Lecture 1 - Statistics PDF

# Lecture 1 ## Monday, March 6, 2023 11:09 PM ## Dr. Fadi Alrimawi ## What is Statistics? Statistics is the science of conducting studies to collect, organize, summarize, analyze, and draw conclusions from data. ## Why Students Study Statistics? 1. To be able to read and understand the various...

# Lecture 1 ## Monday, March 6, 2023 11:09 PM ## Dr. Fadi Alrimawi ## What is Statistics? Statistics is the science of conducting studies to collect, organize, summarize, analyze, and draw conclusions from data. ## Why Students Study Statistics? 1. To be able to read and understand the various statistical studies performed in your field. 2. To conduct research in your field, since statistical procedures are basic to research. 3. You can use the knowledge gained from studying statistics to become better consumers and citizens. ## Descriptive and Inferential Statistics * To gain knowledge about seemingly haphazard situations, statistics collect information for variables, which describe the situations. ## What is the definition of the variable? A variable is a characteristic or attribute that can assume different values. * Data are the values (measurements or observations) that the variables can assume. * Variables whose values are determined by chance are called random variables. * A collection of data values forms a data set. Each value in the data set is called a data value or a datum. ## Statistics Divided into Two Main Areas, Depending on How Data are Used. The Two Areas are: 1. **Descriptive statistics**: which consists of the collection, organization, summarization, and presentation of data. In descriptive statistics the statistician tries to describe the situation. It depends on the data of the population of the study. 2. **Inferential statistics**: which consists of generalizing from samples to populations, performing estimations and hypothesis tests, determining relationships among variables, and making predictions. Here the statistician tries to make inferences from samples to populations. Inferential statistics uses probability. * A population consists of all subjects (human or otherwise) that are being studied. * A sample is a group of subjects selected from the population. * It is very hard to use the entire population for a statistical study; therefore, researchers use samples. * One of the most important areas of the inferential statistics is called hypothesis testing, which is a decision-making process for evaluating claims about a population, based on information obtained from samples. ## Variables and Types of Data ### Variables can be classified as: 1. **Qualitative variables**: Variables that can be placed into distinct categories, according to some characteristic or attribute. (ex: male or female, religions, ...etc.). 2. **Quantitative variables**: Numerical variables which can be ordered or ranked. (ex: heights, weights, temperatures, ... etc.). ## Also, Quantitative Variables can be classified into two groups: 1. **Discrete variables**: Assume values that can be counted (ex: number of children, number of students in a classroom, ... etc.). 2. **Continues variables**: Can assume an infinite number of values between any two specific values. They can be obtained by measuring. They often include fractions and decimals (ex: heights, weights, temperatures, ... etc.). * Since continues data must be measured, answers must be rounded because of the limits of the measuring device. Usually, answers are rounded to the nearest given unit. We can solve this problem by giving boundaries of this continuous variable. * The boundaries of a continuous variable are given in one additional decimal place and always end with the digit 5. Example: | Variable | Recorded Value | Boundaries | |---|---|---| | Length | 15 cm | 14.5-15.5 cm| | Temperature | 86°F | 85.5-86.5°F | | Time | 0.43 sec | 0.425-0.439 sec | | Mass | 1.6g | 1.55-1.65g | * For the Mass 1.6 g the boundaries are 1.55-1.65 g which means all the values from 1.55 1.65 (i.e. the value 1.65 not included ). **In addition to being classified as qualitative or quantitative, variables can be classified by how they are categorized, counted or measured. This type of classification divides into four types:** 1. **Nominal**: The nominal level of measurements classifies data into mutually exclusive categories in which no order or ranking can be imposed on the data. 2. **Ordinal**: The ordinal level of measurements classifies data into categories that can be ranked; however, precise differences between the ranks do not exist. 3. **Interval**: The interval level of measurements ranks data, and precise differences between units of measures do exist; however, there is no meaningful zero. 4. **Ratio**: The ratio level of measurements possesses all the characteristics of interval measurements, and there exists a zero. In addition, true ratios exist when the same variable is measured on two different members of the population. Example of Measurement Scales | Nominal-level data | Ordinal-level data | Interval-level data | Ratio-level data | |---|---|---|---| | Gender(male, female) | Grade (A,B,C,D) | SAT score | Height | | Eye color (blue, brown, ... etc.) | Judging (first place, second place, ...etc.) | IQ| Weight | | Political affiliation | Rating scale (excellent, good, poor, ... etc.) | Temperature | Salary | | Nationality | Ranking of tennis players | | | ## Sampling Methods * To obtain samples that are unbiased, i.e. that give each subject in the population an equally likely chance of being selected, statisticians use four basic methods of sampling: 1. **Random Sampling**: Subjects are selected by random numbers. 2. **Systematic Sampling**: Subjects are selected by using every kth number after the first subject is randomly selected from 1 through k. 3. **Stratified sampling**: Subjects are selected by dividing up the population into groups, and subjects are randomly selected within groups. 4. **Cluster sampling**: Subjects are selected by using an intact group that is representative of the population. ## Observational and Experimental Studies 1. **Observational Studies**: In observational study the researcher merely observes what is happening or what has happened in the past and tries to draw conclusions based on these observations. 2. **Experimental Studies**: In experimental study the researcher manipulates one of the variables and tries to determine how the manipulation influences other variables. | | Advantage | Disadvantage | |---|---|---| | Observational | * It usually occurs in a natural setting. * It can be done in situations where it would be unethical or downright dangerous to conduct an experiment. | * They can be expensive and time-consuming. * The variables are not controlled by the researcher (other factors may have had an effect on the results). | | Experimental | * The researcher can decide how to select subjects and how to assign them to specific groups. *The researcher can control or manipulate the independent variable. | * They may occur in unnatural settings, such as laboratories and special classrooms. * The subjects who knew they were participating in an experiment may change their behavior in ways that affected the results (Hawthorne effect). |