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tokens: catalogue, in units of (100 km s −1 ) 2 . The bin width is 500 km s −1 (redshift). The black dashed line shows the original simulation catalogue; the red solid line with error bars is the average of the perturbed catalogues. The error bars show the standard deviation of the perturbed results, which is regarded as the measurement error. The background contours indicate the cosmic variance from Fig. 2 . Figure 5. The dashed line shows the standard deviation of the cosmic variance of the correlation statistic ψ 1 at the redshift separation bin 0–500 km s −1 of the simulation catalogues as a function of sample size. The solid line indicates measurement error of the perturbed sample averaged over all the bins as a function of sample size, in units of 1000 km 2 s −2 . The contours show the 68 per cent and 95 per cent ranges of the results, whereas the error bars are the standard deviations of the measurement errors. 4.3 Measurement error and sample size Once we have a large enough sample size to adequately probe a volume, we do not expect cosmic variance to change with sample size, since in this case it is due to the variations between volumes of a similar size. To decrease the cosmic variance we would need to increase the depth of our sample; larger volumes should vary less as we approach the scale of homogeneity for the Universe. In contrast, we can reduce the effect of measurement errors by increasing our sample size, even if the volume being probed stays the same. To characterize the effect of sample size on measurement errors, we select new mock surveys with up to 20 000 galaxies by changing in equation ( 1 ) while leaving the other selection function parameters unchanged. We then perturb them using the same method described in Section 4.2 . In Fig. 5 , we show how the cosmic variance and measurement errors of the correlation statistic ψ 1 changes with sample size. Increasing the sample size reduces the statistical errors significantly, while, as expected, the cosmic variance doesn’t show significant difference. 5 CORRELATION RESULTS Fig. 5 shows the relationship between sample size and statistical error. Using this relation, we can calculate the statistical error of CF3 surveys, which have many more data points than the CF2 surveys. Fig. 6 shows the correlation function of CF3-galaxy survey with Hubble constant H 0 = 75 km s −1 Mpc −1 ; this is the value given by Tully et al. ( 2016 ) as the best fit to the data. We see that the correlation function of CF3 is larger than the mean value of correlations of mock catalogues. Hellwing et al. ( 2017 ) show that cosmic variance of local group (LG) observer mocks with a Virgo-like cluster is larger than the Copernican observer mocks without Virgo, which explains the smaller mean correlation value from mocks in Fig. 6 . Figure 6. Velocity correlation functions of CF3-galaxy survey with H = 75 km s −1 Mpc −1 . ψ 1 , ψ 2 , ψ ∥ , and ψ ⊥ are in units of (100 km s −1 ) 2 . The solid line shows the