11.a correlational analysis of students achievement in waec and neco mathematics
Correlational analysis
description
Transcript of Correlational analysis
![Page 1: Correlational analysis](https://reader035.fdocuments.in/reader035/viewer/2022062310/56815d73550346895dcb7dce/html5/thumbnails/1.jpg)
Correlational analysis
![Page 2: Correlational analysis](https://reader035.fdocuments.in/reader035/viewer/2022062310/56815d73550346895dcb7dce/html5/thumbnails/2.jpg)
65 70 75 80 85 90 95
Weight
165
170
175
180
185
190
195
Size
73 74 75 76 77
Weight
165
170
175
180
185
190
195
Size
65 70 75 80 85 90 95
Weight
165
170
175
180
185
190
195
Size
Scatterplot
![Page 3: Correlational analysis](https://reader035.fdocuments.in/reader035/viewer/2022062310/56815d73550346895dcb7dce/html5/thumbnails/3.jpg)
Nominal 1. Phi coefficient2. Cramer’s V3. Pearson χ2 test4. Loglinear analysis
Ordinal 1. Spearman’s Rho2. Kendall’s Tau
Interval 1. Pearson’s r
Correlational tests
![Page 4: Correlational analysis](https://reader035.fdocuments.in/reader035/viewer/2022062310/56815d73550346895dcb7dce/html5/thumbnails/4.jpg)
Correlation coefficient + effect sizeCorrelation coefficient Shared variance (effect
size)r = 0.0 0.00 Kein Zusammenhang
r = 0.1 0.01 (1%) Geringe Korrelationr = 0.2 0.04 (4%)r = 0.3 0.09 (9%) Mittlere Korrelationr = 0.4 0.16 (16%)r = 0.5 0.25 (25%)r = 0.6 0.36 (36%) Hohe Korrelationr = 0.7 0.49 (49%)r = 0.8 0.64 (64%) Sehr hohe Korrelationr = 0.9 0.81 (81%)r = 1.0 1.00 (100%)
![Page 5: Correlational analysis](https://reader035.fdocuments.in/reader035/viewer/2022062310/56815d73550346895dcb7dce/html5/thumbnails/5.jpg)
Beispiel: MLU & Age
Child Age in months MLU123456789101112
242332204358283453464936
2.102.162.251.932.645.631.962.235.193.453.212.84
![Page 6: Correlational analysis](https://reader035.fdocuments.in/reader035/viewer/2022062310/56815d73550346895dcb7dce/html5/thumbnails/6.jpg)
Long: There is an association between age and MLU. The r of .887 showed that 78.6% (r2) of the variation in MLU was accounted for by the variation in age. The associated probability level of 0.001 showed that such a result is unlikely to have arisen from sampling error.
Short: As can be seen in the table above, there is a strong correlation between age and MLU (r = .887, p = .001).
Beispiel: MLU & Age
![Page 7: Correlational analysis](https://reader035.fdocuments.in/reader035/viewer/2022062310/56815d73550346895dcb7dce/html5/thumbnails/7.jpg)
Beispiel: Typicality & Frequency
Words Typicality rank Frequency rankcartrucksports carmotor biketrainbicycleshipboatscat boardspace shuttle
12345678910
12653487910
![Page 8: Correlational analysis](https://reader035.fdocuments.in/reader035/viewer/2022062310/56815d73550346895dcb7dce/html5/thumbnails/8.jpg)
Kendall’s tau ( = .733, p = .003)
Spearman’s rho (rs = .879, p = .001)
Beispiel: Typicality & Frequency
![Page 9: Correlational analysis](https://reader035.fdocuments.in/reader035/viewer/2022062310/56815d73550346895dcb7dce/html5/thumbnails/9.jpg)
Phoneme & Silben r = .898, p = .001Phoneme & Häufigkeit r = .795, p = .006Silben & Häufigkeit r = .677, p = .031
Partial correlation
Phoneme & Häufigkeit r = .578, p = .103(Silben Konstant)
![Page 10: Correlational analysis](https://reader035.fdocuments.in/reader035/viewer/2022062310/56815d73550346895dcb7dce/html5/thumbnails/10.jpg)
Es gibt eine signifikante Korrelation zwischen Geschlecht (Boys vs. Girls) und der Präferenz für ein bestimmtes Spielzeug (mechanisch vs. nicht-mechanisch) (χ2 = 49,09, df = 2, p = .001).
Nominal Daten
Phi-Koeffizient = .70, p < .001Cramer’s V = .70, p < .001
![Page 11: Correlational analysis](https://reader035.fdocuments.in/reader035/viewer/2022062310/56815d73550346895dcb7dce/html5/thumbnails/11.jpg)
Regression
![Page 12: Correlational analysis](https://reader035.fdocuments.in/reader035/viewer/2022062310/56815d73550346895dcb7dce/html5/thumbnails/12.jpg)
Correlational analysis gives us a measure that represents how closely the data points are associated.
Correlation - Regression
Regression analysis measures the effect of the predictor variable x on the criterion y. – How much does y change if you change x.
A correlational analysis is purely descriptive, whereas a regression analysis allows us to make predictions.
![Page 13: Correlational analysis](https://reader035.fdocuments.in/reader035/viewer/2022062310/56815d73550346895dcb7dce/html5/thumbnails/13.jpg)
Types of regression analysis
Predictor variable
Criterion (target) variable
Linear regression 1 interval 1 interval
![Page 14: Correlational analysis](https://reader035.fdocuments.in/reader035/viewer/2022062310/56815d73550346895dcb7dce/html5/thumbnails/14.jpg)
Types of regression analysis
Predictor variable
Criterion (target) variable
Linear regression 1 interval 1 intervalMultiple regression 2+ (some of the
variables can be categorical)
1 interval
![Page 15: Correlational analysis](https://reader035.fdocuments.in/reader035/viewer/2022062310/56815d73550346895dcb7dce/html5/thumbnails/15.jpg)
Types of regression analysis
Predictor variable
Criterion (target) variable
Linear regression 1 interval 1 interval
Multiple regression 2+ (some of the variables can be categorical)
1 interval
Logistic regressionDiscriminant analysis
1+1+
1 categorical1 categorical
![Page 16: Correlational analysis](https://reader035.fdocuments.in/reader035/viewer/2022062310/56815d73550346895dcb7dce/html5/thumbnails/16.jpg)
Line-of-best-fit
20,00 30,00 40,00 50,00 60,00
Age
2,00
3,00
4,00
5,00
6,00
MLU
R-Quadrat linear = 0,786
![Page 17: Correlational analysis](https://reader035.fdocuments.in/reader035/viewer/2022062310/56815d73550346895dcb7dce/html5/thumbnails/17.jpg)
y = bx + a
Linear Regression
y = variable to be predictedx = given value on the variable xb = value of the slope of the line a = the intercept (or constant), which is the
place where the line-of-best-fit intercepts the y-axis.
![Page 18: Correlational analysis](https://reader035.fdocuments.in/reader035/viewer/2022062310/56815d73550346895dcb7dce/html5/thumbnails/18.jpg)
Given a score of 20 on the x-axis, a slope of b = 2, and an interception point of a = 5, what is the predicted score?
Linear Regression
y = (2 20) + 5 = 45
![Page 19: Correlational analysis](https://reader035.fdocuments.in/reader035/viewer/2022062310/56815d73550346895dcb7dce/html5/thumbnails/19.jpg)
Beispiel: MLU & Age
Child Age in months
MLU
123456789101112
242332204358283453464936
2.102.162.251.932.645.631.962.235.193.453.212.84
How much does MLU increase with growing age?
![Page 20: Correlational analysis](https://reader035.fdocuments.in/reader035/viewer/2022062310/56815d73550346895dcb7dce/html5/thumbnails/20.jpg)
There is s strong association between age and MLU (R = 0.887). Specifically, it was found that the children’s MLU increases by an average of .088 words each months (t = 6,069, p < 0.001), which amounts to about a word a year. Since the F-value (36,838, df = 1) is highly significant (p < 001), these results are unlikely to have arisen from sample error.
Linear Regression
![Page 21: Correlational analysis](https://reader035.fdocuments.in/reader035/viewer/2022062310/56815d73550346895dcb7dce/html5/thumbnails/21.jpg)
Several predictor variables influence the criterion.
Multiple Regression
Plane-pf-best-fit
1. Simultaneous multiple regression2. Stepwise multiple regression
![Page 22: Correlational analysis](https://reader035.fdocuments.in/reader035/viewer/2022062310/56815d73550346895dcb7dce/html5/thumbnails/22.jpg)
Eine Universität möchte wissen, welche Faktoren am besten dazu geeignet sind, den Lernerfolg ihrer Studenten vorherzusagen. Als Indikator für den Wissensstand der Studenten gilt die Punktzahl in einer zentralen Abschlussklausur. Als mögliche Faktoren werden in Betracht gezogen: (1) Punktzahl beim Eingangstest, (2) Alter, (3) IQ Test, (4) Punktzahl bei einem wissenschaftlichen Projekt.
Simultaneous Multiple Regression
![Page 23: Correlational analysis](https://reader035.fdocuments.in/reader035/viewer/2022062310/56815d73550346895dcb7dce/html5/thumbnails/23.jpg)
Predictorentrance examageIQScientific project
Simultaneous Multiple Regression
Criterionfinal exam
![Page 24: Correlational analysis](https://reader035.fdocuments.in/reader035/viewer/2022062310/56815d73550346895dcb7dce/html5/thumbnails/24.jpg)
There is s strong association between the predictor variables and the result of the final exam (Multiple R = 0.875; F = 22,783, df = 4, p = .001 ). Together they account for 73% of the variation in the exam succes. If we look at the four predictor variables individually we find that the result of the entrance exam (B = .576, t = 5.431, p = .001) and the IQ score (B = .447, t = 4.606, p = .001) make the strongest contributions (i.e. they are the best predictors). The predictive value of age (B = .099, t = 5.431, p = .327 and the score on the scientific project is not significant (B = 0.141, t = 1,417, p = 0.168.).
![Page 25: Correlational analysis](https://reader035.fdocuments.in/reader035/viewer/2022062310/56815d73550346895dcb7dce/html5/thumbnails/25.jpg)
In stepwise regression you begin with one independent variable and add one by one. The order of addition is automatically determined by the effect of the independent variable on the dependent variable.
Stepwise Multiple Regression
![Page 26: Correlational analysis](https://reader035.fdocuments.in/reader035/viewer/2022062310/56815d73550346895dcb7dce/html5/thumbnails/26.jpg)
Assumptions Multiple Regression
1. At least 15 cases
2. Interval data
3. Linear relationship between predictor variables and criterion.
4. No outliers (or delete them)
5. Predictor variables should be independent of each other
![Page 27: Correlational analysis](https://reader035.fdocuments.in/reader035/viewer/2022062310/56815d73550346895dcb7dce/html5/thumbnails/27.jpg)
In Linguistics, you often use logistic regression: Multiple
factors determine the choice of linguistic alternates:
1. look up the number - look the number up
2. that-complement clauses - zero-complement clause
3. intial adverbial clause - final adverbial clause
4. aspirate /t/ - unaspirated /t/ - glottal stop - flap
Logistic Regression