Reading

Schmidt & Brown (2021). Evidence-Based Practice for Nurses:

• Chapter 13: What Do the Quantitative Data Mean?

Objective

• Define statistics

• Differentiate between descriptive and inferential statistics

• Identify how frequencies can be graphically depicted

• Describe measures of central tendency and their uses

• Name patterns of data distribution correctly

• Describe measures of variability and their uses

• Discuss the purpose of inferential statistical tests

• Explain how statistical testing is related to chance

• Distinguish between type I and type II errors

• Describe alpha levels commonly used in nursing research

• Match common notations with associated statistical tests

• Identify common statistical tests as parametric or nonparametric

• Describe tests used to determine statistically significant differences between groups

• Discuss tests used to determine statistically significant differences among variables

• Assign commonly used statistical tests to examples based on type of research question and level of measurement

• Interpret data reported in statistical tables

• Differentiate between statistical significance and clinical significance

Categorization of Statistical Tests

• Statistics

  • Statistics with a capital S

    • = The branch of mathematics that collects, analyzes, interprets, and presents numerical data in terms of samples and populations

  • statistics with a lowercase s

    • = The numerical outcomes and probabilities derived from calculations on raw data

• Statistical tests can be broadly categorized as (see figure below):

  • Descriptive

    • = Collection and presentation of data that explain characteristics of variables found in the sample

  • Inferential

    • = Analysis of data as the basis for prediction related to the phenomenon of interest

  • Epidemiological

• In this page, descriptive and inferential statistics are covered. For epidemiological statistics, go to the "Epidemiology" page.

• Wondering what nominal, ordinal, interval, and ratio mean? Go to the "Collecting Evidence" page.

Descriptive statistics are used to provide information regarding univariate or bivariate analyses

• Univariate analysis

  • = The use of statistical tests to provide information about one variable

• Bivariate analysis

  • = The use of statistics to describe the relationship between two variables

  • Multivariate analysis

    • = The use of statistics to describe the relationships among three or more variables

• Mean

  • = The mathematical average calculated by adding all values and then dividing by the total number of values

Measures of Variability

• = Measures providing information about differences among data within a set; measures of dispersion

  • Homogenous

    • = The degree to which elements share many common characteristics

  • Heterogeneous

    • = The degree to which elements are diverse or not alike

• Percentile

  • = A measure of rank representing the percentage of cases that a given value exceeds

• Tailedness

  • = The degree to which a tail in a distribution is pulled to the left or to the right

  • Rule of 68-95-99.7

    • = Rule stating that for every sample 68% of the data will fall within one standard deviation of the mean, 95% will fall within two standard deviations of the mean, and 99.7% of the data will fall within three standard deviations of the mean

Use of inferential statistics to test hypotheses is best suited to research questions or hypotheses that ask one of two broad questions:

• Is there a difference between the groups?

• Is there a relationship among the variables?

Regardless of the type of question being asked, the major unanswered question is: What is the likelihood that the findings could have occurred by chance along?

• Probability

  • = Likelihood or chance that an event will occur in a situation

• Sampling error

  • = Error resulting when elements in the sample do not adequately represent the population

Researchers determine whether the results were obtained by chance using inferential statistical tests, sometimes known as tests of significance

• Statistically significant

  • = When critical values fall in the tails of normal distributions; when findings did not happen by chance alone; when findings support rejecting the null hypothesis

• Statistically nonsignificant

  • = When results of the study could have occurred by chance; when findings support accepting the null hypothesis

It's important to differentiate between statistical significance and clinical significance

• Example 1

  • A drug lowered cholesterol levels on average from 195 to 178, and this decrease was statistically significant

    • However, this finding is not clinically significant because any cholesterol value below 200 is considered to be within the normal range

• Example 2

  • An experimental study involving guided imagery: children in the guided imagery group had an average pain ratings of 4.2, while children in the control group had average pain ratings of 5.2

    • Although the difference between these means is not statistically significant, it may be clinically significant to have pain ratings a whole point lower

Reducing Error When Deciding About Hypotheses

The goal is to avoid the two kinds of errors that can be made when making decisions about null hypotheses:

• Type I Error

  • = When the researcher rejects the null hypothesis when it should have been accepted

• Type II Error

  • When the researcher accepts the null hypothesis when it should have been rejected

Adjust the risk of making Type I and Type II errors

• Alpha level

  • = Probability of making a type I error; typically designated as .05 or .01 at the end of the tail in a distribution

  • Implications of alpha values

    • When the alpha level is set at .05, it is likely that 5 times out of 100 the researcher would make a type I error by wrongly rejecting the null hypothesis

    • When the alpha level is set at .01, a researcher would make a type I error only 1 time out of 100

    • In general, although alpha levels of .01 reduce type I errors, the likelihood of making a type II error increases

The Language of Inferential Statistics

• Parametric

  • = Inferential statistical tests involving interval- or ratio-level data to make inferences about the population

• Nonparametric

  • = Inferential statistics used for nominal- or ordinal-level data or when the assumptions for parametric statistics are not be met

• Degree of freedom

  • = A statistical concept used to refer to the number of sample values that are free to vary; n-1

• Sampling distribution

  • = A theoretical distribution representing an infinite number of samples that can be drawn from a population

Inferential Tests

• Compare the chart and Table 13-12 for inferential statistics

• Testing for differences between groups

  • Chi-Square Statistic

    • = A common statistic used to analyze nominal and ordinal data to find differences between groups

  • t Statistic

    • = Inferential statistical test used when the level of measurement is interval or ratio to determine whether a statistically significant difference between two groups exists

    • correlated t-test

      • = A variation of the t-test used when there is only one group or when two groups are related; paired t-test

    • independent t-test

      • = A variation of the t-test used when participants in two groups are independent from one another

  • Analysis of Variance (ANOVA)

    • = Inferential statistical test used when the level of measurement is interval or ratio to determine if a statistically significant difference between two or more groups exists or a variable is measured three or more times

    • Two variations of ANOVA

      • Analysis of Covariance (ANCOVA)

        • = Used to statistically control for known extraneous variables

      • Multivariate Analysis of Variance (MANOVA)

        • = Researchers use MANOVA instead of ANOVA to analyze data when they have more than one dependent variable

  • Nonparametric tests

    • Kolmogorov-Smirnov test

    • Sign test

    • Wilcoxon matched pairs test

    • Signed rank test

    • Median test

    • Mann-Whitney U test

• Testing for relationships among variables

  • Pearson's r

    • = An inferential statistic used when two variables are measured at the interval or ratio level; Pearson product-moment correlation

  • Multiple Regression

    • = Inferential statistical test that describes the relationship of three or more variables

  • Other tests of significance

    • Nominal-level data

      • phi coefficients

      • point biserials

      • contingency coefficients

    • Ordinal-level data

      • Kendall's tau

      • Spearman's rho

      • discriminate function analysis

Quantitative Analysis Part 2 (13:12)

Quantitative Analysis Part 3 (35:33)

Looking for Part 1? Go to the Collecting Data page!