NURS 306, Nursing Research Lisa Broughton, MSN, RN, CCRN RESEARCH STATISTICS

STATISTICAL ANALYSIS OF QUANTITATIVE RESEARCH

UNIVARIATE DESCRIPTIVE STATISTICS Frequency distributions Arrangement of values from lowest to highest with a count of how many times each number was obtained Symmetric distribution: the ‘bell curve’ Skewed distribution Positive skew- the peak is to the left and the tail is greater to the right Negative skew- the peak is to the right and the tail is greater to the left

STATISTICAL PRINCIPLES Univariate, bivariate, or multivariate statistics Univariate describe one variable at a time Bivariate describe relationships between two variables Multivariate describe relationships between three or more variables Either descriptive or inferential Descriptive statistics describe data Percentages to describe gender or educational level Averages such as average age or income level Inferential statistics are used to make inferences about data and relationships Use more complex statistical procedures to determine inferences

BELL CURVE

SKEWED DISTRIBUTIONS

UNIVARIATE DESCRIPTIVE STATISTICS Measures of central tendency Mode The number that occurs most frequently in the distribution Median The point in the distribution that divides score in half Mean Average Range Highest score minus the lowest score- determines whether results are homogeneous or heterogeneous Standard deviation Average amount of deviation from the mean Abbreviated SD or plus/minus

RANGE OF SCORES

STANDARD DEVIATIONS IN A NORMAL DISTRIBUTION

BIVARIATE DESCRIPTIVE STATISTICS Contingency tables Two dimensional frequency distribution where the frequencies of two variables are cross tabulated Correlations To what extent are two variables related to each other? Correlation coefficient determines the intensity and direction of a relationship Range is to 1.00, with -1 and 1 being perfect relationships and zero being no relationship Values between 0 and -1 are negative (inverse) relationships Values between 0 and +1 are positive relationships The higher the absolute value of the number (the closer to -1 or +1, the stronger the relationship Most common correlation index is the product-moment correlation coefficient, or Pearson’s r

CALCULATING RISK WITH DESCRIPTIVE STATISTICS Changes in risk after exposure to a potentially beneficial intervention Odds ratio is most widely used calculation of risk Ratio of the proportion of subjects with the adverse outcome relative to those without it

INFERENTIAL STATISTICS Descriptive statistics only summarize data; inferential statistics provide a way for drawing conclusions about a population from the data gathered from a sample Based upon the assumption of random sampling to get the strongest statistical inferences Consists of parameter estimation and hypothesis testing Parameter estimation Used to estimate a parameter- a mean, a proportion; can be point or interval Point estimation is a single statistic to estimate the parameter- for ex., the mean Confidence intervals are used as interval estimation- the range of values within which the parameter has a specified probability of lying Upper and lower limits are called confidence limits Researchers often use either a 95% or 99% confidence interval, meaning the researcher has 95% or 99% confidence that the mean lies between the range of values

INFERENTIAL STATISTICS Hypothesis testing Decides whether hypotheses should be accepted as true or rejected as false Accomplished through more complex statistical tests Answers how probable is it that observed group differences happen by chance? Type I errors The null hypothesis is rejected, when in fact, it is true (more likely) Type II errors Accepting a null hypothesis, when in fact, it should have been rejected (less likely)

INFERENTIAL STATISTICS Level of significance Referred to as the alpha ( p ) Most researchers use.05 or.01: the lower the number, the less likely of a type I error With an alpha of.05, a true null hypothesis would be wrongly rejected 5 times out of 100 With an alpha of.01, a true null hypothesis would be wrongly rejected 1 time out of 100

INFERENTIAL STATISTICS Level of significance Lowering the risk of a type I error increases the risk of committing a type II error Researchers can reduce the risk of a type II error by increasing the sample size Referred to as beta Sample size should be determined by power analysis When the alpha level ( p ) is <.05, researchers report the results as statistically significant ; the results are not likely to have occurred by chance Statistical significance DOES NOT equal clinical significance

BIVARIATE INFERENTIAL STATISTICAL TESTS t -Tests Differences between the means of two groups of people Analysis of variance (ANOVA) Tests the differences in means between three or more groups of people Can also be used to test the effect of two or more independent variables on a single dependent variable Chi-squared test Tests relationships between proportions of cases (%) within different categories Correlation coefficient Pearson’s r can be both descriptive and inferential

MULTIVARIATE INFERENTIAL STATISTICS Tests three or more variables simultaneously Multiple regression Allows researchers to explain or predict a dependent variable with multiple independent variables Multiple correlation coefficient (R), between 0 and 1.00 ANCOVA Similar to ANOVA but allows for statistical control of confounding variables Tests for statistical significance of differences between group means after adjusting scores of the dependent variable to eliminate the effect of the confounding variables (co-variates)

MULTIVARIATE INFERENTIAL STATISTICS Logistical regression Similar to multiple regression but dependent variable is nominal-level (compliant versus noncompliant) Factor analysis Reduce a large set of variables into a smaller, more manageable set Mainly used to develop, refine, or validate complex instruments Multivariate analysis of variance Similar to ANOVA; difference is tests the significance of differences between the means of two or more groups on two or more dependent variables Covariates can also be included (MANCOVA) Causal modeling Development and statistical testing of a hypothesized explanation of causes of a phenomenon Path analysis or SEM

SELECTING STATISTICAL TESTS Consider : Number of independent variables Number of dependent variables Measurement level of all variables Desirability of controlling for confounding variables Match with research questions

ANALYSIS OF QUALITATIVE DATA

QUALITATIVE DATA Transcribing interviews and field notes Begin by organizing data by developing a method to classify and index their data Data must be converted to smaller, more manageable sections Categories are determined, then data is coded into the categories Data analysis Begins with a broad search for broad categories or themes A theme captures the nature of an experience into a meaningful whole Uncovers commonalities across participants Data management software can be used for managing coded data and analyzing relationships