CORRELATION PILLAR FIRST PART REVIEWER.PPTX

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1. STATISTICS & PROBABILITY

2. CORRELATION  

3. A correlation is a statistical measure of the relationship between two variables. The measure is best used in variables that demonstrate a linear relationship between each other. The fit of the data can be visually represented in a scatterplo t. Using a scatterplot, we can generally assess the relationship between the variables and determine whether they are correlated or not. Definition:

4. ( also called a scatterplot, scatter graph, scatter chart, scattergram, or scatter diagram ) - a type of plot or mathematical diagram using Cartesian coordinates to display values for typically two variables for a set of data. Scatter Plot

5. Example of a Scatter Plot Diagra m Day Temperature(X) Sales(Y) 1 30 123k 2 32 143k 3 31 110k 4 34 156k 5 33 181k 6 29 100k Let’s examine the example below showing the graph of atmospheric temperature per day and sales. 30 28 32 34 36 38 120k 100k 160k 140k 180k Therefore, based on the diagram we have we can say that the trend is diagonally upward indicating there are an increase in temperature implies increase in sales.

6. Pearson Product-Moment Correlation(r) The most familiar of statistical tool in quantifying the linear relationship between two random variables, x and y. FORMULA :  

7. Degree of Association Verbal Interpretation r Verbal Interpretation No relation Slight Correlation Low Correlation Moderate Correlation High Correlation Very High Correlation Perfect Correlation r Verbal Interpretation No relation Slight Correlation Low Correlation Moderate Correlation High Correlation Very High Correlation Perfect Correlation

8. Steps in testing hypothesis State the null (H ) and alternative (H 1 ) hypothesis. Identify the level of significance and its critical value. Perform an appropriate  statistical test . Compare the critical value and its statistical value. Decide whether the null hypothesis is accepted or rejected. Present the findings in your  results  and  discussion  section.

9. Example #1. Solve using Pearson r and test the significant correlation at 5% level of significance and interpret the result: x y 1 2 2 4 3 6 4 8 5 10

10. Example #1. Solve using Pearson r and test the significant correlation at 5% level of significance and interpret the result: x y 1 2 2 4 3 6 4 8 5 10 Solution:     1 4 9 16 25 4 16 36 64 100 2 8 18 32 50       55   220    

11. EXAMPLE #1 GIVEN: ASKED: STEP 1: STEP 2:   There is no significant correlation between x and y.   There is significant correlation between x and y.   , , and   Test if there is significant correlation between x and y.        

12. EXAMPLE #1 GIVEN: ASKED: STEP 1: STEP 2:   There is no significant correlation between x and y.   There is significant correlation between x and y.   , , and   Test if there is significant correlation between x and y.     STEP 3:       STEP 4:   STEP 5: Reject   FALSE STEP 6: Therefore, there is significant correlation between x and y. It also implies that x influenced y and the result of r implies a positive perfect correlation.

13. Example #2. The teacher wants to determine if the grades in MAT1 had significant correlation with the grades in MAT3. Solve for Pearson r at 1% level of significance. MAT1(x) MAT3(y) 93 98 85 88 79 81 81 73 72 71 95 99 85 85 83 84 96 99 85 80

14. 98 88 81 73 71 99 85 84 99 80 Example #2. The teacher wants to determine if the grades in MAT1 had significant correlation with the grades in MAT3. Solve for Pearson r at 1% level of significance. MAT1 MAT3 93 98 85 88 79 81 81 73 72 71 95 99 85 85 83 84 96 99 85 80   858               8,649 7,225 6,241 6,561 5,184 9,025 7,225 6,889 9,216 7,225 9,604 7,744 6,561 5,329 5,041 9,801 7,225 7,056 9,801 6,400 9,114 7,480 6,399 5,913 5,112 9,405 7,225 6,972 9,504 6,800

15. EXAMPLE #2 GIVEN: ASKED: STEP 1: STEP 2:   There is no significant correlation with the grades in MAT 1 and MAT3   There is significant correlation with the grades in MAT 1 and MAT3   , 73,924, and   Test if there is significant correlation with the grades in MAT 1 and MAT3.        

16. GIVEN: ASKED: STEP 1: STEP 2:   There is no significant correlation with the grades in MAT 1 and MAT3   There is significant correlation with the grades in MAT 1 and MAT3   , 73,924, and   Test if there is significant correlation with the grades in MAT 1 and MAT3     STEP 3:       STEP 4:   STEP 5: Reject   FALSE STEP 6: Therefore, there is significant correlation with the grades in MAT 1 and MAT3. It also implies that x influenced y and the result of r implies a very high positive correlation. EXAMPLE #2

17. TRY THIS!!! Solve using Pearson r and test the significant correlation at 1% level of significance and interpret the result: x y 14 23 25 41 42 61 52 18 14 11

18. That’s all for today!!