This document discusses four types of correlation coefficients: Pearson's product-moment correlation, Spearman's rank-order correlation, Phi coefficient, and point-biserial correlation. It provides definitions, formulas, examples and interpretations for each type of correlation. Pearson's correlation is used with interval or ratio scales, while Spearman's correlation is for ordinal scales. Phi coefficient is for nominal scales, and point-biserial is used when one variable is nominal and one is interval.
Fundamental of Statistics and Types of CorrelationsRajesh Verma
Fundamental of Statistics and Types of Correlations. Pearson r, Point Biserial, Phi Coefficient, Biserial, Tetrachoric, Spearman Rank Difference, Kendall's tau, Inferential Statistics, Descriptive Statistics
Fundamental of Statistics and Types of CorrelationsRajesh Verma
Fundamental of Statistics and Types of Correlations. Pearson r, Point Biserial, Phi Coefficient, Biserial, Tetrachoric, Spearman Rank Difference, Kendall's tau, Inferential Statistics, Descriptive Statistics
Pearson Product Moment Correlation - ThiyaguThiyagu K
The coefficient of correlation computed by product moment coefficient of correlation or Pearson's correlation coefficient and symbolically represented by r. This presentation explains the concept, computation, merits and demerits of Pearson Product Moment Correlation.
The phi coefficient is that system of correlation which is computed between two variables, where neither of them is available in a continuous measures and both of them are expressed in the form of natural or genuine dichotomies. This presentation slides describes the concept and procedures to do the computation of phi coefficient of correlation.
Multiple Correlation Coefficient denoting a correlation of one variable with multiple other variables. The Multiple Correlation Coefficient, R, is a measure of the strength of the association between the independent (explanatory) variables and the one dependent (prediction) variable. This presentation explains the concept of multiple correlation and its computation process.
The Spearman’s Rank Correlation Coefficient is the non-parametric statistical measure used to study the strength of association between the two ranked variables. This method is applied to the ordinal set of numbers, which can be arranged in order, i.e. one after the other so that ranks can be given to each. This presentation slides explains the procedure to find out the Rank Difference correlation and its applications.
According to Wikipedia point estimation involves the use of sample data to calculate a single value (known as a point estimate since it identifies a point in some parameter space) which is to serve as a "best guess" or "best estimate" of an unknown population parameter (for example, the population means).
Pearson Product Moment Correlation - ThiyaguThiyagu K
The coefficient of correlation computed by product moment coefficient of correlation or Pearson's correlation coefficient and symbolically represented by r. This presentation explains the concept, computation, merits and demerits of Pearson Product Moment Correlation.
The phi coefficient is that system of correlation which is computed between two variables, where neither of them is available in a continuous measures and both of them are expressed in the form of natural or genuine dichotomies. This presentation slides describes the concept and procedures to do the computation of phi coefficient of correlation.
Multiple Correlation Coefficient denoting a correlation of one variable with multiple other variables. The Multiple Correlation Coefficient, R, is a measure of the strength of the association between the independent (explanatory) variables and the one dependent (prediction) variable. This presentation explains the concept of multiple correlation and its computation process.
The Spearman’s Rank Correlation Coefficient is the non-parametric statistical measure used to study the strength of association between the two ranked variables. This method is applied to the ordinal set of numbers, which can be arranged in order, i.e. one after the other so that ranks can be given to each. This presentation slides explains the procedure to find out the Rank Difference correlation and its applications.
According to Wikipedia point estimation involves the use of sample data to calculate a single value (known as a point estimate since it identifies a point in some parameter space) which is to serve as a "best guess" or "best estimate" of an unknown population parameter (for example, the population means).
Overviews non-parametric and parametric approaches to (bivariate) linear correlation. See also: http://en.wikiversity.org/wiki/Survey_research_and_design_in_psychology/Lectures/Correlation
In statistics, regression analysis is a statistical process for estimating the relationships among variables. It includes many techniques for modeling and analyzing several variables, when the focus is on the relationship between a dependent variable and one or more independent variables. More specifically, regression analysis helps one understand how the typical value of the dependent variable (or 'Criterion Variable') changes when any one of the independent variables is varied, while the other independent variables are held fixed. Most commonly, regression analysis estimates the conditional expectation of the dependent variable given the independent variables – that is, the average value of the dependent variable when the independent variables are fixed. Less commonly, the focus is on a quantile, or other location parameter of the conditional distribution of the dependent variable given the independent variables. In all cases, the estimation target is a function of the independent variables called the regression function. In regression analysis, it is also of interest to characterize the variation of the dependent variable around the regression function which can be described by a probability distribution.
TOPIC OUTLINE: 1. The Normal Curve
a. Definition/Description
b. Area Under Normal Curve
2. Standard Scores
a. Z-Scores
b. T-Scores
c. Other Standard Scores
Karl Friedrich Gauss:
one of the scientist that developed the concept of normal curve.
Normal Curve
is a continuous probability distribution in statistics
Karl Pearson:
first to refer to the curve as “Normal Curve”
Asymptotic:
approaching the x-axis but never touches it
Symmetric:
made up of exactly similar parts facing each other
STANDARD SCORES
-is a raw score that has been converted from one scale to another scale.
Z-scores
called a zero plus or minus one scale
Scores can be positive and negative
T-Scores
a none of the scores is negative. It can be called a 50 plus or minus ten scale. ( 50 mean set and 10 SD set )
Stanine: Standard Nine
(STAndard NINE) is a method of scaling test scores on a nine-point standard scale with a mean of five and a standard deviation of two.
This session demonstrates the practical method of hand-calculation of Pearson correlation. Differentiate between covariance and correlation. Derivation of correlation formula and how it is associated with covariance. An example was explained using the hand calculation of correlation. and the result was described
This slide describe the stepwise methods of hand calculation of Pearson correlation coefficient. it involves the hypothesis making and testing. Two methods are explained, one with covariance and second with direct formula. The formula derivation is also explained and at the last the graphic presentation is also given to show the line of fitness and direction of the correlation.
Most of the variables show some kind of relationship. For example, there is relationship between profits and dividends paid, income and expenditure, etc. with the help of correlation analysis we can measure in one figure the degree of relationship existing between the variables.
Correlation analysis contributes to the understanding of economic behaviour, aids in locating the critically important variables on which others depend, may reveal to the economist the connection by which disturbances spread and suggest to him the paths through which stabilizing forces may become effective.
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Chapter 10: Correlation and Regression
10.1: Correlation
Unit-I, BP801T. BIOSTATISITCS AND RESEARCH METHODOLOGY (Theory)
Correlation: Definition, Karl Pearson’s coefficient of correlation, Multiple correlations -
Pharmaceuticals examples.
Correlation: is there a relationship between 2
variables.
1. Calculate the Pearson Product Moment Correlation Coefficient
2. Solve problems involving correlation analysis.
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Data Processing and Statistical Treatment: Spreads and CorrelationJanet Penilla
A hyperlinked presentation. The objectives of the topic were written. The presentation was started with the variance and then the standard deviation provided with examples. It also answers on when to use the sample standard deviation and the population standard deviation or what type of data should we use when we calculate a standard deviation. The presentation also includes Correlations and other correlation techniques(Pearson-product moment correlation; Spearman - rank order correlation coefficient; t-test for correlation).
Adjusting primitives for graph : SHORT REPORT / NOTESSubhajit Sahu
Graph algorithms, like PageRank Compressed Sparse Row (CSR) is an adjacency-list based graph representation that is
Multiply with different modes (map)
1. Performance of sequential execution based vs OpenMP based vector multiply.
2. Comparing various launch configs for CUDA based vector multiply.
Sum with different storage types (reduce)
1. Performance of vector element sum using float vs bfloat16 as the storage type.
Sum with different modes (reduce)
1. Performance of sequential execution based vs OpenMP based vector element sum.
2. Performance of memcpy vs in-place based CUDA based vector element sum.
3. Comparing various launch configs for CUDA based vector element sum (memcpy).
4. Comparing various launch configs for CUDA based vector element sum (in-place).
Sum with in-place strategies of CUDA mode (reduce)
1. Comparing various launch configs for CUDA based vector element sum (in-place).
As Europe's leading economic powerhouse and the fourth-largest hashtag#economy globally, Germany stands at the forefront of innovation and industrial might. Renowned for its precision engineering and high-tech sectors, Germany's economic structure is heavily supported by a robust service industry, accounting for approximately 68% of its GDP. This economic clout and strategic geopolitical stance position Germany as a focal point in the global cyber threat landscape.
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🔑 Key findings include:
🔍 Increased frequency and complexity of cyber threats.
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This report aims to equip stakeholders across public and private sectors with the knowledge to enhance their defensive strategies, reduce exposure to cyber risks, and reinforce Germany's resilience against cyber threats.
Levelwise PageRank with Loop-Based Dead End Handling Strategy : SHORT REPORT ...Subhajit Sahu
Abstract — Levelwise PageRank is an alternative method of PageRank computation which decomposes the input graph into a directed acyclic block-graph of strongly connected components, and processes them in topological order, one level at a time. This enables calculation for ranks in a distributed fashion without per-iteration communication, unlike the standard method where all vertices are processed in each iteration. It however comes with a precondition of the absence of dead ends in the input graph. Here, the native non-distributed performance of Levelwise PageRank was compared against Monolithic PageRank on a CPU as well as a GPU. To ensure a fair comparison, Monolithic PageRank was also performed on a graph where vertices were split by components. Results indicate that Levelwise PageRank is about as fast as Monolithic PageRank on the CPU, but quite a bit slower on the GPU. Slowdown on the GPU is likely caused by a large submission of small workloads, and expected to be non-issue when the computation is performed on massive graphs.
2. Content
1. Pearson’s product moment correlation
2. Spearman rank-order correlation (Rho)
3. Phi coefficient
4. Point biserial correlation
3. Types of Correlation Coefficients
Correlation Coefficient Types of scales
Pearson’s product moment Both scales interval
Spearman rank-order Both scales ordinal
Phi Both scales nominal
Point biserial One interval, one nominal
Which formula should I use?
4. Pearson's correlation coefficient when applied to a population is
commonly represented by the Greek letter ρ (rho) and may be
referred to as the population correlation coefficient or
the population Pearson correlation coefficient.
The formula for r is:
Cov: covariance
S(x), S(y): the standard deviation of X and Y
1. Pearson’s product moment correlation
5. • The Mean is the average of the numbers.
• The Standard Deviation is just the square root of Variance.
E.g. The following data relates to Number of hours studying
and number of correct answers
1. Pearson’s product moment correlation
6. • The Mean is the average of the numbers.
Mean =
0+1+2+3+5+5+6
7
= 3,142
• Now we calculate each scores differences from the Mean.
+ The Mean is 3.1427.
+ The differences are : - 3.142, -2.142, -1.142, -0.142, 1.858, 1.858,
2.858.
1. Pearson’s product moment correlation
7. • The Variance is:
σ2
=
(−3.142)2+ (−2.142)2+ (−1.142)2+ (−0.142)2+ 1.8582+ 1.8582+ 2.8582
7
=
30.763384
7
= 4.394
• And the Standard Deviation is just the square root of Variance.
σ = 4.394= 2.096 = 2 (to the nearest score)
1. Pearson’s product moment correlation
8. • If working with raw data, the Pearson product moment
correlation formula is as follows:
1. Pearson’s product moment correlation
11. Conclusion: There is a strong, positive correlation between X and
Y. The more X is, the more Y is.
Exercise
? Find the persons coefficient of correlation between price of
studying facilities and demand from the following data. Then make
your conclusion about their relationship.
1. Pearson’s product moment correlation
12. 2. Spearman rank-order correlation (Rho)
- A measure of the strength and direction of association that exists
between two ranked variables on ordinal scale.
- Denoted by the symbol rs (or the Greek letter ρ, pronounced rho).
−1 ≤ 𝜌 ≤ 1
13. Assumption
- Two variables are either ordinal, interval or ratio.
- There is a monotonic relationship between two variables.
2. Spearman rank-order correlation (Rho)
14. 2. Spearman rank-order correlation (Rho)
English
(mark)
Math
(mark)
56 66
75 70
45 40
71 60
62 65
64 56
58 59
80 77
76 67
61 63
- Ranking Data
• The score with the highest
value should be labeled "1"
and vice versa.
16. 2. Spearman rank-order correlation (Rho)
English
(mark)
Math
(mark)
56 66
75 70
45 40
71 60
61 65
64 56
58 59
80 77
76 67
61 63
- Ranking data
• The score with the highest
value should be labeled "1"
and vice versa.
• When you have two or more
identical values in the data, you
need to take the average of
their ranks
23. 3. Phi coefficient
A. Definition
- The Phi (ϕ) statistic is used when both of the nominal variables
are dichotomous.
- The obtained value for Phi suggests the relationship between the
two variables.
24. 3. Phi coefficient
B. Formula
Formula:
VARIABLE Y
VARIABLE X
A B A+B
C D C+D
A+C B+D
D)+C)(B+D)(A+B)(C+(A
BC-AD
=
25. 3. Phi coefficient
C. Example
E.g. A class of 50 Ss are asked whether they like using the language
lab. The answer is either yes or no. The Ss are from either Japan or
Iran.
The observed values:
Then:
Japan Iran
Yes 24 8 32
No 6 12 18
30 20
D)+C)(B+D)(A+B)(C+(A
BC-AD
=
41
88.587
0
345600
0
20301832
681224
0.=
24
=
24
=
))()()((
))((-))((
=
26. 3. Phi coefficient
D. Steps
D.1. Using the suggested interpretations of Measure
of Association
1. State the Null hypothesis
2. Determine the Phi coefficient
3. Using the suggested table to state the conclusion
27. 3. Phi coefficient
Suggested Interpretations of Measures of Association
Values Appropriate Phrases
+.70 or higher Very strong positive relationship.
+.50 to +.69 Substantial positive relationship.
+.30 to +.49 Moderate positive relationship.
+.10 to +.29 Low positive relationship.
+.01 to +.09 Negligible positive relationship.
0.00 No relationship.
-.01 to -.09 Negligible negative relationship.
-.10 to -.29 Low negative relationship.
-.30 to -.49 Moderate negative relationship.
-.50 to -.69 Substantial negative relationship.
-.70 or lower Very strong negative relationship.
Source: Adapted from James A. Davis, Elementary Survey Analysis. Englewood Cliffs, NJ: Prentice-Hall, 1971, 49.
28. 3. Phi coefficient
D.2. Transform the Phi coefficient into Chi-square
1. State the Null hypothesis.
2. Choose the Alpha level and determine p-value.
3. Apply the formula for Phi coefficient and determine Chi-
square value:
4. Compare Chi-square value and p-value. State the
conclusion.
22
N=
30. 4. Point biserial correlation
4.1. Definition & Function
4.2. Formula
4.3. Meaning of point-biserial coefficient
31. 4. Point biserial correlation
4.1. Definition & Function
“When one of the variables in the correlation is nominal, the point
biserial correlation is used to determine the relationship between
the levels of the nominal variable and the continuous variable.”
(Hatch & Farhady, 1982, pp. 204)
E.g. the correlation between each single test item and the total test
score:
- Nominal variable: answers to a single test item
- Continuous variable: total test score
32. 4. Point biserial correlation
4.1. Definition & Function
- Functions:
o To analyze test items
o To investigate the correlation between some language
behaviors for male/female
o To investigate the correlation between any other nominal
variable and test performance
33. 4. Point biserial correlation
4.2. Formula
a. By hand
rpbi =
𝑋 𝑝
−𝑋 𝑞
𝑠
𝑝𝑞
𝑋 𝑝: the mean score on the total test of Ss answering the item right
𝑋 𝑞: the mean score on the total test of Ss answering the item wrong
𝑝: proportion of cases answering the item right
𝑞: proportion of cases answering the item wrong
𝑠:standard deviation of the total sample on the test
34. 4. Point biserial correlation
4.2. Formula
E.g. the correlation between each single test item and total test score
Table 2. Sample Student Data Matrix (Varma, n.d., pp. 4)
35. 4. Point biserial correlation
4.2. Formula
E.g. the correlation between test item 1 and total test score
𝑋 𝑝=
9+8+7+7+7+4
6
=7
𝑋 𝑞=
4+3+2
3
= 3
𝑝 =
6
9
= .67 ; 𝑞 =
3
9
= .33
Mean =
9+8+7+7+7+4+4+3+2
9
= 5.67
𝑠 =
(9−5.67)2+ …+ (2−5.67)2
9−1
= 2.45
Items
Students
4 Total test
scores
Kid A 1 9
Kid B 1 8
Kid C 1 7
Kid D 1 7
Kid E 1 7
Kid F 0 4
Kid G 1 4
Kid H 0 3
Kid I 0 2
rpbi =
7−3
2.45
.67 (.33) = .77 .
36. 4. Point biserial correlation
4.2. Formula
Exercise. the correlation between test item 4 and total test score
Answer:
𝑋 𝑝= 7 ; 𝑋 𝑞= 4
𝑝 = .56 ; 𝑞 = .44
𝑠 = 2.8
rpbi= .53
Items
Students
6 Total test
scores
Kid A 1 9
Kid B 1 8
Kid C 1 7
Kid D 0 7
Kid E 1 7
Kid F 0 4
Kid G 1 4
Kid H 0 3
Kid I 0 2
37. 4. Point biserial correlation
4.3. Meaning of point-biserial coefficient
- A high point-biserial coefficient means that students selecting
more correct (incorrect) responses are students with higher
(lower) total scores
discriminate between low-performing examinees and high-
performing examinees
- Very low or negative point-biserial coefficients computed after
field testing new items can help identify items that are flawed.
38. Reference
BBC. (n.d.). Variation and classification. Retrieved from
http://www.bbc.co.uk/bitesize/ks3/science/organisms_behaviour_health/
variation_classification/revision/3/
Hatch, E. & Farhady, H. (1982). Research design and statistics for applied
linguistics. Rowley: Newburry.
Lund, A. & Lund, M. (n.d.). Retrieved from https://statistics.laerd.com/statistical-
guides/spearmans-rank-order-correlation-statistical-guide.php
39. Reference
Nominal measure of correlation (n.d.). Retrieved from
http://www.harding.edu/sbreezeel/460%20files/statbook/chapter15.pdf
Varma, S. (n.d.). Preliminary item statistics using point-biserial correlation and p-
values. Morgan Hill, CA: Educational Data Systems.
Editor's Notes
Mean: average; standard deviation: the amount by which a measurement is different from standard