ONE WAY ANOVA WITH SHORTCUT METHOD AND SPSS

1. ONE WAY ANOVA

2. WHAT IS ANOVA?
 ANALYSIS OF VARIANCE ABBREVIATED AS ANOVA
 STATISTICAL TECHNIQUE
 DEVELOPED BY R.A. FISHER
 USED IN THE AREAS OF BUSINESS,INDUSTRIES,ECONOMICS,PSYCHOLOGY,ETC
 PREFERRED WHEN THERE IS MORE THAN ONE SAMPLE
 STATISTICAL TECHNIQUE USED TO MEASURE THE MEANS OF TWO VARIABLES
 IT INVOLVES ONE INDEPENDENT VARIABLE AND ONE DEPENDENT VARIABLE

4. What does this test do?
 The one-way ANOVA compares the means between the groups you are
interested in and determines whether any of those means are statistically
significantly different from each other. Specifically, it tests the null
hypothesis:
 where µ = group mean and k = number of groups. If, however, the one-way
ANOVA returns a statistically significant result, we accept the alternative
hypothesis (HA), which is that there are at least two group means that are
statistically significantly different from each other.

5. ASSUMPTIONS
1) The values in each group are normally distributed.
2) The variance within each group should be equal for all groups.
3) The error (variation of each value around its own group mean) should be
independent for each value.

6. STEPS TO CARRY OUT THE TEST
1. STATE NULL AND ALTERNATIVE HYPOTHESIS
H0 : all sample means are equal
At least one sample has different mean
i  ...H 210
equalaretheofallnotHa i

7. 2. STATE ALPHA
 = 0.05
3. CALCULATE DEGREE OF FREEDOM
K-1 & n-1
k= No of Samples,
n= Total No of observations

8. 4. STATE DECISION RULE
If calculated value of F > table value of F, reject Ho
5. CALCULATE TEST STATISTIC
-Calculate variance between samples
-Calculate variance within the samples
-Calculate F statistic
-If F is significant perform post hoc test
6. STATE RESULTS AND CONCLUSION

9. X1 (X1) 2 X2 (X2 )2 X3 (X3 )2
10 100 9 81 14 196
10 100 5 25 9 81
16 256 18 324 13 169
9 81 4 16 14 196
15 225 6 36 5 25
Total 60 762 42 482 55 667
Total sum of all observations = 60 + 42 + 55 = 157
Correction factor = T2 / N=(157)2 /15= 24649/15=1643.26667
Total sum of squares (SST)= 762 + 482 + 667 – 1643.26667 = 267.73333
Sum of square b/w samples (SSB)=(60)2/5 + (42)2 /5 + (55) 2 /5 –
1643.26667=34.5333
Sum of squares within samples= (SST) – (SSB)
=267.73333 – 34.5333= 233.20003

10. Formulas for shortcut method
 Total sum of all observation = X1 + X2 + X3 + … + Xn
 Correction factor = T2 / N
 Total sum of squares (SST) = X12 + X22 + X32 + … + Xn2 - T2 / N
 Sum of squares between samples (SSB)
= (X1)2 /n1 + (X2)2 /n2 + (X3)2 /n3 + … + (Xn)2 /n - T2 / N
 Sum of squares within samples (SSW) = (SST) – (SSB)

11. ONE WAY ANOVA IN SPSS

12. Click Analyze > Compare Means > One-Way ANOVA... on the top menu, as shown below.

13. You will be presented with the One-Way ANOVA dialogue box:

16. Click the Button. Tick the Descriptive checkbox in the –Statistics– area, as shown below:

17. THANKYOU!