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The **normal curve tests of means and proportions** refer to those tests that are basic methods of testing the possible differences between two samples. The normal curve tests of means and proportions can also be referred to as parametric tests under the assumption that the population follows a normal distribution. Normal curve tests of means and proportions are used when the size of the sample is more than 29.

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There are certain conceptual terms that are helpful to know to better understand the normal curve tests of means and proportions.

The deviation scores in normal curve tests of means and proportions are defined mathematically as the difference between the observed score and the mean for any particular variable. The deviation score in normal curve tests of means and proportions is generally zero, since half of the deviations are above the mean value and the other half are below the mean value.

The standard error in normal curve tests of means and proportions is used to estimate the variability of the sample means. Since there is only one sample in the normal curve tests of means and proportions, the estimated standard error can be computed by the ration between the standard deviation and the square root of the sample size.

The confidence limits in the normal curve tests of means and proportions set the upper and the lower bounds on an estimate for a given level of significance. In the normal curve tests of means and proportions, these limits are regarded by the researchers as they provide additional information about the estimates.

The normal curve tests of proportions in normal curve tests of means and proportions are used to test the difference in the proportions or the percentages rather than the means.

When two independent samples are tested by the researcher in the normal curve tests of means and proportions, then some different formulas are used, although the main aim remains the same. Thus, the comparison of the z values with the critical values in the table is done under the normal curve.

When the correlated two samples test is used by the researcher in the normal curve tests of means and proportions, then the two correlated samples are factored into the formulas for the two sample means and proportions test. The notations that are in these samples of the normal curve tests of means and proportions are similar to the previous samples with an addition of the Pearsonian correlation.

There are also certain assumptions in the normal curve tests of means and proportions.

The first assumption of the normal curve tests of means and proportions is that as the name suggests, the variable of interest should be normally distributed in the population.

The second assumption of the normal curve tests of means and proportions is that the data should be of interval scale.

The third assumption of the normal curve tests of means and proportions is that the size of the sample should not be small.

The fourth assumption of the normal curve tests of means and proportions is that there should be homogeneity within the variances. This assumption of the normal curve tests of means and proportions is used in two sample testing cases.

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