Significance of changes in mean values over time I have 5 mean life satisfaction values for 5 different years; I have to find out if there is a significant relationship between the survey year and life satisfaction. How should I proceed?
I was thinking about a t-test, but I am not sure about such solution. 
A million thanks to anybody who takes the time to explain.
 A: With 5 observations you can't do much unless the values are very different. 
Examples in MATLAB:
very different:
y=[10 10 15 10 10]';
fitlm([0 0 1 0 0]',y)

ans = 


Linear regression model:
    y ~ 1 + x1

Estimated Coefficients:
                   Estimate        SE          tStat         pValue  
                   ________    __________    __________    __________

    (Intercept)    10          9.7334e-08    1.0274e+08    2.0336e-24
    x1              5          2.1765e-07    2.2973e+07    1.8189e-22


Number of observations: 5, Error degrees of freedom: 3
Root Mean Squared Error: 1.95e-07
R-squared: 1,  Adjusted R-Squared 1
F-statistic vs. constant model: 5.28e+14, p-value = 1.82e-22

not very different
y=[9 10 15 12 13]';
fitlm([0 0 1 0 0]',y)  


ans = 


Linear regression model:
    y ~ 1 + x1

Estimated Coefficients:
                   Estimate      SE       tStat      pValue  
                   ________    _______    ______    _________

    (Intercept)    11          0.91287     12.05    0.0012299
    x1              4           2.0412    1.9596      0.14491


Number of observations: 5, Error degrees of freedom: 3
Root Mean Squared Error: 1.83
R-squared: 0.561,  Adjusted R-Squared 0.415
F-statistic vs. constant model: 3.84, p-value = 0.145

Because your sample size is so small, there's not much you can do. In the simplest model with just one dummy for year 3 you need to estimate 3 parameters on 5 observations. With 5 observations you can barely estimate one parameter reliably, mean. 
So, when you have year really sticking out like in the first example, you can be quite confident that its mean is different. In the second example year 3 is different, but given the variation of results in other years this difference is barely distinguishable. The mean is years 1,2,4,5 is 11 and standard deviation is 1.83, so 15 is not that far from that mean. 
These examples tell you that given a tiny sample size you have find some hypothesis that can be reliably tested on your data. Without looking at the data it's impossible to say what will work.
