Consider the data in the table below, which records the silver content (percent
ID: 3126465 • Letter: C
Question
Consider the data in the table below, which records the silver content (percent Ag) of 24 coins discovered in Cyprus. The coins were grouped into three classes, corresponding to three different coinages during the reign of King Manuel I Comnenus (1143-1180). Archcologists were interested in whether there were significant differences in the silver content of coins minted at different age-pcriods in King Manuel's reign. Use your calculator to perform analysis of the above data. Make sure you submit the complete write-up. Repeat calculations by SAS. Here, provide only the SAS code and the SAS output. You do not have to repeat the write-up. Use calculator to perform aposteriori analysis if relevant.Explanation / Answer
Here we use ANOVA because there are three groups.
And we have to test the hypothesis that,
H0 : mu1 = mu2 = mu3 Vs H1 : Atleast one of the mean is differ than 0.
where mu1, mu2 and mu3 are population means of three groups.
Assume alpha = level of significance = 5% = 0.05
n1 = number of observations for column1 = 9
n2 = number of observations for column2 = 7
n3 = number of observations for column3 = 8
ANOVA we can done by using EXCEL.
syntax :
Enter data in the EXCEL sheet --> Data --> Data analysis --> Anova : Single factor --> ok --> Input Range : select all range of data --> Grouped by : Column --> alpha : 0.05 --> Output Range : select any empty cell --> ok
Output is :
We see that F = 24.9716
P-value = 2.81E-06
F critical = 3.4668
P-value < alpha
Reject H0 at 5% level of significance.
Conclusion :
Atleast one of the mean is differ than 0.
We can done ANOVA using TI-83 calculator also.
steps :
STAT --> ENTER --> Input data in three columns --> STAT --> TESTS --> F: ANOVA(select all the three columns L1, L2 and L3 by using the keys shift+1, shift+2, shift+3 respectively).--> ENTER
THese steps will also gives the same output.
Anova: Single Factor SUMMARY Groups Count Sum Average Variance Column 1 9 60.7 6.744444 0.295278 Column 2 7 57.1 8.157143 1.189524 Column 3 8 43.9 5.4875 0.24125 ANOVA Source of Variation SS df MS F P-value F crit Between Groups 26.60813 2 13.30407 24.97163 2.81E-06 3.4668 Within Groups 11.18812 21 0.532767 Total 37.79625 23