![PEARSON PRODUCT MOMENT CORRELATION MEASURE OF CORRELATION
2
Testing Correlation
The Pearson Product Moment Correlation formula shows the relationship between X and Y variables. It
can be seen from the coefficient presented by r.
The following values are:
∑X = 1240
∑Y = 2040
∑XY = 101400
∑X2
= 64800
∑Y2
= 168000
The computation as follows:
rxy =
𝑁(∑𝑋𝑌)−(∑𝑋)(∑𝑌)
√[𝑁∑𝑋2−(∑𝑋)2][𝑁∑𝑌2−(∑𝑌)2
=
25(101400)−(1240)(2040)
√[25(64800)−(1240)2][25(168000)−(2040)2
=
2535000−2529600
√[1620000−1537600][4200000−4161600]
=
5400
√[82400][38400]
=
5400
√31641600
=
5400
5625.086
= 0.959](data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)
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Pearson product mometnt correlation
- 1. PEARSON PRODUCT MOMENT CORRELATION MEASURE OF CORRELATION 1 NAME : SISKA V. LUMAPOW NIM : 11 311 179 CLASS/SEM : G/VI APPLIED STATISTICS PEARSON PRODUCT MOMENT CORRELATION Table 1. The Computation of X, Y, X2, Y2 , XY Students X Y X2 Y2 XY 1 40 90 1600 8100 3600 2 50 90 2500 8100 4500 3 60 80 3600 6400 4800 4 40 70 1600 4900 2800 5 40 90 1600 8100 3600 6 70 90 4900 8100 6300 7 60 90 3600 8100 5400 8 60 80 3600 6400 4800 9 60 80 3600 6400 4800 10 60 70 3600 4900 4200 11 70 80 4900 6400 5600 12 40 80 1600 6400 3200 13 30 80 900 6400 2400 14 30 70 900 4900 2100 15 40 90 1600 8100 3600 16 40 90 1600 8100 3600 17 40 80 1600 6400 3200 18 40 70 1600 4900 2800 19 60 80 3600 6400 4800 20 50 90 2500 8100 4500 21 50 70 2500 4900 3500 22 60 80 3600 6400 4800 23 40 90 1600 8100 3600 24 50 70 2500 4900 3500 25 60 90 3600 8100 5400 Total 1240 2040 64800 168000 101400
- 2. PEARSON PRODUCT MOMENT CORRELATION MEASURE OF CORRELATION 2 Testing Correlation The Pearson Product Moment Correlation formula shows the relationship between X and Y variables. It can be seen from the coefficient presented by r. The following values are: ∑X = 1240 ∑Y = 2040 ∑XY = 101400 ∑X2 = 64800 ∑Y2 = 168000 The computation as follows: rxy = 𝑁(∑𝑋𝑌)−(∑𝑋)(∑𝑌) √[𝑁∑𝑋2−(∑𝑋)2][𝑁∑𝑌2−(∑𝑌)2 = 25(101400)−(1240)(2040) √[25(64800)−(1240)2][25(168000)−(2040)2 = 2535000−2529600 √[1620000−1537600][4200000−4161600] = 5400 √[82400][38400] = 5400 √31641600 = 5400 5625.086 = 0.959
- 3. PEARSON PRODUCT MOMENT CORRELATION MEASURE OF CORRELATION 3 The result of the computation of the correlation denotes a moderate criterion in reference to the criteria put forward by Arikunto (1998:260). Besarnya nilai r Interpretasi 0.800 to 1.000 Tinggi 0.600 to 0.800 Cukup 0.400 to 0.600 Agak rendah 0.200 to 0.400 Rendah 0.000 to 0.200 Sangat rendah (tak berkorelasi). Based on the criteria above, the result is clear: Since the coefficient of correlation rxy = 0.959, the relationship between students’ speaking ability and vocabulary mastery is high enough. Deciding The Acceptance of Hypothesis The null hypothesis tested sounds there is no significant relationship between students’ speaking ability and vocabulary mastery. To decide whether or not to reject the null hypothesis and to accept the alternative hypothesis, the following criterion is applied: Ho is accepted if rxy ≤ r in the table. Ho is rejected if rxy ≥ r in the table. Therefore, after computing rxy, the result has to be distributed to the table of r for the Pearson Product Moment Correlation Coefficient. The result of rxy = 0.959 The table value of r = 0.413 in df 23, ∝ = 0.05 It means that rxy ≥ r. Thus, the null hypothesis that there is no significance relationship between students’ speaking ability and vocabulary mastery is rejected. In other words, the alternative hypothesis that there is a significant relationship between students’ speaking ability and vocabulary mastery is accepted. Besides, the data of numbers support the that there is relationship between them.