Data Measurement & Descriptive Stats: Levels, Types, & Techniques, Exams of Nursing

Download Data Measurement & Descriptive Stats: Levels, Types, & Techniques and more Exams Nursing in PDF only on Docsity! PUBH 8500 MEASUREMENT STUDY GUIDE MIDTERM 2024 Levels of Measurement  Data are collected and coded into numbers  Levels define what the numbers assigned to variables represent  There are 4 levels or scales o Nominal: numbers represent assigned or named categories (e.g., 1 = male, 2 = female) o Ordinal: numbers represent ranked or ordered categories that are not necessarily equal in size (e.g., 1 = low, 2 = medium, 3 = high) o Interval: numbers represent values of equal units (e.g., temperature, age in years). Note: temperature of 0°C is not the same as 0°F and 0° on both scales does not mean there is no temperature; age in years is not ratio because 0 years old is anywhere between birth and the day before the first year. o Ratio: numbers represent values of equal units and there is a set zero point (height, weight, blood pressure) Note: with ratio data ONLY, values can be compared as ratios (e.g., a risk factor doubled the odds of disease, a diet supplement resulted in a 5% weight loss) Rules:  Higher level data can be converted to a lower level Examples: o ratio data for weight loss can be arranged in 5 lb. interval groups; o interval age in years can be converted to ordinal age groups such as 5-17, 18-44, 45-64, >65 years; o ordinal ranks can be combined in nominal categories as in 1 = agree and strongly agree, 2 = disagree and strongly disagree, 3 = no opinion, (where there is no specific order)  Lower level data cannot be converted to a higher level Data types:  There are 3 data types o Categorical: nominal and ordinal data; numbers represent categories (examples: gender, race/ethnicity) o Ordinal: categorical data that are ranked; not everyone makes this distinction (examples: low, medium, high) o Continuous: interval and ratio data; numbers represent numerical values (examples: age, height, weight) Rules (extension of the rules for levels of measurement): o Continuous data can be transformed to categorical data o Categorical data cannot be transformed to continuous data Descriptive Statistics  Descriptive statistics describe the data  Types of descriptive statistics o Frequency data ▪ How often (or frequent) a measurement occurs in the sample or population ▪ Used primarily with categorical data ▪ Often presented as numbers (sample “n” or population “N”) and percentages (%) of observations Examples: n (%) male, n (%) female in a cohort; N (%) age <18, N (%) age 18-44, N (%) age 45-64, N (%) age ≥65 in a population ▪ Can describe relationships between two variables Examples: a study showing n (%) females with BMI ≥30 and n (%) males with BMI ≥30; N (%) <18 years who have smoked, N (%) <18 years who never smoked ▪ Usually presented in tables (tabular format) o Measures of central tendency ▪ Show where the bulk of the data lie; where most of the data are centered. ▪ Includes the Mean, Median, and Mode ▪ The level of measurement can determine which descriptive statistic can be used Mean  Sum of measurement values divided by the number of observations  Should only be used with continuous data  Is affected by extreme values Median  The midpoint or the center of all data in a variable level  Can be used with continuous and ordinal data, but NOT nominal data  There are equal numbers of observed values above and below the median  Is not summed  Not affected by extreme values; always remains in the center Mode  The most frequently occurring value  Can be used with ALL data types – categorical, ordinal AND continuous o Measures of variability or dispersion ▪ Includes Range and Percentiles, Variance and Standard Deviation  An adaptation of the z score that does not require that the population mean or standard deviation be known  Data must be continuous and the variable(s) of interest must be normally distributed  Compares the means of two groups; it cannot compare more than two  Used with small samples (≤ 30). Assumptions: o The distribution must be close to normal (so the data are continuous) o The grouping variable must be categorical and dichotomous  t statistic is used to estimate the magnitude of difference in the means of two groups; the bigger the t statistic, the greater the difference and the more significant the difference  Uses sample data when population mean and standard deviation which are not known  t statistic helps determine confidence intervals associated with a statistical hypothesis about the mean of a population or the means of two populations  significance is based on the confidence interval  sample size influences the interpretation of the t statistic, but not the interpretation of the 95% confidence interval Variations of the t test: Paired t test - tests the null hypothesis that there is no difference in the means of two groups that share characteristics Assumptions: o The distribution is close to normal (so the data are continuous) o Grouping variable is categorical and dichotomous o Groups are not independent Examples of groups that are not independent: Repeated tests of the same individual Different parts of the same individual (two legs, two eyes) Identical twins with identical genes Independent t tests: tests the null hypothesis that there is no difference in the means of two groups that different Assumptions: o The distribution is close to normal (so the data are continuous) o Grouping variable is nominal (categorical) and dichotomous o Groups are independent Pooled t test Performed when group variances are essentially equal Separate t test Performed when group variances are not equal F-statistic o used to compare variances o Used with populations or large samples o similar to t statistic, but compares variances of two groups rather than means o significance is based on a p value (not the confidence interval) z score  A standardization where the mean is 0 and the standard deviation is 1  Based on a population with a normal distribution  The true the population mean and standard deviation are known Chi Square Test Statistic and Distribution  Compares the observed results to the expected ones based on: o Known theories o Hypothesis o Comparison groups Assumptions:  Groupings are categorical  Categorical groups are mutually exclusive – there can be no overlap (data in one group cannot also be in another group)  Adequate sample size  Groupings are meaningful because there is a theoretical basis for them Comparing observed results to expected results use the following formula: 2 = Σ(Observed – Expected)2 or 2 = Σ(Observed – Expected)2 / Expected Expected o Using this formula, look up the result (the chi square statistic) on a chi square table to determine whether the results are significant. In the Forthofer text, the critical values listed are probabilities below table value. We are mainly interested in the values above the curve. Thus, a number equal to or larger than that found under the 0.95 column for 1 degree of freedom would be significant because the probability of the result occurring by chance is less than 1 – 0.95 = 0.05 or 5%. Comparing two groups to see if they are significantly different, you can also use a 2 x 2 contingency table or cross tabulation with the following formula: Disease Exposure Yes No Total Yes a b n No c d n Total n n N 2 = (ad – bc)2 * N (a+c)(b+d)(a+b)(c+d) o Using the chi square table and interpreting the chi square statistic: Step 1. Plug the numbers you have in the table Step 2. Calculate the numerator and denominator Step 3. Divide the numerator by the denominator Step 4. Look up the chi square result with 1 degree of freedom in the chi square table at the back of the text (p. 466 in Forthofer, Lee, & Hernandez) Degrees of freedom = (# in rows – 1) * (# in columns – 1) = 1 Step 5. With 1 degree of freedom, if the number falls in a column ≥0.95, there is a significant difference. In general, a large 2 means the two groups are not similar; a small 2 means the two groups are similar. It is important to remember there may be times when you do not want the chi square to show a significant difference (e.g., testing for differences in 2 arms in a randomized trial, where you want the two groups to be as similar as possible). Examples of comparisons using chi square: 1. Comparing an observed distribution to a normal distribution 2. Comparing a current distribution to a previous or other distribution pattern 3. Looking for an association between 2 nominal variables 4. Testing the independence of 2 nominal variables