particular value.)

interval = ordinal + distance between values is of constant size (e.g. temperature)

ratio = interval + (i) there is a meaningful zero and (ii) the ratio between two numbers is meaningful (e.g. weight, distance, number of children)

 ratio and interval data can be either discrete (i.e. there are gaps between values, e.g. number of children) or continuous (i.e. there are no gaps

between values (e.g. weight, height).

Type of Question Level of Data /

Assumptions

Examples Statistical Test

Degree of relationship or

dependence among variables

Is there a relationship between one trait and another? (I.e. does the observed frequency of one trait depend on the frequency of another?) Both nominal or one nominal and one ordinal (i) Is eye colour independent of hair colour? (ii) Is opinion about a government policy independent of political affiliation? Contingency table Is there a relationship between two continuous variables? interval, ratio (i) Does GPA depend on IQ? (ii) Does weight depend on height? t-test for correlations using Pearson‟s correlation coefficient Is there a relationship between two ordinal variables? ordinal (i) How strong is the relationship between the starting grid position of a race driver and their finishing position? t-test for correlations using Spearman‟s r s

Student Services, The University of Queensland Are the observed frequencies the same as an expected set of frequencies? All (though often nominal) (i) Are the absentee rates the same for each day of the week? (ii) Are the number of workplace accidents the same for each hour of the day? (iii) Is the observed set of scores normally distributed? Goodness-of-fit Significance of group differences Is a population mean or proportion (as estimated by a sample statistic) the same or different from a specified value?

  • For means, data is interval or ratio level, the population is normal with a known variance.
  • For proportions, the variable is a binomial nominal variable (i) Is the mean weight of soup in a can the same as stated on the label? (ii) Are 90% of pizza orders delivered within 30 minutes? (Success = delivered within 30 minutes, failure = delivered over 30 minutes.) z - test for large samples, t - test for small samples. Is there a difference between the means or proportion of “successes” for two populations? (Comparative experiments.) Populations approximately normal and with same variances; samples independent (i) Is there a difference in the mean lifetimes of Battery A and Battery B? (ii) Is there a difference in the proportion of consumers who bought Product A before and after an advertising campaign? (iii) Did a group of trainees score significantly better on some test after training compared to before training? (Dependent samples.) If samples are independent, two-sample t - test (small samples) or z - test (large samples), related sample t - test if samples are dependent. As above Data at least ordinal; can be used if t - test assumptions not met Mann-Whitney Are the means of three or more populations (as estimated by samples) the same? Interval or ratio level data (^) H 0 : 1 = 2 = … = (^) k ANOVA As above Ordinal data and/or populations not normal Kruskal-Wallis As above, but more than one independent variable. (i) Sleep score versus amount of exercise and whether exercise was in the morning or the afternoon. (ii) Time of travel from A to B versus route taken and driver. Factorial ANOVA (Looking for „main‟ and „interaction‟ effects) Multiple comparison of means Interval or ratio level data (^) e.g. H 0 : 1 = 2 = 3 > 4 = 5 Linear contrast