Comparing continuous case counts across groups without group means Biostatistics student here hoping for some helpful input.
I am working on an assignment, and have a dataset containing summed disease case counts for a country - one case count per year. I've been asked to use the total case count for each year as my outcome variable. The assignment is asking me to test whether there are statistically significant differences in case counts between a set of six different years (2005 - 2010), and the assignment states that total case count should be treated as a continuous variable.
Normally if I were comparing continuous outcomes between six groups, an ANOVA would be my go to. However, I don't have means for these various "groups" (years) - just the total counts for each year. Is there a statistical test that will allow me to test whether there are significant differences between yearly case counts? I'm stuck, currently working in R, and would appreciate any thoughts!

If all you have is counts, I believe your only option is using a chi-squared test or something equivalent. For instance, say you have these data for the six years:
df <- data.frame(count = c(900, 500, 1220, 1300, 1500, 1600),
                 year = c(2005, 2006, 2007, 2008, 2009, 2010))

Then you can do:
chisq.test(xtabs(df$count ~ df$year))

# Chi-squared test for given probabilities

# data:  xtabs(df$count ~ df$year)
# X-squared = 713.68, df = 5, p-value < 2.2e-16

However, this is very different from what an ANOVA does. This only tells you that your count values seem to be unrelated. If there was more consistency across your counts, then you would get a larger p-value. e.g:
df2 <- data.frame(count = c(1020, 1000, 1004, 1005, 1010, 999),
                 year = c(2005, 2006, 2007, 2008, 2009, 2010))

chisq.test(xtabs(df2$count ~ df2$year))

# Chi-squared test for given probabilities

# data:  xtabs(df2$count ~ df2$year)
# X-squared = 0.29944, df = 5, p-value = 0.9977

