Chi-Square test for independence of attributes / Chi-Square test for checking association between two categorical variables, Chi-Square test for goodness of fit
Hypothesis Testing is important part of research, based on hypothesis testing we can check the truth of presumes hypothesis (Research Statement or Research Methodology )
INTRODUCTION
CHARACTERISTICS OF A HYPOTHESIS
CRITERIA FOR HYPOTHESIS CONSTRUCTION
STEPS IN HYPOTHESIS TESTING
SOURCES OF HYPOTHESIS
APPROACHES TO HYPOTHESIS TESTING
THE LOGIC OF HYPOTHESIS TESTING
TYPES OF ERRORS IN HYPOTHESIS
Hypothesis Testing is important part of research, based on hypothesis testing we can check the truth of presumes hypothesis (Research Statement or Research Methodology )
INTRODUCTION
CHARACTERISTICS OF A HYPOTHESIS
CRITERIA FOR HYPOTHESIS CONSTRUCTION
STEPS IN HYPOTHESIS TESTING
SOURCES OF HYPOTHESIS
APPROACHES TO HYPOTHESIS TESTING
THE LOGIC OF HYPOTHESIS TESTING
TYPES OF ERRORS IN HYPOTHESIS
v When to Choose a Statistical Tests OR When NOT to Choose? v Parametric vs. Non-Parametric Tests (Comparison)
v Parameters to check when Choosing a Statistical Test:
- Distribution of Data
- Type of data/Variable
- Types of Analysis (What’s the hypothesis)
- No of groups or data-sets
- Data Group Design
v Snapshot of all statistical test and “How” to Choose using above parameters v Explanation using Examples:
- Mann Whitney U Test
- Wilcoxon Sign Rank Test
- Spearman’s co-relation
- Chi-Square Test
v Conclusion
Chi Square test for independence of attributes / Testing association between two categorical variables, Chi-Square test for Goodness of fit / Testing significant difference between observed and expected frequencies
v When to Choose a Statistical Tests OR When NOT to Choose? v Parametric vs. Non-Parametric Tests (Comparison)
v Parameters to check when Choosing a Statistical Test:
- Distribution of Data
- Type of data/Variable
- Types of Analysis (What’s the hypothesis)
- No of groups or data-sets
- Data Group Design
v Snapshot of all statistical test and “How” to Choose using above parameters v Explanation using Examples:
- Mann Whitney U Test
- Wilcoxon Sign Rank Test
- Spearman’s co-relation
- Chi-Square Test
v Conclusion
Chi Square test for independence of attributes / Testing association between two categorical variables, Chi-Square test for Goodness of fit / Testing significant difference between observed and expected frequencies
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This presentation will clarify all basic concepts and terms of hypothesis testing. It will also help you to decide correct Parametric & Non-Parametric test for your data
A chi-squared test is a statistical hypothesis test that is valid to perform when the test statistic is chi-squared distributed under the null hypothesis, specifically Pearson's chi-squared test and variants
differences between the observed values
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Concept of Correlation, Simple Linear Regression & Multiple Linear Regression and its analysis using SPSS. How it check the validity of assumptions in Regression
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t test for single mean, t test for means of independent samples, t test for means of dependent sample ( Paired t test). Case study / Examples for hands on experience of how SPSS can be used for different hypothesis testing - t test.
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Different type of test which are used for large sample has been included in this presentation. Steps for each test and a case study is included for concept clarity and practice.
This ppt is to guide students opting for Statistics major. It gives an idea of skills required and job prospects. It also emphasizes on the important life skills along with Statistics knowledge, analytical thinking and hands on analytical software .
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http://sandymillin.wordpress.com/iateflwebinar2024
Published classroom materials form the basis of syllabuses, drive teacher professional development, and have a potentially huge influence on learners, teachers and education systems. All teachers also create their own materials, whether a few sentences on a blackboard, a highly-structured fully-realised online course, or anything in between. Despite this, the knowledge and skills needed to create effective language learning materials are rarely part of teacher training, and are mostly learnt by trial and error.
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2. Chi- Square Statistic
If X~𝑁(𝜇, 𝜎2) then 𝑍 =
𝑋−𝜇
𝜎
~𝑁(0,1) and
𝑍2
=
𝑋−𝜇
𝜎
2
~𝜒2
with 1 d.f. and
𝑋−𝜇
𝜎
2
~𝜒2
with n d.f.
3. Chi- Square
test
There are three types of chi-square tests.
• A Chi-square goodness of fit test determines if distribution of
sample data matches with the distribution of population.
• A Chi-square test for independence is to test whether two
categorical variables differ from each another.
• A Chi-square test for variance of single sample is to test
whether there is significant difference between sample variance
and population variance
4. Chi- Square test
– Independence of
Attributes
Chi-Square test is a statistical method to determine if
two categorical variables have a significant
correlation/association between them.
5. To test independence of attributes
Step 1: H0: Two attributes (categorical variables) are independent
Step 2: H1: Two attributes (categorical variables) are dependent
Step 3: Test statistics: χ2 =
(𝑂𝑖−𝐸𝑖)2
𝐸𝑖
where 𝐸𝑖 =
𝑅𝑜𝑤 𝑡𝑜𝑡𝑎𝑙 ∗𝐶𝑜𝑙𝑢𝑚𝑛 𝑡𝑜𝑡𝑎𝑙
𝐺𝑟𝑎𝑛𝑑 𝑡𝑜𝑡𝑎𝑙
Step 4: Conclusion
• If p ≤ Level of significance (∝), We Reject Null hypothesis
• If p > Level of significance (∝), We fail to Reject Null hypothesis
[Note: In 2*2 contingency table if expected is less than 5, use Yate’s correction i.e. Continuity
correction in the SPSS output]
6. Example
A public opinion poll surveyed a simple random sample of 1000 voters. Respondents were
classified by gender (male or female) and by voting preference (Party A, Party B, or Party C).
Results are shown in the contingency table below. Is voting preference affected by gender?
Gender
Voting Preference
Party A Party B Party C
Male 200 150 50
Female 250 300 50
7. Null & Alternative
Hypothesis
Step 1: H0: Gender and voting preferences are independent.
Step 2: H1: Gender and voting preferences are not independent.
13. Output
The Chi-square value is 16.204 and p value = 0.000 < 0.05.
We reject the Null hypothesis.
∴ Gender and voting preferences are not independent.
i.e. voting preference is affected by gender
14. To test goodness of fit
Step 1: H0: There is no significant difference between observed and expected frequencies
Step 2: H1:There is significant difference between observed and expected frequencies
Step 3: Test statistics: χ2 =
(𝑂𝑖−𝐸𝑖)2
𝐸𝑖
and p value
Step 4: Conclusion
• If p ≤ Level of significance (∝), We Reject Null hypothesis
• If p > Level of significance (∝), We fail to Reject Null hypothesis
15. Example1
The number of road accidents on a particular highway during a week is given below. Can it be
concluded that the proportion of accidents are equal for all days?
Day Mon Tue Wed Thu Fri Sat Sun
Accidents 14 16 8 12 11 9 14
16. Hypothesis
Null Hypothesis: H0: Proportion of accidents are equal for
all days
Alternative Hypothesis: H1: Proportion of accidents are
not equal for all days
20. Output
Chi-Square statistics = 4.167
p value = 0.657 > 0.05
Ho is accepted
So, it can be concluded that the proportion of
accidents are equal for all days
21. Example 2
Suppose it was suspected an unusual distribution
of blood groups in patients undergoing one type of
surgical procedure. It is known that the expected
distribution for the population served by the
hospital which performs this surgery is 44% group
O, 45% group A, 8% group B and 3% group AB. A
random sample of 187 routine pre-operative blood
grouping results are given below. Do this sample
match with the expected distribution.
Blood
Group
O A B AB
Patients 67 83 29 8
Results for 187 consecutive patients:
22. Hypothesis
Null Hypothesis: H0: There is no significant difference
between observed and expected distribution of patients
with respect to blood group
[Sample follows expected distribution]
Alternative Hypothesis: H1: There is significant difference
between observed and expected distribution of patients
with respect to blood group
[Sample does not follows expected distribution]
24. Case Study 1
Expected distribution for the
population served by the hospital
which performs this surgery is
44% group O,
45% group A,
8% group B and
3% group AB.
Blood
Group
Observed
freq.
Probability Expected freq. =
N*Prob
O 67 0.44 187*0.44 = 82.28
A 83 0.45 187*0.45 = 84.15
B 29 0.08 187*0.08 = 14.96
AB 8 0.03 187*0.03 = 5.61
Total N = 187 1 187
28. Output
Chi-Square statistics = 17.048
p value = 0.001 < 0.05
Ho is rejected
So, there is significant difference between observed
and expected distribution of patients with respect to
blood group.
29. THANK YOU
Dr Parag Shah | M.Sc., M.Phil., Ph.D. ( Statistics)
pbshah@hlcollege.edu
www.paragstatistics.wordpress.com
