A caution: "data" is neither stationary nor non-stationary. Stationarity is a characteristic of the random function and in geostatistics the data is a non-random sample from one realization of the random function. ANOVA is based on an assumption of random sampling (to assure the assumption of independence). Random selection of the data locations is not the same thing as random samplling as the term is used in statistics. Having said all this there are some tools to examine whether an assumption of stationarity (of the random function) is reasonable. Make a scatter plot of the data versus the horizontal coordinate and likewise for the vertical coordinate, if there appears to be a trend in either of these it is not reasonable to assume stationarity. Try fitting the data to a trend surface, if any of the coefficients is significantly non-zero then it is not reasonable to assume stationarity. Compute and plot the sample variogram, if it shows a growth rate of two or greater then it is not reasonable to assume stationarity. The scatter plots will also provide some insight into whether an assumption of constant variance is reasonable, i.e. does the scatter of the data values change with the value of  the horizontal/vertical  coordinate