# Sampling Distribution of the Mean

Respond using one or more of the following approaches:

Ask a probing question, substantiated with additional background information, and evidence.

Share an insight from having read your colleagues’ postings, synthesizing the information to provide new perspectives.

Group B

Inferential Statistics- Based on probability; used to draw conclusions or make generalizations about a given population or problem.

Example: “What can I infer about 5-minute Apgar scores of premature babies (the population) after calculating a mean Apgar score of 7.5 in a sample of 300 premature babies?” (McGonigle & Mastrain, p. 376, 2017).

Sampling Distributions- A sampling distribution is the frequency distribution of a statistic over many random samples from a single population.

Sampling Distribution of the Mean – as an example we randomly draw test scores from 25 students out of a total group of 5,000. We then calculate the mean, then draw a new group and repeat; each mean will serve as one datum, or data point.

Hypothesis Testing- is the use of statistics to determine the probability that a given hypothesis is true.

Null Hypothesis- the hypothesis that there is no significant difference between specified populations; or differences can be attributed to sampling or experimental error

Type 1 Error- This error occurs when we reject the null hypothesis when we should have retained it.

Type 2 Error- This error occurs when we fail to reject the null hypothesis. In other words, we believe that there isn’t a genuine effect when actually there is one.

Parametric statistics – A class of statistical tests that involve assumptions about the distribution of the variables and the estimation of a parameter.

Nonparametic statistics – A class of statistical tests that do not involve stringent assumptions about the distribution of variables. Between-subject design – A research design in which separate groups of people are compared (e.g. smokers and nonsmokers; intervention and control group subjects). Within-subject design – A research design in which a single group of participants is compared under different conditions or different points in time (e.g. before and after surgery).

Two classes of Statistical Tests:

Parametric tests – tests involving an estimation of a parameter, the use of interval or ratio-level data, and the assumption of normally distributed variables. Include t-tests and ANOVA.

Nonparametric tests – used when the data are nominal or ordinal or when a normal distribution cannot be assumed. Include the Mann-Whitney U test, Wilcoxon signed – rank test, and Kruskal – Wallis test.

Statistical Tests

T-test parametric procedure identifying mean differences for two independent groups, like experiment versus control or dependent groups, like pretreatment and post-treatment scores.

One – way ANOVA – tests the relationship between one categorical independent variable, such as different interventions, and a continuous dependent variable.

Independent t-test – used to compare mean values of a single group to a hypothesized value.

Two- way ANOVA – tests multiple hypotheses with two independent variables

Paired t -test – Obtaining two measurements from the same people or from a paired set of participants. This measures the difference between two related groups. Used when the means for two sets of scores are not independent.

Repeated – measures ANOVA – tests the same group using three or more measures of the same dependent variable.

ANOVA – parametric procedure for testing differences between means when there are more than three groups.

Chi-Square test – used to test hypothesis about group differences in proportions. It is computed by comparing observed frequencies and expected frequencies, in which there was no relationship between variables.

One-tailed test – A statistical test in which only values in one tail of distribution are considered in determining significance. A one-tailed test allots all of your alpha to testing the statistical significance in the one direction of interest.

Two-tailed test – Statistical tests in which both ends of the sampling distribution are used to determine improbable values. A two-tailed test allots half of your alpha to testing the statistical significance in one direction and half of your alpha to testing statistical significance in the other direction.

There are different types of statistical methodologies, inferential statistics are based on probability. Ali and Bhaskar (2016) define probability as “the likelihood that an event will occur” (para. 21). According to Hyatt, Powell, Johnson, and Caldwell (2017) a working knowledge of inferential statistics is needed to understand, interpret, and critically evaluate research studies. The basic premise of inferential statistics is to generate data from random samples and use it to describe or make inferences about an entire population (Ali & Bhaskar, 2016). A basic understanding of inferential tests will help nurses implement research into evidence-based pracitce.

While there are various inferential tests, it is important to understand that they all use probability to infer meaning; that meaning is subsequently applied mathematically to a larger population. For example, Polit and Beck (2017) report that the T-tests is a hypothesis testing tool which compares two groups of data sets to find the difference between them. In nursing research, this test can be utilized to determine if there is causality or any relationship between data sets. Analysis of variance (ANOVA) involves mathematically analyzing data. This test is useful in comparative analysis. For example, the efficacy of interventions, such as different ambulation protocols can be compared with through ANOVA. Inferential statistics also facilitate comparisons of proportions; this is achieved with the Chai Square test. This test is often used to compare differences between the interventional and the control groups (Polit, Beck 2017). While it is unlikely that non-researchers will retain knowledge of the various statistical tests, being able to identify the statistical methodology will help them to better interpret research results.

References

Ali, Z., & Bhaskar, S. B. (2016). Basic statistical tools in research and data analysis. Indian journal of anaesthesia, 60(9), 662–669. doi:10.4103/0019-5049.190623

Polit, D. F., & Beck, C. T. (2017). Nursing research: Generating and assessing evidence for Nursing practice (10th Ed.). Philadelphia, PA: Wolters Kluwer.Chapter 17, “Inferential Statistics”

Hayat, M. J., Powell, A., Johnson, T., & Cadwell, B. L. (2017). Statistical methods used in the public health literature and implications for training of public health professionals. PloS one, 12(6), e0179032. doi:10.1371/journal.pone.0179032