Example B: Raw Score Method
You may wish to test the effects of a number of experimental treatments (counselling approaches): group counselling, peer counselling and individual counselling on the selfconcepts of students. In this case, the independent variable, counselling approach has three levels. Necessarily there should be three groups randomly selected from the school population which will be exposed to three different counselling approaches.
The dependent variable, selfconcept, may be measured through a standardized selfconcept instrument which yields interval scores for the subjects.
In this problem, application of the onefactor ANOVA will test the following hypothesis: There is no significant difference in selfconcept among the three groups of students exposed to different counselling approaches. Step 1 Enter the data in a worksheet table. (See below.)
Step 2 Find the square of each raw score (X2).
Step 3 Compute the sum of N for each group, the total N, the sums of the raw scores and the sums of the squared scores. N1 = 6; N2 = 6; N3 = 6; Nt = 18
ƩX1 = 366; ƩX2 = 492: ƩX3 = 510: ƩXt = 1368
ƩX21 = 23, 866; ƩX22 = 40, 798; ƩX23 = 43, 652; ƩX2t = 108, 316 WORKSHEET TABLE for the OneWay ANOVA
Counselling Conditions
Group (1)Peer (2)Individual (3)
X1X21X2X22X3X23
786084775929786084
462116836889918281
411681979409979409
502500694761826724
694761796241857225
826724877569775929
SUMS366238664924079851043652ƩXt=1368
Means618285ƩX2t = 108, 316
N666Nt = 18
Step 4 Compute Sums of Squares.
a.SSt (SS for total variability)
=ƩXt2 – (ƩXt)2
N
SSt = 108,316 – 13682 = 4348
18
b.SSb (SS for between group variability)
= (ƩX1)2 + (ƩX2)2 + (ƩX3)2 – (ƩXt)2
N1 N2 N3 Nt
= 3662 + 4922 + 5102  13682
6 6 6 18
= 106,020 – 103,968 = 2052
c.SSw = (SS for within group...
...Oneway repeated measure ANOVA
In a oneway repeated measures ANOVA design,each subject is exposed to two or more different conditions, or measured on the continuous scale onthree or more occasions. It can also be used to compare respondents’ responses to two or more questions or items. These questions, hiwever, must be meausred using the same scale.( Likert scale)
Example of research question: Is there a change in confidence scores over the three time periods?
What you need: One group of participants measured on the same scale on three different occasions or under three different conditions, or each person measured on three different questions or items ( using the same scale). This involves teo variables:
● one indepenedet variable ( categorical) ( e.g. Time 1/Time 2/Time 3)
● one dependent variable ( numerical) (e.g scores on the confidence in coping with statistics test). The scores on the test for each time point will appear in the data file in different columns.
What it does: This technique will tell you if there is a significant difference somewhere among the three sets of scores
Assumptions: Same as ANOVA
Nonparametric alternative: Friedman Test
Example
A group of students were invited to participate in an intervention designed to increase their confidence in their ability to do statistics. The confidence levels wer...
...carried out in the 0–50 °C range. To measure Tabs, 24 thermocouples were bonded to the inner surface of the absorber plate at equal distances from each other (to verify the isothermal assumption). A single thermocouple in front of the unit (shielded from the lamps) was used to measure Tamb while another behind the unit indicated whether or not this measurement was biased by radiative ﬂux. Two other probes measured the exhaust temperature before the fan (Tout) and in the fullydeveloped downstream exhaust zone (to estimate air density). Another probe was located in the laboratory far from the apparatus and a ﬁnal probe was positioned just outside the exhaust. A complete view is given in Badache (2010). 4. Analysis of the experimental plan Since one of the aims of this study was to establish a relationship between the four control parameters and the response of the system (gcoll), a secondorder model that takes into account the main eﬀects of factors and their twofactor interactions was chosen. This model can be expressed as follows: Y ¼ b0 þ b1 X 1 þ b2 X 2 þ b3 X 3 þ b4 X 4 þ b11 X 2 1 þ b22 X 2 þ b33 X 2 þ b44 X 2 þ b12 X 1 X 2 þ b13 X 1 X 3 2 3 4 þ b14 X 1 X 4 þ b23 X 2 X 3 þ b24 X 2 X 4 þ b34 X 3 X 4 þ ei ð2Þ where ei is the random error component associated with the nth observation, and b0, bi, and bij are regression coeﬃcients estimated by the least squares technique (Montgomery, 2008). There are ﬁfteen coeﬃcients, of which six refer to nonlinear...
...Analysis of Variance (ANOVA)
Indian Institute of Public Health Delhi
MSc CR 201315
Outline of the session
• Need for Analysis of Variance
• Concept behind onewayANOVA
• Example
• Nonparametric alternative
When dependent variable is continuous
Type of
Dependent
variable
Type of
Independent
variable
Number
of
Groups
Continuous
Categorical
More
than
two
Nonparametric (Wilcoxon sign
rank)
Paired t – test
Not normal
Nonparametric (Wilcoxon sign
rank)
Independent z or t – test
Not normal
Nonparametric (Wilcoxon rank
sum or MannWhitney U )
Not normal
Unrelated or
independent
Not normal
Normal
Two
z or one sample t – test
Normal
Related
Choice of Significance test
Normal
NA
Distribution of
dependent
variable
Normal
One
Related/
Dependent
OnewayANOVA/linear
regression
Nonparametric (Kruskal Wallis)
Normal
Repeated ANOVA
Not normal
Nonparametric (Friedmans test)
Unrelated
Related
Background
• When you have more than two groups to compare,
you can apply ttest multiple times
• But this is not done, why???
• Probability of type I error increases
• This increases as the number of comparison
increases
• Analysis of variance (ANOVA) is oneway of dealing...
...
Analyzing with ANOVA 
TwoWay 
 
1/23/2013 

Submit your answers to the following questions using the ANOVA source table below. The table depicts a twowayANOVA in which gender has two groups (male and female), marital status has three groups (married, single never married, divorced), and the means refer to happiness scores (n = 100):
a. What is/are the independent variable(s)? What is/are the dependent variable(s)?
The independent variables are gender and marital status. The dependent variable is the happiness.
b. What would be an appropriate null hypothesis? Alternate hypothesis?
Alternate hypothesis about gender can be that females will have greater happiness mean score than males. There is also an alternative hypothesis in marital status that females who are married would have lower happiness mean scores than males that are married. The Null hypothesis in both situations would be that differences would not exist.
c. What are the degrees of freedom for 1) gender, 2) marital status, 3) interaction between gender and marital status, and 4) error or within variance?
1. A1= There are 2 groups of gender; male and female, so it would be 21=1 as the degree of freedom.
2. B1= There are 3 groups for marital status; married, single, and divorced, so it would be 31=2 as the degree of freedom.
3. (A1)*(B1) = That would be the answer from...
...SPSS Basics for OnewayANOVA
As an illustration of the process, consider the data given in Example 118, pp. 593 – 595,
of Bluman’s Elementary Statistics: A Brief Version.
Problem Statement: A researcher wishes to try three different techniques to lower the
blood pressure of individuals diagnosed with high blood pressure. The subjects are
randomly assigned to three groups; the first group takes medication, the second group
exercises, and the third group follows a special diet. After four weeks, the reduction in
each person’s blood pressure is recorded. At α = 0.05 , test the claim that there is no
difference among the means. The data are:
Medication Exercise Diet
10
6
5
12
8
9
9
3
12
15
0
8
13
2
4
Defining Variables and Entering the Data
Begin by defining the variables in an SPSS Data file in the Variable View window of the
SPSS Data Editor; be sure to safe the data file and the resulting output file. Here’s how
this might be done.
First name the variables; let “Bp” represent the variable for blood pressure and “Tr” the
categorical variable for treatment method. Note that even though “Tr” is categorical, it is
assigned numerical (integer) values. SPSS will interpret these values as identifying which
group each value of “Bp” belongs to. For both variables, set the number of decimal
places to be zero. Next, give each variable a (short) label, and finally assign labels to...
...INTRODUCTION TO ONEWAY ANALYSIS OF VARIANCE
Dale Berger, Claremont Graduate University http://wise.cgu.edu
The purpose of this paper is to explain the logic and vocabulary of oneway analysis of variance (ANOVA). The null hypothesis tested by onewayANOVA is that two or more population means are equal. The question is whether (H0) the population means may equal for all groups and that the observed differences in sample means are due to random sampling variation, or (Ha) the observed differences between sample means are due to actual differences in the population means.
The logic used in ANOVA to compare means of multiple groups is similar to that used with the ttest to compare means of two independent groups. When onewayANOVA is applied to the special case of two groups, onewayANOVA gives identical results as the ttest.
Not surprisingly, the assumptions needed for the ttest are also needed for ANOVA. We need to assume:
1) random, independent sampling from the k populations;
2) normal population distributions;
3) equal variances within the k populations.
Assumption 1 is crucial for any inferential statistic. As with the ttest, Assumptions 2 and 3 can be relaxed when large samples are used, and...
...European and American business companies offered their services through the World Wide Web. Since then people began to associate a word "ecommerce" with the ability of purchasing various goods through the Internet using secure protocols and electronic payment services.
The amount of trade conducted electronically has grown extraordinarily with widespread Internet usage. The use of commerce is conducted in this way, electronic funds transfer, supply chain management, Internet marketing, online transaction processing, electronic data interchange (EDI), inventory management systems, and automated data collection systems. Modern electronic commerce typically uses the World Wide Web at least at some point in the transaction's lifecycle, although it can encompass a wider range of technologies such as email, mobile devices and telephones as well.
A large percentage of electronic commerce is conducted entirely electronically for virtual items such as access to premium content on a website, but most electronic commerce involves the transportation of physical items in some way. online shopping has affected industry structure in two areas that have seen significant growth in ecommerce, bookshops and travel agencies. Online retailers are sometimes known as etailers and online retail is sometimes known as Almost all big retailers have electronic commerce presence on the World Wide Web.
In the United States, some electronic commerce activities are...
...Analysis of Variance
(ANOVA)
Dr. H. Johnson
ANOVA
• Analysis of variance (ANOVA) is a powerful hypothesis
testing procedure that extends the capability of ttests
beyond just two samples.
• Many types of ANOVAs, today we will learn about a oneway independentmeasures ANOVA
• Later we’ll learn oneway repeatedmeasures ANOVA .
• We’ll also learn twofactorANOVA after that.
• These ANOVAs are by no means all of them! There are a
LOT more types!
OneWayANOVA
• The independent measures ANOVA is used in the same types of
situations that the independent measures ttest had been used,
except that the ANOVA allows for the comparison of more than
just two groups.
• Before the advent of the computer, if someone had three
groups in an experiment, they would often use a series of ttests
to compare all possible combinations of means.
• If you had three samples to compare then, using ttests, we
would have to do M1 vs. M2, M1 vs. M3, and M2 vs. M3
• Each time we do a ttest, the type I error rate is equal to a.
• The experimentwise error rate (a) is held at .05 in an ANOVA.
OneWayANOVA
Preliminary Example
Pretend you wanted to know the effects of different temperatures on
the ability...