Proportions

An exceptionally high signal noise ratio obscuring genuine variances existing between examined groups thereby confounding outcomes sought after examinations conducted suitably designed experiments investigative studies alike.

Overly conservative critical regions established criteria whereby virtually impossible ever refute initial presumptions regardless findings actuality.

High type II errors probablities inherent methodology employed meaning true existent discrepancies going undetected frequently.

Lack adequate power due insufficiently large sampled data set given underlying variance populations themselves.

Calculates P-value by comparing the observed statistic to the theoretical null hypothesis, thus aiding the decision-making process.

Generates confidence intervals around the parameter estimate, providing an alternative method of establishing the importance of the result.

Provides a visual representation of critical regions under the curve to assist in conceptual understanding.

Performs calculations necessary to derive the margin of error, which supplements the determination of precision.

Consistency Across Trials Strengthening Evidence Against Alternative Hypothesis

Large Sample Sizes Increasing Power Detecting Actual Differences

Agreement with Null Values Reducing Impact of Sampling Variability on Outcomes

Small Effect Size Decreasing Likelihood of Observing Statistically Significant Outcome

Reject the null hypothesis

Inconclusive

Fail to reject the null hypothesis

Accept the null hypothesis

Reject the null hypothesis

Accept the null hypothesis

Fail to reject the null hypothesis

Inconclusive

To calculate the effect size

To evaluate the statistical significance of the results

To determine the type of test statistic to use

To determine the sample size

Systematic random sampling

Simple random sampling

Cluster sampling

Convenience sampling

p = 0.4

p = 0.7

p = 0.5

p = 0.56

When analyzing data which shows minimal variability and thus requires less stringent testing.

When assessing public health risks where even slight deviations from expected proportions could have serious consequences.

When the population/sample size is large enough that any resultant statistical difference is likely due to random chance.

When preliminary results suggest the true population proportion is likely close to the hypothesized proportion, thus justifying more lenient criteria.

The sample proportion should equal the hypothesized population proportion exactly.

The population distribution must be uniform across all categories.

Each individual outcome within the sample should have equal probability.

The sample size needs to be large enough so that $np$ and $n(1-p)$ are both greater than 10.