Ppt of statistics for teachers

F-Test (One way Anova)
Statistics for Teachers (Mathematics)
Presented by:
Netra Kumar Manandhar
Kathmandu University
School of Education
Course Facilitator: Mr. Durga Pd. Dhakal
6/7/2017
manandharnetra999@gmail.com
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“Statistics are like bikini, what they reveal is interesting but what they hide is vital.”
- Aaron Levenstein

Presentation Outlines:
1. What is F-test ?
2. Six assumption for using F-Test (one way Anova)?
3. Test procedures for one way Anova in spss.
4. Illustration and analysis of two particular research problems.
5. Conditions for interpreting the result.
6/7/2017manandharnetra999@gmail.com
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What is One way Anova (F-test)
 Propounded by father of modern statistics ‘Sir Ronald Aylmer Fisher’
 Test statistic used to compare three or more than three population means
 F – test is also used to analyse two population variances
 Data consists of one dependent variable and more than two independent
factor
o Dependent variable:- numeric, interval and ratio
o Independent factors- categorical factors (levels, nonmetric factors etc.)
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Assumptions for One way anova:
Assumption 1:- our dependent variable should be measured at the interval or ratio
level (i.e., they are continuous)
Assumption 2:- our independent variable should consist of three or more
categorical, independent groups
Assumption 3:- we should have independence of observations
Assumption 4:- There should be no significant outliers
Assumption 5:- our dependent variable should be approximately normally
distributed for each category of the independent variable.
Assumption 6:- There needs to be homogeneity of variances. (i.e. the dependent
variable should have the same variance in each category of ind. Var.)
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Example
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A manager wants to raise the productivity at his company by increasing the speed at
which his employees can use a particular spreadsheet program. As he does not have the
skills in-house, he employs an external agency which provides training in this
spreadsheet program. They offer 3 courses: a beginner, intermediate and advanced
course. He is unsure which course is needed for the type of work they do at his company,
so he sends 10 employees on the beginner course, 10 on the intermediate and 10 on the
advanced course. When they all return from the training, he gives them a problem to
solve using the spreadsheet program, and times how long it takes them to complete the
problem. He then compares the three courses (beginner, intermediate, advanced) to see
if there are any differences in the average time it took to complete the problem.
 In this research question, we have
o Dependent variable:- Time to complete the set problem
o Independent variables:- Three groups (beginner, intermediate, advanced)

1. Click Analyze > Compare Means > One-Way ANOVA... on the
top menu, as shown below.
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2. You will be presented with the One-Way ANOVA dialogue box and do the same
as given below:
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3. Click on the selected button in options menu as shown in the figure.
4. Click on ‘Tukey’ button for ‘post hoc’ test (if necessary).
5. Finally click the and then button to get spss output.
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Let’s see one research problem
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 Here, Dependent Variable:- Weight
 Independent Variable:- Factor- university and three categories of university A,
B and C.

Contd.
10 The research was conducted among N = 1975 students of three different universities

Conditions for rejecting or accepting H0
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Condition 1:- if our p-value or sig. value is ≥ 0.05 (5%), then we accept our null
hypothesis and conclude that there is no significance difference between the means.
Condition 2:- if our p-value or sig. value is < 0.05 (5%), then we reject our null
hypothesis and conclude that there is significance difference between the means.
Condition 3:- If the p-value is < 0.05 then there is significant difference between the
means of two group.
Condition 4:- And to figure out which they are, we go for ‘POST HOC TEST’

Analysis using Anova
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According to above table the significant p-value = 0.000 < 0.05.
Decision:- Since the p-value is less than 0.05. So, we cannot accept our null hypothesis
and conclude that there is at least two means are significantly different. To determine
which is, we go for ‘POST HOC’ test.

Post Hoc test analysis
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Conclusion
 Research question: Is there an association between weight and type of
university?
 Null Hypothesis H0: Average weight A = Average weight B = Average weight
C
 Alternative Hypothesis Ha : At least two averages are different
 Statistical test: F-test = 13.293; p< 0.05
 Conclusion: There is a significant relationship between weight and type of
university. Based on the post Hoc test, differences in average of weight are
between B and C.
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Example No.: 02
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 We have conducted a survey among 303 students (sample) in order to find out the
relationship between fathers’ education and students’ affective engagement in
learning.
 Research Question:- Is there any significant difference among the means of
affective engagement according to student’s fathers’ education.
 In this research problem:
oDependent Variable: Affective Engagement in Learning
o Independent Variable (Factor): Fathers’ education (Level of Degree they have)
 Hypotheses are:
o Null Hypothesis: μ1 = μ2 = μ3 = μ4 = μ5 = μ6 (i.e. there is no significant difference
among the means of affective engagement according to fathers’ education level)
o Alternative Hypothesis: There is at least one mean is different from another.

Descriptive analysis
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The research was conducted among N = 303 students of school level

Analysis using Anova
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Decision:- Since the significant p-value is 0.329 (33% aprox.) > 0.05 (5%). so we
accept our null hypothesis and conclude that there is no significant difference among
the means of affective domain according to their fathers’ education level.
SPSS
OUTPUT

Question
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When do we use ‘POST HOC’ test in one way anova (f-test)?

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