Lecture 10 Basic Statistics PDF

RESEARCH METHODS IN DENTISTRY Basic Statistics Assoc. Prof. Büşra YILMAZ School of Dental Medicine Department of Oral and Maxillofacial Radiology [email protected] Definition Statistics is a branch of mathematics dealing with the collection, analysis, interpretation, and presentation of ma...

RESEARCH METHODS IN DENTISTRY Basic Statistics Assoc. Prof. Büşra YILMAZ School of Dental Medicine Department of Oral and Maxillofacial Radiology [email protected] Definition Statistics is a branch of mathematics dealing with the collection, analysis, interpretation, and presentation of masses of numerical data. Key Statistical Concepts Population: In statistics, the term population is used to mean the totality of cases (items) in an investigation. Sample: Any subset or subgroup of a population. Parameter: A descriptive measure of a population. Key Statistical Concepts Statistic: A descriptive measure of a sample. Variable: Some characteristic of a population or sample. Any characteristic of an individual or entity. A variable can take different values for different individuals. Typically denoted with a capital letter: X, Y, Z… Eg: - student grades. The Different Types of Variables. Quantitative and Qualitative :  Quantative Variables that have are measured on a numeric or quantitative scale Eg : country's population, a person's shoe size, or a car's speed. Qualitative variables that is not numerical. It describes data that fits into categories. Eg: Eye colors (variables include: blue, green, brown, hazel). The Different Types of Variables. Discrete and Continuous :  Discrete variable is a variable whose value is obtained by counting. Continuous variable is a variable whose value is obtained by measuring. Dependent and independent :  A variable whose value depends on that of another (dependent).  A variable whose variation does not depend on that of another (independent). Data It is observed values of a variable. The different Data types are: Nominal Ordinal Interval Ratio Data Types Nominal: Categorical variables with no inherent order or ranking sequence such as names or classes (e.g., gender). Value may be a numerical, but without numerical value (e.g., I, II, III). The only operation that can be applied to Nominal variables is enumeration. Ordinal: Variables with an inherent rank or order, e.g. mild, moderate, severe. Can be compared for equality, or greater or less, but not how much greater or less. Data Types Interval: Values of the variable are ordered as in Ordinal, and additionally, differences between values are meaningful, however, the scale is not absolutely anchored. Eg : Calendar dates and temperatures on the Fahrenheit scale Ratio: Variables with all properties of Interval plus an absolute, nonarbitrary zero point. Eg : age, weight, temperature. Descriptive Statistics Descriptive statistics are used to describe the basic features of the data in a study. They provide simple summaries about the sample and the measures. Together with simple graphics analysis, they form the basis of virtually every quantitative analysis of data. Data collection Information you gather can come from a range of sources. Likewise, there are a variety of techniques to use when gathering primary data. Some of the most common data collection techniques used for collecting data: Interviews, Questionnaires and Surveys, Documents and Records Interviews Interviews can be conducted in person or over the telephone Interviews can be done formally (structured), semi-structured, or informally Questions should be focused, clear, and encourage open-ended responses Interviews are mainly qualitative in nature Ex: - One-on-one conversations with parent of at-risk youth who can help you understand the issue. Questionnaires and Surveys Responses can be analyzed with quantitative methods by assigning numerical values to Likert-type scales Results are generally easier (than qualitative techniques) to analyze Pre-test/Post-test can be compared and analyzed  Ex: - Results of a satisfaction survey or opinion survey Documents and Records Consists of examining existing data in the form of databases, meeting minutes, reports, attendance logs, financial records, newsletters, etc. This can be an inexpensive way to gather information, but may be an incomplete data source Ex: - To understand the primary reasons students miss school, records on student absences are collected and analyzed Data Presentation The visual representation of data may be used not only to present results/findings in the data but may also be used to learn about the data.  Graphical Method (Bar Diagram, Pie Diagram,Line chart)  Tabular method Graphical Method-Bar Diagram A bar graph is a chart that uses bars to show comparisons between categories of data. Graphical Method-Pie Diagram A pie chart displays data, information, and statistics in an easy-to-read 'pieslice' format with varying slice sizes telling you how much of one data element exists. The bigger the slice, the more of that particular data was gathered. The main use of a pie chart is to show comparison. Graphical Method-Line chart A line chart or line graph is a type of chart which displays information as a series of data points called 'markers' connected by straight line segments. Tabular Method Frequency table  The only allowable calculation on nominal data is to count the frequency of each value of the variable. We can summarize the data in a table that presents the categories, and their counts called a frequency distribution. A relative frequency distribution lists the categories and the proportion with which each occurs. Tabular Method  Cumulative frequency  It defined as a running total of frequencies. The frequency of an element in a set refers to how many of that element there are in the set. Cumulative frequency can also define as the sum of all previous frequencies up to the current point. Characterize Data/Summary Measures Summary measures summarize and provide information about your sample data. It tells you something about the values in your data set. This includes where the average lies and whether your data is skewed. Summary measures fall into two main categories. They are Measures of location (also called central tendency or central measurement) and Measures of spread (also called Measures of variation) Characterize Data/Summary Measures Methods of central Measurement Mean  Mean is the average of all values of a variable and is computed by summing all the scores and dividing it by the number of scores.it does not have to be an observed value.  It tends to be the most stable estimate of the population mean from sample mean. Mean of 20, 30, 40 is (20+30+40)/3 = 30. Methods of Central Measurement Median  The median is the “middle” observation when the data are arranged in ascending or descending order. The median does not have to be an observable value.  If number of observation is odd, the median is the middle number  If number of observation is even, the median is the average of the two middle numbers. Methods of Central Measurement Mode  The value which is most frequent.it represents the most common response.  Used for either numerical or categorical data  There may be no mode  There may be several modes Measures of Variation Variability refers to how spread out a group of data is. In other words, variability measures how much your scores differ from each other. The common measures of variation; Range, Variance, Standard Deviation. Range The range is the simplest measure of variability to calculate. The range is simply the highest score minus the lowest score. Variance The variance of a set of observations is the average of the squares of the deviations of the observations from their mean. Standard Deviation Square root of the variance. The standard deviation of the above example is 2. Example - The following sample consists of the number of jobs six randomly selected students applied for: 17, 15, 23, 7, 9, 13.Find the sample mean, variance and standard deviation. References  Basic Statistics, T.V. Sathianandan, Safeena P. K and Ramees Rahman • Allan Hackshaw, Elizabeth Paul, Elizabeth Davenport. Evidence-Based Dentistry, An Introduction. 1st Edition. Wiley-Blackwell. June 2021. ISBN: 978-1-4051-2496-6