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Case study on One way ANOVA
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Transcript of Case study on One way ANOVA
Outline of case study presentation
a)Introduction
b)Research Question
c) Research hypothesis
d)Normality test
e) Statistic hypothesis (Ho and Ha)
f) Descriptive analysis(bar chart/ pie chart /mean,
standard deviation, median,IQR)
g) Inferential analysis (t, F, r, X2)
h)Conclusion (follow APA style)
The Pearson Correlation (r)
Is an index of relationship between two variables
Is represented by the symbol ‘r’
Reflects the degree of linear relationship between two
variables
It is symmetric. The correlation between x and y is the
same as the correlation between y and x.
It ranges from +1 to -1.
Significance of the Test
Correlation is a useful technique for investigating the
relationship between two quantitative, continuous
variables. Pearson's correlation coefficient (r) is a
measure of the strength of the association between the
two variables.
The Pearson Correlation (r)
A perfect
linear
relationship,
r = 1
A perfect
negative
linear
relationship,
r = - 1
A correlation
of 0 means
there is no
linear
relationship
between the
two variables,
r = 0
A correlation of .8 or .9 is regarded as a high correlation
there is a very close relationship between scores on
one of the variables with the scores on the other.
A correlation of .2 or .3 is regarded as low correlation
there is some relationship between the two variables,
but it’s a weak one.
Formula Used (for manual calculation):
Where:
x : Independent variable (BMI)
y : Dependent variable (Systolic)
r = Ʃxy
(Ʃx2) (Ʃy2)
Statement of the Problem
To correlate the relationship between the following demographicvariables. For our group, we have to find the correlation betweensystolic and the BMI (weight and height) among the adults . Does thelevel of systolic being influence by the BMI level of a person?
a. Ageb. Racec. Smoking habitd. Level of COe. Systolicf. Diastolicg. Waisth. HipI . Highj . Weightk. Glucosel. Cholesterol
BMI = Weight (kg)Height 2(m)
Is there a correlation between the systolic level and the BMI
reading of 96 adults?
BMI = Independent VariableSYSTOLIC = Dependent Variable
RESEARCH HYPOTHESIS
There is a linear relationship between the systolic level and the BMI reading.
Ho : Data is normally distributed
Ha : Data is not normally distributed
For normality test, we referred to Shapiro –Wilk (sample size is < 100). From
the Normality table, W (Sig. Shapiro-Wilk) = 0.099 for BMI , 0.281 for Systolic.
Since Shapiro-Wilk sig value is more than alpha value (α > 0.05) thus the
normality assumption is not violated.
Conclusion : Data is normally distributed.
PROBLEM:
Is there a correlation between the
systolic level and the BMI reading of
96 adult?
n = 96
Statistic Hypothesis (Ho and Ha)
Ho: = 0
Ha: ≠ 0
: Rho
Scatter Plot
This scatterplot shows that there is a linear relationship between the two variables.
Putting the Formula together:
ANALYSIS IS DONE USING SPSS VERSION22
At alpha a = 0.05 compare the sig. value from correlation table in
SPSS output.
The Pearson Correlation (r) between Systolic and BMI is 0.228. This
correlation is statistically significant (Sig < 0.05)
Pearson Correlation = 0.228
N= 96
Sig (2-tailed) = 0.025
r = 0.228 , The systolic and BMI are moderately correlated
Coefficient of correlation, r2 = 0.052x100% = 5.2%
That is 5.2% of the variability in systolic can be predicted
by variability of BMI
Effect Sizer > 0.5 strong correlation
0.2< r < 0.3 moderate
correlation
0< r <0.1 weak correlation
Conclusion
To assess the size and direction of the linear relationship
between systolic and BMI, a bivariate Pearson’s product-movement
correlation coefficient ( r ) was calculated. The bivariate correlation
between these two variables was positive but moderate.
r(94) = 0.228 , α , 0.05
Degree of freedom for bivariate correlation are
defined as N – 2 (where N is the total sample)
Prior to calculating r, the assumptions of normality was assessed and
found to be supported. A visual inspection of the box plot and histogram
for each variable confirmed that both were normally distributed. In
conclusion, the Pearson’s Correlation (r) between systolic and BMI is
0.228. This correlation is moderately correlated and statistically significant
(Sig. <0.05).
Rerefences
Allen, P., & Bennett, K. (2010). PASW STATISTIC BY
SPSS: A PRACTICAL GUIDE VERSION 18.0. Australia:
CENCAGE Learning.
Cheong, W. K., & Kai Lit, P. (2006). Statistics Made
Simple for Healthcare and Social Science
Professionals and Students. Malaysia: Universiti
Putra Malaysia Press.
SUGGESTION
Although it shows that there is a correlationbetween systolic level and BMI with moderatecorrelation between this two variables (r= 0.228),but the assumption of linearity cannot be met.
When assumption of linearity cannot be met, thesuitable alternative to the Pearson’s correlation isSpearman’s Rho and Kendall’s Tau- B.