Unit 3 Statistical Essentials 2 Variables and Data PDF

Variables and Data ‫…يجري التحميل‬ Investigators define variables and collect data to answer their research questions. A variable is a trait or characteristic that varies or changes, and data are the values of variables when they vary. ‫ڡٮ"ﻢ‬$ ‫هى‬...

Variables and Data ‫…يجري التحميل‬ Investigators define variables and collect data to answer their research questions. A variable is a trait or characteristic that varies or changes, and data are the values of variables when they vary. ‫ڡٮ"ﻢ‬$ ‫هى‬ & ‫ﺎت‬+‫ٮٮ"ﺎٮ‬- ‫ واﻟ‬،‫ ٮ"ﺮ‬3‫تﻌ‬$‫ٮﻠﻒ أو ٮ‬$ ‫ﺤ‬$+ ‫ ٮ"ﺮ ﻫﻮ ﺳﻤﺔ أو ﺳﻤﺔ ٮ‬3‫ﻌ‬$‫اﻟﻤٮ‬.‫ٮﻠﻒ‬$ ‫ﺤ‬$+ ‫ٮﺪﻣﺎ ٮ‬+ ‫ ٮ"رات ﻋ‬3‫ﻌ‬$‫اﻟﻤٮ‬ For example, systolic blood pressure(SBP) is a variable because it is a characteristic that fluctuates, both from one person to another and at different times within the same person. Each blood pressure measurement is a data value. A collection of these data values is a data set.  variable Ordinal interval ratio quantitative qualitative Discrete Continuous Nominal  Variables and Data Variables may be qualitative or quantitative. Qualitative variables have values that are nonnumeric Quantitative variables have values that are numeric. ‫…يجري التحميل‬ Example: Systolic blood pressure may be either qualitative—high, normal, or low— or quantitative—120 mmHg. In this text, we will confine ourselves to numeric variables, as these are amenable to statistical analyses.  Quantitative (Numeric) Variables TYPES of quantitative variable: Numeric variables may be either discrete or continuous. Discrete variables have values that are countable but do not include the fractions between countable categories. Continuous variables have every possible value on a continuum. Gender may be counted, as in there are 10 women in a waiting area, and is an example of a discrete variable; this is because, in the real world, there is no such thing as 10.5 women. In contrast, systolic blood pressure ranging from 0 to 200 mmHg is an example of a continuous variable because we could measure the pressure anywhere between 0 and 200 mmHg. Conceivably, we could measure systolic blood pressure to the nearest hundredth mmHg, for example 120.05  Independent and Dependent Variables Variables can also be characterized as independent or dependent when an investigator is investigating the interaction between variables for statistical hypothesis testing. The variable that is manipulated by the investigator or affects another variable is the independent variable. The dependent variable is affected by an independent variable. For example, suppose an investigator is examining whether hepatitis B antigen affects liver function test results. The presence or absence of the hepatitis B antigen is the independent variable, as it affects the liver function test results, and the liver function test result is the dependent variable, as it is affected by hepatitis B antigen.  Levels of Measurement There are four common levels of measurement: nominal, ordinal, interval, and ratio. It is important to understand the level of measurement because different statistical procedures require different levels of measurement on the variables of interest. Measurement is also important for application of research to practice. 1. Nominal level of measurement: As Data are classified into mutually exclusive categories where no ranking or ordering is imposed on categories. The word nominal simply means to name or category. Common examples in this level of measurement are gender and ethnicity; an investigator can classify the subjects as men, women, or transgender for gender and as different ethnic groups (e.g., Caucasian, African American, Asian, or Hispanic), respectively, Blood  Levels of Measurement: 2. Ordinal Level In ordinal level of measurement, data are also classified into mutually exclusive categories. However, ranking or ordering is imposed on categories. A common example in this level of measurement is grouped age. People can be categorized into one of the following groups: (1) 18 and under, (2) 19–30, (3) 31–49, and (4) 50 and above. Here, we not only have distinctive categories with no overlapping (mutually exclusive categories), but there is a clear ranking or ordering among categories. Category (2) has older people than category (1), but younger people than categories (3) and (4). Other examples of ordinal level of measurement include letter grade (A, B, C, D, F), Likert- type scales (strongly disagree, somewhat disagree, neutral, somewhat agree,  ‫ﻌﺪ‬#‫ٮٮ‬% ‫ﺴ‬%‫ ﺎت وٮ‬+‫ڡ‬-‫ٮٮ‬+ ‫ﺼ‬%‫ڡﺌﺎت ذات ٮ‬+ ‫ﺎت إﻟﻰ‬+‫ﺎٮ‬-‫ٮٮ‬# ‫ﻒ اﻟ‬-‫ٮٮ‬+ ‫ﺼ‬%‫ٮﻢ ٮ‬% - ‫ ٮ‬،‫ﺎس‬-‫ڡٮ‬% ‫ ﺎﺻﻞ اﻟﺰﻣﲏ ﻟﻠ‬+‫ٮوى اﻟڡ‬% ‫ى ﻣﺴ‬B ‫ڡ‬+ ‫ﺎس‬-‫ڡٮ‬% ‫يﱯ ﻟﻠ‬%‫ٮﺮٮ‬% ‫ٮوى اﻟ‬% ‫ى اﻟﻤﺴ‬B ‫ڡ‬+ ‫ﻌﺾ ﻛﻤﺎ ﻫﻮ اﻟﺤﺎل‬#‫ﻌﻀﻬﺎ اﻟٮ‬#‫ٮ‬ Levels of Measurement: 3. Interval Level In interval level of measurement, data are classified into categories with rankings and are mutually exclusive as in ordinal level of measurement. In addition, specific meanings are applied to the distances between categories. These distances are assumed to be equal and can be measured. Temperature, for example, is measured on categories with equal distance, and any value is possible; the distance or interval between 35°F and 40°F is the same as the distance or interval between 55°F and 60°F. However, in interval level of measurement, there is no absolute value of “zero.” Zero degrees Fahrenheit is different from zero degrees Celsius. Therefore, there is no absolute or unconditional meaning of zero. In addition, we cannot say 25°F is three times as cold as 75°F—that is, there is no concept of ratio, or equal  Levels of Measurement: 4. Ratio Level In ratio level of measurement, all characteristics of interval level of measurements are present; in addition, there is a meaningful zero, and ratio or equal proportion is present. For example, income is measured on scales with equal distance and a meaningful zero. The ‫…يجري التحميل‬ measurement of income for someone will be zero if they have no source of livelihood. We may also say that someone making $60,000 a year makes exactly twice as much as someone making $30,000 a year. Blood pressure is another example of ratio level of measurement, as it is possible to have a blood pressure of zero, and a systolic pressure of 100 mmHg is twice that of 50 mmHg. Other examples of ratio level of measurement are age, height, and weight. Summary of all the levels of measurement  Statistical Tests According to Level of Measurement  Reliability and Validity In addition to determining what level of measurement will be needed for any given variable, the investigator designing a research or an evidence-based practice study needs to choose the best measurement tools. A tool or instrument is a device for measuring variables. Examples include paper-and- pencil surveys or tests, scales for measuring weight, and an eye chart for estimating visual acuity. There may be one or more measurement tools available for variables of interest, or there may be none, and that a tool will need to be created. Strong instruments will reduce the likelihood of measurement error.  Measurement Error Measurement error is the difference between the measured value and the true value. Measurement error is unavoidable in research and can be either random or systematic errors. Systematic errors occur consistently because of known causes, and random errors occur by chance and are the result of unknown causes. One common source of systematic error is the incorrect use of tools or instruments. For example, suppose that you need to measure depression in older adults, and you found an instrument, Beck’s Depression Inventory (BDI). Would you start measuring older adults’ depression levels using the BDI right away? Probably not! First, you would want to make sure that the BDI is a good measurement tool to assess depression in older.‫ٮﻤرار أم ﻻ‬% ‫ﺎﺳ‬#‫ﺮ ٮ‬-‫ ٮ‬W‫ﻌ‬%‫ﺎس اﻟﻤٮ‬-‫ڡٮ‬% ‫ٮﻬﺎ‬+ ‫ﻤﻜ‬- ‫ﺎر أو اﻷداة ٮ‬#‫ٮٮ‬% ‫اﻻﺣ‬ + ‫ﺔ ﻣﺎ إذا ﰷن‬-‫ڡٮ‬% ‫ﺎ اﻟﻤﻮٮ`ﻮ‬+‫ﺮٮ‬#‫ﺤٮ‬%+ ‫ٮ‬ Reliability Reliability tells us whether or not a test or tool can consistently measure a variable. If a patient scores 35 on the Beck’s Depression Inventory (BDI) over and over again, it means that Beck’s Depression Inventory (BDI) is reliable, because it is measuring depression consistently at different times. Whether you are engaged in research, evidence-based practice, quality improvement, or process improvement, choosing a dependable measurement tool is important. There are three commonly used statistical evaluations of reliability, and they are all correlation coefficients: internal consistency, test–retest, and interrater reliability. Internal consistency is used to measure whether items within a tool, such as a depression scale, measure the same thing (i.e., are they consistent with one another?). Cronbach’s alpha, the most commonly used coefficient, ranges from 0 to 1, with a higher coefficient  Reliability Test–retest reliability is used to address the consistency of the measurement from one time to another. If the tool is reliable, the subjects’ scores should be similar at different times of measurement. Investigators commonly correlate measurements taken at different times to see if they are consistent. The higher the correlation coefficient, the stronger the test–retest reliability. Interrater reliability is used to determine the degree of agreement between individuals’ scores on ratings (i.e., are they giving consistent ratings?). Cohen’s kappa is commonly used and ranges from 0 to 1, with a coefficient of 1 signifying perfect agreement. For example, pressure ulcers are often scored on a scale reflecting depth, area, color, and drainage. If two nurses are using a rating scale to score the seriousness of pressure ulcers,  Validity Validity tells us whether a tool, an instrument, or a scale measures the variable that it is supposed to measure. There are three main types of validity: content validity, criterion- related validity, and construct validity. ‫ٮﻤﺎم‬% ‫ڡﻜﺮة اﻻﻫ‬+ ‫ﺐ‬+‫ﺣواٮ‬# ‫ﺣﻤيﻊ‬# ‫ﺲ‬-‫ڡٮ‬% %‫ﺎس ٮ‬-‫ڡٮ‬% ‫ﺖ أداة اﻟ‬+‫ﻤﺎ إذا ﰷٮ‬#‫ٮوى ٮ‬% ‫ﺔ اﻟﻤﺤ‬-‫تﻌﻠﻖ ﺻﻼﺣٮ‬%‫ٮ‬ Content validity has to do with whether a measurement tool measures all aspects of the idea of interest. For example, the BDI would not be a valid measure of depression if it did not include somatic symptoms of depression..‫ﻦ‬-‫ﺎر ﻣﻌٮ‬-‫ﺎر أو ﻣﻌٮ‬-‫ﻤﻌٮ‬#‫ﺎط اﻷداة ٮ‬#‫ٮ‬%‫ﻤﺪى ارٮ‬#‫يﺮ ٮ‬- ‫ﺎﻟﻤﻌﺎٮ‬#‫ﺔ ٮ‬%‫ٮﻌﻠڡ‬% ‫ﺔ اﻟﻤ‬-‫تﻌﻠﻖ اﻟﺼﻼﺣٮ‬%‫ٮ‬ Criterion-related validity is about how well a tool is related to a particular standard or benchmark. For example, suppose you wanted to validate the usefulness of a new depression scale, the Patient Health Questionnaire depression scale (PHQ-9)..‫ﺎﺳﻪ‬-‫ڡٮ‬% ‫ى‬B ‫ڡ‬+ ‫ ﺐ‬+‫ﺮﻋ‬+‫ٮﺎء اﻟﺬي ٮ‬+ ‫ٮ‬# ‫ﺎﻟ‬#‫ﺎس ٮ‬-‫ڡٮ‬% ‫درﺣﺎت أداة اﻟ‬ # ‫ﺎط‬#‫ٮ‬%‫هى ﻣﺪى ارٮ‬ B ‫ٮﺎء‬+ ‫ٮ‬# ‫ﺻﺤﺔ اﻟ‬ Construct validity is the extent to which scores of a measurement tool are correlated with a construct that we wish to measure. A construct may be thought of as an idea or concept.  ‫ﻄﺔ‬#‫ٮ‬%‫ٮﻤﺪة ﻣﺮٮ‬% ‫ﻠﺔ واﻟﻤﻌ‬%‫ٮڡ‬% ‫رات اﻟﻤﺴ‬-‫ ٮ‬W‫ﻌ‬%‫ﻦ أن اﻟﻤٮ‬-‫ڡٮ‬% - ‫ﺄي ٮ‬#‫ول ٮ‬%‫ٮڡ‬+ ‫ٮﺎ أن‬+ ‫ٮ‬+ ‫ﻤﻜ‬- ‫هى إﻟﻰ أي ﻣﺪى ٮ‬ B ‫ﺔ‬-‫اﻟﺪاﺣﻠٮ‬ + ‫ﺔ‬-‫اﻟﺼﻼﺣٮ‬.‫ﻌﺾ‬#‫ﻌﻀﻬﺎ اﻟٮ‬#‫ٮٮ‬# ‫ﻚ‬#‫ﻂ أو ﻣرٮ‬#‫ٮﻀٮ‬+ ‫ﺮ ﻣ‬-‫ ٮ‬+‫ﺮ ﻋ‬-‫ ٮ‬W‫ﻌ‬%‫ٮﺎك أي ﻣٮ‬+ ‫ٮﺎء ﻋﲆ ﻣﺎ إذا ﰷن ﻫ‬+ ‫ٮ‬# ‫ﺔ ﻟﻠﺪراﺳﺔ‬-‫اﻟﺪاﺣﻠٮ‬ + ‫ﺔ‬-‫ڡﻮة اﻟﺼﻼﺣٮ‬% ‫يﻢ‬-‫ڡٮ‬% %‫ٮﻢ ٮ‬% - ‫ﺎ ﻣﺎ ٮ‬#‫ ﺎﻟٮ‬+‫ ﻋ‬ Internal and External Validity Internal validity is the extent to which we can say with any certainty that the independent and dependent variables are related to each other. The strength of the internal validity of a study is often evaluated based on whether there is any uncontrolled or confounding variable that may influence this relationship between independent and dependent variables. Such confounding variables may include outside events that happened during the study, in addition to the variable under study. These confounding events can actually cause a change in scores or measurement and result in less accurate findings.  Internal and External Validity External validity is about whether the results of a study can be generalized beyond the study itself..‫ ﺴﻬﺎ‬+‫ڡ‬+‫ﺤﺎوز اﻟﺪراﺳﺔ ٮ‬# ‫ٮ‬% - ‫ﻤﺎ ٮ‬#‫ٮﺎﺋﺞ اﻟﺪراﺳﺔ ٮ‬% ‫ٮ‬+ ‫ﻢ‬-‫ﻌﻤٮ‬%‫ﻤﻜﻦ ٮ‬- ‫ﻤﺎ إذا ﰷن ٮ‬#‫ﺔ ٮ‬-‫ﺎرﺣٮ‬ # ‫اﻟﺤ‬ + ‫ﺔ‬-‫تﻌﻠﻖ اﻟﺼﻼﺣٮ‬%‫ٮ‬ Can we make accurate inferences about the population from the sample we have selected? Can we verify with any confidence the hypothesis that we are testing? External validity is influenced by the quality of the sample. If the characteristics of the sample used in the study do not represent the population, the results from the study should not be generalized or inferred to the population. External validity is also influenced by measurement. If our measures are unreliable or inaccurate measures of the variables of interest, then we cannot make useful inferences about those variables.