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543957106-Introduction-Basic-Concepts-in-Statistics-PPT - Copy.pptx
- 1. INTRODUCTION & BASIC CONCEPTS IN STATISTICS Social Work Statistics
- 2. WHAT IS STATISTICS Statistics is used in business and economics. It plays an important role in the exploration of new markets for a product, forecasting of business trends, control and maintenance of high-quality products, improvement of employer-employee relationship and analysis of data concerning insurance, investment, sales, employment, transportation, communications, auditing and accounting procedures.
- 3. STATISTICS is the branch of mathematics that deals with the theory and method of collecting, organizing, presenting, analyzing and interpreting data. Two Main Divisions/Phases of Statistics 1. DESCRIPTIVE STATISTICS refers to the summary statistic that quantitatively describes or summarizes features from a collection of data under investigation. The goal is to describe. Numerical measures are used to tell about features of a set of data.
- 4. EXAMPLES: The average, or measure of the center of a data set, consisting of the mean, median, mode, or midrange The spread of a data set, which can be measured with the range or standard deviation Overall descriptions of data such as the five number summary Measurements such as skewness and kurtosis The exploration of relationships and correlation between paired data The presentation of statistical results in graphical form
- 5. 2. INFERENTIAL STATISTICS- statistical tools that are used to examine the relationships between variables within a sample and then make generalizations or predictions about how those variables will relate to a larger population. • Example: Tests of significance or hypothesis testing where scientists make a claim about the population by analyzing a statistical sample. By design, there is some uncertainty in this process. This can be expressed in terms of a level of significance.
- 6. Two Branches of Statistics 1. Statistical Theory – is concerned with the formulation of theories, principles, and formulas which are used as bases in the solution of problems related to Statistics. 2. Statistical Methods – is concerned with the application of the theories, principles and formulas in the solution of everyday problems.
- 7. OTHER STATISTICAL TERMS: • POPULATION – a set of data consisting of all conceivable possible observations of a certain phenomenon. It refers to the totality of the observations. Population is denoted by capital N. • SAMPLE – a finite number of items selected from a population possessing identical characteristics with those of the population from which it was taken. Sample is denoted by small letter n • PARAMETERS – are characteristics/measures computed from the population • STATISTIC/S – are characteristics/measures computed from the sample
- 8. • VARIABLE – refers to a fundamental quantity that changes in value from one observation to another within a given domain and under a given set of conditions. Variables may be represented by the letters X, Y, etc. • DISCRETE VARIABLE - is a variable whose value is obtained by counting. • CONTINUOUS VARIABLE- is a variable whose value is obtained by measuring. • CONSTANT – refers to fundamental quantities that do not change in value.
- 9. FOUR LEVELS OF DATA MEASUREMENT Nominal –also called the categorical variable scale, is defined as a scale used for labeling variables into distinct classifications and doesn’t involve a quantitative value or order. This scale is the simplest of the four variable measurement scales. Calculations done on these variables will be futile as there is no numerical value of the options. (ex. Sex, gender, place of residence, political affiliation) Ordinal –a variable measurement scale used to simply depict the order of variables and not the difference between each of the variables. These scales are generally used to depict non-mathematical ideas such as frequency, satisfaction, happiness, a degree of pain, etc.
- 10. • Ordinal Scale maintains description qualities along with an intrinsic order but is void of an origin of scale and thus, the distance between variables can’t be calculated. Description qualities indicate tagging properties similar to the nominal scale, in addition to which, the ordinal scale also has a relative position of variables. Origin of this scale is absent due to which there is no fixed start or “true zero”. Examples: High school class ranking: 1st, 9th, 87th… Socioeconomic status: poor, middle class, rich. The Likert Scale: strongly disagree, disagree, neutral, agree, strongly agree. Level of Agreement: yes, maybe, no. Time of Day: dawn, morning, noon, afternoon, evening, night. Political Orientation: left, center, right.
- 11. • Interval Scale is defined as a numerical scale where the order of the variables is known as well as the difference between these variables. Variables that have familiar, constant, and computable differences are classified using the Interval scale. It is easy to remember the primary role of this scale too, ‘Interval’ indicates ‘distance between two entities’, which is what Interval scale helps in achieving. • These scales are effective as they open doors for the statistical analysis of provided data. Mean, median, or mode can be used to calculate the central tendency in this scale. The only drawback of this scale is that there no pre-decided starting point or a true zero value. • Interval scale contains all the properties of the ordinal scale, in addition to which, it offers a calculation of the difference between variables. The main characteristic of this scale is the equidistant difference between objects.
- 12. Interval Scale Examples There are situations where attitude scales are considered to be interval scales. Apart from the temperature scale, time is also a very common example of an interval scale as the values are already established, constant, and measurable. Calendar years and time also fall under this category of measurement scales. Likert scale, Net Promoter Score, Semantic Differential Scale, Bipolar Matrix Table, etc. are the most-used interval scale examples. Celsius Temperature. Fahrenheit Temperature. IQ (intelligence scale). SAT scores. Time on a clock with hands.
- 13. • Ratio Scale: 4th Level of Measurement • is defined as a variable measurement scale that not only produces the order of variables but also makes the difference between variables known along with information on the value of true zero. It is calculated by assuming that the variables have an option for zero, the difference between the two variables is the same and there is a specific order between the options. • With the option of true zero, varied inferential, and descriptive analysis techniques can be applied to the variables. In addition to the fact that the ratio scale does everything that a nominal, ordinal, and interval scale can do, it can also establish the value of absolute zero. The best examples of ratio scales are weight and height. In market research, a ratio scale is used to calculate market share, annual sales, the price of an upcoming product, the number of consumers, etc.
- 14. • Examples of Ratio scale Age Weight Height Sales Figures Ruler measurements. Income earned in a week
- 15. STEPS IN A STATISTICAL INQUIRY OR INVESTIGATION start with a problem 1. Collection of data 2. Presentation of data 3. Analysis of data 4. Interpretation of data
- 16. DATA COLLECTION AND DATA PRESENTATION What are DATA? • Data are plain facts, usually raw numbers, words, measurements, observations or just description of things. Think of a spreadsheet full of numbers with no meaningful description. In order for these numbers to become information, they must be interpreted to have meaning. TWO TYPES OF DATA 1. QUALITATIVE DATA is descriptive in nature ex., color, shapes 2. QUANTITATIVE is numerical information ex. weight, height
- 17. DATA COLLECTION • Data collection is concerned with the accurate gathering of data; although methods may differ depending on the field, the emphasis on ensuring accuracy. The primary goal of any data collection is to capture quality data or evidence that easily translates to rich data analysis that may lead to credible and conclusive answers to questions that have been posed.
- 18. M E T H O D S O F D A T A C O L L E C T I O N 1. THE INTERVIEW or DIRECT METHOD The researcher or interviewer gets the needed data from the respondent or interviewee verbally and directly face-to-face contact. 2. THE QUESTIONNAIRE or INDIRECT METHOD The questionnaire is a tool for data gathering and research that consists of a set of questions in a different form of question type that is used to collect information from the respondents for the purpose of either survey or statistical analysis study.
- 19. 3. REGISTRATION METHOD This method is used by the government such as the records of births at the Philippine Statistics Authority (PSA), registration record at the COMELEC 4. OBSERVATION This method is a way of collecting data through observing. The observer gains firsthand knowledge by being in and around the social setting that is being investigated. 5. EXPERIMENTATION An experiment is a procedure carried out to support, refute, or validate a hypothesis. An experiment is a method that most clearly shows cause-and-effect because it isolates and manipulates a single variable, in order to clearly show its effect.
- 20. DATA PRESENTATION Once data has been collected, it has to be classified and organized in such a way that it becomes easily readable and interpretable, that is, converted to information. TYPES OF DATA PRESENTATION 1. TEXTUAL PRESENTATION This type of presentation combines text and figures in a statistical report. Example: news item in the newspaper 2. TABULAR PRESENTATION This type of presentation uses tables consisting of vertical columns and horizontal rows with headings describing these rows and columns. The data are presented in more brief and orderly manner. Example: frequency table 3. GRAPHICAL PRESENTATION It is a most effective means of presenting statistical data because important relationships are brought out more clearly in graphs.
- 21. DIFFERENT TYPES OF GRAPHS COMMONLY USED IN DATA PRESENTATION 1. BAR GRAPH A bar chart or bar graph is a chart or graph that presents categorical data with rectangular bars with heights or lengths proportional to the values that they represent. The bars can be plotted vertically or horizontally.
- 22. LINE GRAPH A line graph is a graphical display of information that changes continuously over time. A line graph may also be referred to as a line chart. Within a line graph, there are points connecting the data to show a continuous change. The lines in a line graph can descend and ascend based on the data. We can use a line graph to compare different events, situations, and information.
- 23. PIE GRAPH A pie chart is a circular chart divided into wedge-like sectors, illustrating proportion. Each wedge represents a proportionate part of the whole, and the total value of the pie is always 100 percent. Pie charts can make the size of portions easy to understand at a glance. They're widely used in business presentations and education to show the proportions among a large variety of categories including expenses, segments of a population, or answers to a survey.
- 24. SCATTER DIAGRAM A scatter diagram also called a scatterplot, is a type of plot or mathematical diagram using Cartesian coordinates to display values for typically two variables for a set of data. If the points are coded (color/shape/size), one additional variable can be displayed. The data are displayed as a collection of points, each having the value of one variable determining the position on the horizontal axis and the value of the other variable determining the position on the vertical axis.
- 25. 5. PICTOGRAPH/PICTOGRAM A pictograph is a chart or graph, which uses pictures to represent data. A pictograph is one of the simplest forms of data visualization.
- 26. TWO TYPES OF SAMPLING • Probability sampling • Simple random • Systematic • Stratified • Cluster • Non-probability sampling • Convenience/Accidental • Judgmental/Purposive • Quota • Snowball
- 27. PROBABILITY VS NON-PROBABILITY SAMPLING 1. Probability or Random Sampling Provides equal chances to every single element of the population to be included in the sampling. 2. Non-Probability Sampling The samples are selected in a process that does not give all the individuals in the population equal chances of being selected. Samples are selected on the basis of their accessibility or by the purposive personal judgment of the researcher.
- 28. PROBABILITY-BASED SAMPLING Simple Random Sampling Lottery Method Fish Bowl Method Table of Random Numbers
- 29. PROBABILITY-BASED SAMPLING Systematic Sampling Step 1. Identify the population (N) Step 2. Identify the number of sample (n) to be drawn from the population Step 3. Divide N by n to find nth interval Example Population is 1,000. Desired sample size is 100. Sampling interval is 10 Get a random start from 1 to 10 in the list as first sample and every 10th in the list
- 30. PROBABILITY-BASED SAMPLING Stratified Sampling Used to ensure that different groups in the population are adequately represented in the sample Step 1. Identify the population and divide the population into different groups or strata according to criteria. Step 2. Decide on the sampling size or actual percentage of the population to be considered as sample. Step 3. Get a proportion of sample from each group Step 4. Select the respondents by random sampling Example : Population = 2000 Desired Sample Size = 10% Proportion of sample per stratum = 10% 500 students x .10 = 50 600 businessman x .10 = 60 400 teachers x .10 = 40 500 farmers x .10 = 50 Total sample = 200 Select the 200 by random sampling.
- 31. PROBABILITY-BASED SAMPLING Cluster Sampling Often called geographic sampling Used in large scale surveys The population is divided into multiple groups called clusters . The clusters are selected with simple random or systematic sampling technique for data collection and data analysis. Example: the Population includes elementary schools in the Province. The province is first divided into Districts which are treated as clusters and are randomly selected. From the districts, the schools can be picked out at random and then classes and then students are selected at random
- 32. NON-PROBABILITY SAMPLING 1. Accidental or Convenience Sampling Researcher selects subjects that are more readily accessible or available. 2. Purposive Sampling Subjects are selected based on the needs of the study.
- 33. NON-PROBABILITY-BASED SAMPLING Quota Sampling Researcher takes a sample that is in proportion to some characteristic or trait of the population The population is divided into groups or strata (the basis may be age, gender, education level, race, religion etc. Samples are taken from each group to meet a quota. Care is taken to maintain the correct proportions representative of the population. Example : The population consists of 60% female and 40% male. The desired sample size is 200. Therefore, the sample should consist of ____ females and ____ males.
- 34. NON-PROBABILITY-BASED SAMPLING A study on science teaching is to be conducted in high schools of a region. There are 4,641 teachers grouped according to area of specialization. There are 2,243 biology teachers, 1,406 chemistry teachers and 992 physics teachers. The desired sample size is 300. Select the sample according to the Quota Sampling technique.
- 35. NON-PROBABILITY-BASED SAMPLING 4. Snowball Sampling This type of sampling starts with known sources of information, who or which will in turn give other sources of information . As this goes on, data accumulates. This is used to find socially devalued urban populations such as drug addicts, alcoholics, child abusers and criminals because they are usually hidden from outsiders.