Nursing 6052

Group B: Chapter 17

Guadalupe Smith

Jessenia Martinez

Kharen Dreyfus

Kelly Flack

**Chapter 17: Inferential Statistics Based on The Laws of Probability**

**Inferential Statistics:** provide a way to generalize what a population might think or be, based on data gathered from a sample of the population. Inferential statistics help the researcher to make objective judgments about the reliability of sample estimates.

In inferential statistics, the researchers usually take a small sample of data from a more substantial set of statistics to get information on the populations. A sample is a smaller subset of the population therefore researchers must be very careful while collect data to make sure the sample is random and not to create unintentional bias. To be a truly random sample, every member of the population considered has the same chance. Also, the selection of one member is independent of another. In theory, the collection of the random sample is made by pure chance to keep the data uncompromised (Polit & Beck, 2017).

The three main ideas this chapter discusses are the following: importance of nurses reviewing and understanding research studies, the description of statistical methods and the explanation of the key statistical tests and how they measure.

**The Importance of Nursing Reviewing and Understanding Research Studies**

Research studies are the integration the research and evidence-based practice. Nurses discussed research to gather information that provided the foundation for nursing practice that optimizes the delivery of quality of bio-psycho-social interventions. The goal of the nursing research is the generation of knowledge to guide practice. Nurses must continue to comprehend the significances of care we provided wether is intended or unintended needs to be based on best evidence-based practice. Research allows nurses to continually advance to improve the quality of care and meet the requirements of patients. Research agendas provide direction and guidance to nurses via evidence-based practice. Which the goal is to provide a better more reliable way to deliver care to the patients (Given, 2009).

**Statistical Methods and Examples of Use**

__One Tailed and Two Tailed Tests__

· **One Tailed Tests **– Means both tails of the sampling distribution are used to determine improbable values.

· Example: If you wanted to test whether intervention A is better than intervention B, a one tailed test will tell you whether intervention A is better than intervention B, but won’t tell you if it was worse or the same as.

· **Two Tailed Tests **– Uses both positive and negative results.

· Example: If you want to tell if intervention A is either better or worse than intervention B.

__Parametric Test__

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

· Example: study testing the effect of early hospital discharge on maternal competence of primiparas

· **Independent t-test **used to compare values of a single group, to a hypotheses value.

· Example: Study of effects of early discharge of maternity patients on perceived maternal competence.

· A **paired t-test** is used for dependent groups when the means for two sets of scores are not independent.

· Example: Study comparing BMI of college student in their freshman and senior years.

· **Analysis of variance (ANOVA): **parametric procedure for testing differences between means when there are more than three groups.

· **F-ratio** is when variation between groups is contrasted to variation within groups. When differences between groups are relative to variation within groups, the probability is high that the independent variable is related to group differences.

· **One-Way ANOVA **tests the relationship between one independent variable, like a specific intervention and a continuous dependent variable.

· Example: study that tests the effect of different smoking cessation interventions on first day cigarette consumption and then one month after the intervention in at least three groups of smokers.

· A **Two-Way ANOVA **enables studies with two and three hypotheses to be analyzed.

· Example: study that tests if two smoking-cessation interventions were equally effective in both men and women participants.

· **Repeated-measures ANOVA **can be used for a single group that is studied longitudinally or in a crossover design with three or more conditions.

· Example: study of three interventions for preterm infants regarding feeding rates, nonnutritive sucking, nonnutritive sucking plus music or music alone.

__Nonparametric Tests__

· The **Mann-Whitney U test** is a nonparametric test which involves assigning ranks to two groups of scores. Sums can then be compared using the U statistic.

· The** Wilcoxin signed-rank test **is a nonparametric test that can be used when ordinal-level data are paired. It involves taking the difference between compared scores and ranking the absolute difference.

· The **Kruskal-Wallis test** is the nonparametric analog to ANOVA which assigns ranks to the scores of various groups. It is used with multiple groups (independent variables).

· The **Friedman test** for analysis of variance by ranks is used when multiple measures (dependent variables) are obtained from the same subjects.

__Testing Differences in Proportions:__

· The **Chi-square test** is 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.

· Example: study to test whether poverty status and race was related to sleep-related death in infants.

· **Fisher’s exact test** can be used to test the significance of differences in proportions.

· **McNemar’s test** is used to test the significance of differences in proportions when the proportions being compared are from two paired groups.

__Statistical tests used when both the independent and dependent variables are ordinal, interval, or ratios__

· **Pearson’s r** is the correlation coefficient calculated when two variables are measured on at least the interval scale. The null hypothesis is that there is no relationship between two variables.

· Example: study that mother's postpartum psychological state is related to breast milk secretory immunoglobin.

· **Kendall’s tau or Spearman’s rho** are correlation coefficients that can be used when data is at the ordinal-level or violation of the parametric test has occurred.

· **Spearman’s rho** measures the relationship between two variables and the direction and strength of the linear relationship, both variables can increase or decrease together, or both variables may be opposite.

· **Kendall’s tau** is used to show the degree of an association among ordinal variables.

· Power Analysis and Effect Size:

· The probability of a type II error is **beta** (β). The **power** of a statistical test is the probability that it detects a true relationship or group difference.

· **Power analysis** is used at the onset of a study to decrease the likelihood of Type II error and to boost the statistical conclusion validity through early estimation of the sample size needed.

· There are four components to power analysis, which include: sample size (N), effect size (ES), power (1-β), and significance criterion (α).

· α represents the level of significance and is usually set at .05 & power is standardly represented by .80 (leaves 20% risk of committing type II error)

· To determine N, the effect size must be estimated. The **effect size **is the magnitude of the relationship between research variables.

· When relationships are strong, they can be detected with smaller sample sizes. When relationships are weak, large samples must be used to prevent type II errors.

· Effect size is estimated by the researcher and based on prior research findings of similar studies or the researchers’ expectation that small, medium, or large effects will occur.

· Sample size estimates for testing two different means

· In two-group situations, ES is designated as Cohen’s d. It is found by dividing the effect size (*d*) by the population standard deviation (σ).

· The effect size (*d*) is the difference between two population means.

· The population values are not known but must be estimated.

· Alternative approaches exist using ANOVA, Pearson’s r, or chi-square as the basis of the power analysis

· Power analysis is sometimes completed after analysis is complete to determine the population effect on the actual population.

· Effect sizes provide readers and clinicians with estimates about the magnitude of effects, or the importance of the findings, which helps to support evidence-based practice.

**References**

Given, B. (2009). Guest editorial. 2009-2013 Oncology Nursing Society research agenda: why is it important? Oncology Nursing Forum, 36(5), 487-488. doi:10.1188/09.ONF.487-488

Polit, D. F., & Beck, C. T. (2017). *Nursing research: Generating and assessing evidence for nursing practice *(10th ed.). Philadelphia, PA: Wolters Kluwer.