University:
American Career College
Course:
NURS115 | Intermediate Medical
Academic year:

2020
Views:

234

Pages:

70
Author:

Gracie Bullock

Descriptive Statistics Statistics Includes: Descriptive statistics 1) Collecting 2) Organizing 3) Summarising 4) Presenting Data Statistics Includes: Inferential statistics 1) Making Inference 2) Hypothesis Testing 3) Determining Relationships 4) Making Prediction Definition Statistics is a science of converting data into information, It is defined as “The science of Collecting, organizing, summarizing, analysing data and making inferences from data” For example, 32 years (for the variable age), or female (for the variable sex). Variables and data A variable is a characteristic that takes different values (vary). For example, age, sex, blood type and job are variables. Data are measurement or observations of a variable. Types of data Data may take many different forms. Each variable (data) will be one of two types: 1. Quantitative (numerical) 2. Qualitative (categorical) Types of data I- Numerical (quantitative) variable When the variable is a number. Numeric variable is subdivided into two types. 1. Discrete variable: when the variable can only take certain whole numerical values. Discrete variables Basic characteristics of Discrete variables: a. Can be counted b. Have units of measurement ‘numbers of things’. c. Data are real numbers. Example: • Counts of family members • The number of visits to a GP in a year. • The number of episodes of illness over the last years. 2. Continuous variable When there is no limitation on the values. Can contain fraction Example: Weight, Height , Haemoglobin , BMI Basic characteristics of Continuous variables: 1. Continuous variables can be measured 2. Have units of measurement. 3. The data are real numbers. Examples Discrete Continuous Frequency HB level of hospital HbA1C admission Urea Family size Weight height BMI Frequency of C/S Blood pressure II- Categorical (qualitative) variable 1. Nominal variable: the categories are not ordered but simply have names. 2. ordinal variable: the categories have a meaningful order Nominal variable Basic characteristics of Nominal variables: a. The data do not have units of measurement. b. The categories cannot be ordered in meaningful way. Examples: • Blood group (A, B, AB, and O) • Marital status (married/widowed/ single etc.). 2. Ordinal variable • The categories are ordered in some way. Basic characteristics of Ordinal variables: 1. The data do not have units of measurement. 2. The categories are ordered in a meaningful way 2. Ordinal variable Examples: • Disease staging systems (advanced, moderate, mild, none) • Degree of pain (severe, moderate, mild, none). Binary or dichotomous A categorical variable is binary or dichotomous when there are only two possible categories. • Examples – Yes/No – Dead/Alive – Patient has disease/ patient does not have disease. An algorithm to help identify variable type. Variable types in research question Independent variables 1.Independent variables (effect variables): • Precede dependent variable in time. • Are often manipulated by the researcher Example Treatment or intervention that is used in a study. Dependent variables 2. Dependent variable (outcome variable): • The value which is measured as an outcome in a study. • It is dependent on the effect variable (independent variable). • E.g. blood pressure, response to treatment Dependent and independent variable Variable name Alternative name/s Axis for plot, table Effect variable Independent variable Risk factor Exposure variable Predictor X axis Row in tables Outcome variable Dependent variable Y axis Column in table Summarizing data 1. With tables 2.With graphs Graphs •Important way of visually representing data •Provides a significant amount of information, showing trends and patterns •Relationships are more easily identified in graphs as compared to a table 1. Pie chart A circular 'pie' is split into sections, one for each category The area of each section is proportional to its frequency. Pie chart is used for: 1. Nominal categorical variable 2. Ordinal categorical variable 1. Pie chart A disadvantages of a pie chart: 1. It can only represent one variable. 2. It loses clarity if it is used to represent more than five categories 2. Bar chart •A separate horizontal or vertical bar is drawn for each category • Length of each bar proportional to the frequency in that category. •The bars are separated by small gaps 2. Bar chart Bar chart is used for: 1. Nominal categorical variable 2. Ordinal categorical variable 3. Discrete quantitative variables. Graphs for quantitative data 1.Histogram • Similar to a bar chart, but no gaps between the bars (the data are continuous). • Constructed by dividing the range of a variable into intervals. • Rectangles are then constructed • The heights of the rectangles are proportional to the relative frequency of that interval. 1.Histogram Used for continuou s variables Histogram of age in years of 405 patients 2.Frequency polygon 2. Line graph (Frequency polygon) • Useful for comparing two or more distribution. • Connecting the midpoint of each rectangle of histogram intervals. • The vertical axis still represents the frequencies. 2.Frequency polygon 2.Frequency polygon It is suitable only for quantitative data (continuous and discrete) 3. Frequency curve • By smoothing the sharp edges of frequency polygon we will get a frequency curve (The midpoint of rectangle in histogram are connected with smooth curve). Used for continuous variables, can be used for more than one group. 3. Frequency curve 4. Box plot • Box plot (five numbers summary plot) • This is a vertical or horizontal rectangle, with the ends of the rectangle corresponding to the upper and lower quartiles of the data values. • A line drawn through the rectangle corresponds to the median value. 4. Box plot minimum, Q1, median, Q3, maximum Whiskers, starting at the ends of the rectangle, usually indicate minimum and maximum values. First quartile (Q1) and third (Q3) quartiles are marked. Descriptive measures Measures of central tendency Measures of variability Normal distribution & Skeweness To describe a distribution, use…  Center  Spread  Shape Measures of central tendency • It is a method of summarizing data • Measure of location in a data set. • AVERAGE (for the mean), MEDIAN, and MODE are the measures of central tendency. Measures of central tendency The arithmetic mean • The arithmetic mean, simply called the mean. • calculated by adding up all the values and dividing the sum by the number of values. (ΣX)/N The mean is “the sum of values divided by their numbers”. It uses all the data values in a sample or population. The mean has one great weakness: one extreme values can distort the most typical value. It is calculated by the following formula Calculating the Mean • Calculate the mean of the following data: 1 5 4 3 2 • Sum the scores (ΣX): 1 + 5 + 4 + 3 + 2 = 15 • Divide the sum (ΣX = 15) by the number of scores (N = 5): 15 / 5 = 3 • Mean ( X )= 3 43 The arithmetic mean Example : The systolic blood pressure of seven middle aged men were as follows: 151, 124, 132, 170, 146, 124 and 113. ( ) The mean is 151 + 124 + 132 + 170 + 146 + 124 + 113 7 = 137.14 137.1 x= The Median • If the sample data are arranged in an increasing order, the median is (i) the middle value if n is an odd number, or (ii) midway between the two middle values if n is an even number The Mode • The mode is the score that occurs most frequently in a set of data • Uni-modal distribution if there is one mode. • If there are numerous obvious peaks, we say there are multiple modes. • One peak  unimodal • Two peaks  bimodal • More than two peaks  multiple modes 46 The Mode 6 6 5 4 Frequency Frequency 5 3 2 4 3 2 1 1 0 0 75 80 85 90 Score on Exam 1 95 75 80 85 90 Score on Exam 1 47 95 Example The reordered systolic blood pressure data seen earlier are: 113, 124, 124, 132, 146, 151, and 170. The Median is the middle value of the ordered data, i.e. 132. Two individuals have systolic blood pressure = 124 mm Hg, so the Mode is 124. Mean versus Median • Large sample values tend to inflate the mean. This will happen if the histogram of the data is rightskewed. • The median is not influenced by large sample values and is a better measure of centrality if the distribution is skewed. • Note if mean=median=mode then the data are said to be symmetrical Measures of Dispersion Measures of dispersion characterise how spread out the distribution is, i.e., how variable the data are. Commonly used measures of dispersion include: 1. 2. 3. 4. Range Variance & Standard deviation Coefficient of Variation (or relative standard deviation) Inter-quartile range The Range • The range is defined as the difference between the largest score in the set of data and the smallest score in the set of data, XL - XS • It is easy to calculate Blood pressure example: min=113 and max=170, so the range=57 mmHg • useful for “best” or “worst” case scenarios. • sensitive to extreme values. • It is a poor measure of dispersion. Standard Deviation • Standard deviation is the most commonly used in medical and health research. • It is a measure of the spread of data about their mean Standard Deviation • The sample standard deviation, s, is the square-root of the variance n s= 2 ( ) ∑ xi − x i =1 n −1 Sample Variance The sample variance, s2, is the arithmetic • mean of the squared deviations from the sample mean: n ∑ (xi − x ) s 2 = i =1 2 n −1 > Example Example Data 151 124 132 170 146 124 113 Sum = 960.0 x = 137.14 Deviation 13.86 -13.14 -5.14 32.86 8.86 -13.14 -24.14 Sum = 0.00 Deviation2 192.02 172.73 26.45 1079.59 78.45 172.73 582.88 Sum = 2304.86 Example (contd.) Example 10 ∑ (x − x ) i =1 2304.86 s= 7 −1 = 19.6 i = Inter-quartile range (IQR) • The Median divides a distribution into two halves. • The first and third quartiles (denoted Q1 and Q3) are defined as follows: – 25% of the data lie below Q1 (and 75% is above Q1), – 25% of the data lie above Q3 (and 75% is below Q3) • The inter-quartile range (IQR) is the difference between the first and third quartiles, i.e. IQR = Q3- Q1 Box-plots • Gives a useful idea of the sample distribution without portraying it fully. • Compute the median, the lower quartile, QI, (the twenty-fifth percentile) and the upper quartile, Q3 (the seventy-fifth percentile) Normal Distribution • The arithmetic mean, median, and mode of the distribution are equal and located at the peak. • thus half the area under the curve is above the mean and half is below it. • symmetrical about its mean • and has a single peak at the exact centre of the distribution Normal Distribution Normal Distribution Many things closely follow a Normal Distribution: Heights of people Blood pressure Marks on a test Bell chapped Mean=Median=Mode Normal Distribution • One of the most important distributions in statistics • completely described by two parameters, the mean (µ) and the variance (σ2); • symmetrical about its mean. Normal distribution 68% of values are within 1 standard deviation of the mean 95% of values are within 2 standard deviations of the mean 99.7% of values are within 3 standard deviations of the mean Normal Distribution Skewness • Skewness of distribution is measured by comparing the relative position of mean, median and mode. • Symmetrical distribution Mean =Median =Mode • Right skewed distribution Mean is greater than Median • Left skewed distribution the Median is greater than the Mean Skewness Right-Skewed Shape • A set of data values in which mean > median The right tail of the distribution is longer than the left tail • Also known as positive skew. • Right or positive skewness occurs when the data set contains some extremely high data values (that increase the mean). Right-Skewed Shape Skewness Left-Skewed Shape • A set of data values in which the mean < the median • The left tail of the distribution is longer than the right tail of the of the distribution. • Also known as negative skew. Left-Skewed Shape Skewness Skewness