FC: CAN'T STOP THE | COMPILATION OF HANDOUTS IN STATISTICS
1: I alone of English writers have consciously set myself to make music out of what I may call the sound of sense. | INTRODUCTION TO STATISTICS
2: What is Statistics? Statistics deals with experimental designs and procedures which include data collection, classification, organization and interpretation, and decision making regarding these data. It can be broken down into two essential areas: descriptive statistics and inferential statistics or statistical inference. Descriptive Statistics refers to the methods of data collection, organization, classification, summarization, and presentation. It includes the procedures for constructing graphs, tables, and charts. It also refers to the calculation of statistical descriptions such as the measures of central tendency and the measures of variability. It summarize the population data by describing what was observed in the sample numerically or graphically. Numerical descriptors include mean and standard deviation for continuous data types (like heights or weights), while frequency and percentage are more useful in terms of describing categorical data (like race). Inferencial Statistics or statistical inference, on the other hand, refers to the process of arriving at a conlcusion about a population based on the information obtained from a sample. A number that describes a characteristic of a population is called parameter. A number that describes a characteristic of a sample is called a statistic. Research analysts use statistical inference to estimate an unknown population parameter by using a sample statistic.
3: If music be the food of love, play on. | Importance of Statistics a) Science and Technology b) Psychology c) Business and Economics Business Economics d) Education e) Other field of profession In Astronomy: In Accounting and Auditing: In Banking: In State Management (Administration)
4: If one plays good music, people don't listen and if one plays bad music people don't talk. | VARIABLE | All experiments examine some kind of variable(s). A variable is not only something that we measure, but also something that we can manipulate and something we can control for.
5: Types of Variable Dependent and Independent Variables An independent variable is exactly what it sounds like. It is a variable that stands alone and isn't changed by the other variables you are trying to measure. For example, someone's age might be an independent variable. Other factors (such as what they eat, how much they go to school, how much television they watch) aren't going to change a person's age. In fact, when you are looking for some kind of relationship between variables you are trying to see if the independent variable causes some kind of change in the other variables, or dependent variables. Just like an independent variable, a dependent variable is exactly what it sounds like. It is something that depends on other factors. For example, a test score could be a dependent variable because it could change depending on several factors such as how much you studied, how much sleep you got the night before you took the test, or even how hungry you were when you took it. Usually when you are looking for a relationship between two things you are trying to find out what makes the dependent variable change the way it does. (Independent variable) causes a change in (Dependent Variable) and it isn't possible that (Dependent Variable) could cause a change in (Independent Variable).
6: Categorical and Continuous Variables Categorical variables are also known as discrete or qualitative variables. Categorical variables can be further categorized as either nominal, ordinal or dichotomous. Nominal variables are variables that have two or more categories but which do not have an intrinsic order. For example, a real estate agent could classify their types of property into distinct categories such as houses, condos, co-ops or bungalows. So "type of property" is a nominal variable with 4 categories called houses, condos, co-ops and bungalows. Of note, the different categories of a nominal variable can also be referred to as groups or levels of the nominal variable. Another example of a nominal variable would be classifying where people live in the USA by state. In this case there will be many more levels of the nominal variable (50 in fact). Dichotomous variables are nominal variables which have only two categories or levels. For example, if we were looking at gender, we would most probably categorize somebody as either "male" or "female". This is an example of a dichotomous variable (and also a nominal variable). Another example might be if we asked a person if they owned a mobile phone. Here, we may categorize mobile phone ownership as either "Yes" or "No". In the real estate agent example, if type of property had been classified as either residential or commercial then "type of property" would be a dichotomous variable. Ordinal variables are variables that have two or more categories just like nominal variables only the categories can also be ordered or ranked. So if you asked someone if they liked the policies of the Democratic Party and they could answer either "Not very much", "They are OK" or "Yes, a lot" then you have an ordinal variable. Why? Because you have 3 categories, namely "Not very much", "They are OK" and "Yes, a lot" and you can rank them from the most positive (Yes, a lot), to the middle response (They are OK), to the least positive (Not very much). However, whilst we can rank the levels, we cannot place a "value" to them; we cannot say that "They are OK" is twice as positive as "Not very much" for example.
7: Any good music must be an innovation. | Continuous variables are also known as quantitative variables. Continuous variables can be further categorized as either interval or ratio variables. Interval variables are variables for which their central characteristic is that they can be measured along a continuum and they have a numerical value (for example, temperature measured in degrees Celsius or Fahrenheit). So the difference between 20C and 30C is the same as 30C to 40C. However, temperature measured in degrees Celsius or Fahrenheit is NOT a ratio variable. Ratio variables are interval variables but with the added condition that 0 (zero) of the measurement indicates that there is none of that variable. So, temperature measured in degrees Celsius or Fahrenheit is not a ratio variable because 0C does not mean there is no temperature. However, temperature measured in Kelvin is a ratio variable as 0 Kelvin (often called absolute zero) indicates that there is no temperature whatsoever. Other examples of ratio variables include height, mass, distance and many more. The name "ratio" reflects the fact that you can use the ratio of measurements. So, for example, a distance of ten metres is twice the distance of 5 metres.
8: Music is a moral law. It gives soul to the universe, wings to the mind, flight to the imagination, and charm and gaiety to life and to everything. | Population vs. Sample Population "The term "population" is used in statistics to represent all possible measurements or outcomes that are of interest to us in a particular study." Examples: Cedar Crest students; trees in North America; automobiles with four wheels; people who consume olive oil Sample "The term "sample" refers to a portion of the population that is representative of the population from which it was selected." Examples assuming the populations stated above: 47 Cedar Crest students chosen randomly; 8463 trees randomly selected in North America; 20 sample autos from each make (e.g., GM, Ford, Toyota, Honda, etc.); 1% of the oil consuming population per country Population is the area in which you are trying to get information from. Sample is a section of your population that you are actually going to survey. It is important to have a sample that will represent your entire population in order to minimize biases. For example: You want in know how American citizens feel about the war in Iraq. Your population: The United States Your sample: 500 citizens selected randomly from each state. Since the answers all over the US would greatly vary, it is important to have everyone in the population represented in your sample. This is usually done through random sampling, which assumes no biases seeing as the subjects were selected at random.
9: Music is the voice that tells us that the human race is greater than it knows. | Qualitative data Qualitative data is a categorical measurement expressed not in terms of numbers, but rather by means of a natural language description. In statistics, it is often used interchangeably with "categorical" data. Quantitative data Quantitative data is a numerical measurement expressed not by means of a natural language description, but rather in terms of numbers. However, not all numbers are continuous and measurable. For example, the social security number is a number, but not something that one can add or subtract. Quantitative data always are associated with a scale measure.
10: Measurement Scales Different measurement scales allow for different levels of exactness, depending upon the characteristics of the variables being measured. The four types of scales available in statistical analysis are: Nominal: A scale that measures data by name only. For example, religious affiliation (measured as Christian, Jewish, Muslim, and so forth), political affiliation (measured as Democratic, Republican, Libertarian, and so forth), or style of automobile (measured as sedan, sports car, SUV, and so forth). Ordinal: A scale that measures by rank order only. Other than rough order, no precise measurement is possible. For example, medical condition (measured as satisfactory, fair, poor, guarded, serious, and critical); socioeconomic status (measured as lower class, lower-middle class, middle class, upper-middle class, upper class); or military officer rank (measured as lieutenant, captain, major, lieutenant colonel, colonel, general). Such rankings are not absolute but rather relative to each other: Major is higher than captain, but we cannot measure the exact difference in numerical terms. Is the difference between major and captain equal to the difference between colonel and general? We cannot say.
11: Music is everybody's possession. It's only publishers who think that people own it. | Interval: A scale that measures by using equal intervals. Here you can compare differences between pairs of values. The Fahrenheit temperature scale, measured in degrees, is an interval scale, as is the centigrade scale. The temperature difference between 50C and 60C (10 degrees) equals the temperature difference between 80C and 90C (10 degrees). Note that the 0 in each of these scales is arbitrarily placed, which makes the interval scale different from ratio. Ratio: Similar to an interval scale, a ratio scale includes a 0 measurement that signifies the point at which the characteristic being measured vanishes (absolute zero). For example, income (measured in dollars, with 0 equal to no income at all), years of formal education, items sold, and so forth, are all ratio scales.
12: COLLECTION AND PRESENTATION OF DATA
13: A. SAMPLING TECHNIQUES | B. METHODS OF COLLECTING DATA
14: A.SAMPLING TECHNIQUES Simple Random Sampling – Simple Random Sampling (SRS) is a process of selecting a sample from a set of all sampling units or a population such that each sampling unit is given a chance of being included in the sample. In doing this, we obtain a simple random sample that is representative of the population and not biased in any way. The simplest method is to use physical mixing or the popularly called lottery sampling. Stratified Random Sampling - Stratified Sampling is a variant on simple random and systematic methods and is used when there are a number of distinct subgroups, within each of which it is required that there is full representation. A stratified sample is constructed by classifying the population in sub-populations (or strata), base on some well-known characteristics of the population, such as age, gender or socio-economic status. The selection of elements is then made separately from within each strata, usually by random or systematic sampling methods. Systematic Random Sampling - Systematic Sampling is a frequently used variant of simple random sampling. When performing systematic sampling, every kth element from the list is selected (this is referred to as the sample interval) from a randomly selected starting point. For example, if we have a listed population of 6000 members and wish to draw a sample of 2000, we would select every 30th (6000 divided by 200) person from the list. In practice, we would randomly select a number between 1 and 30 to act as our starting point. Cluster Sampling – Cluster Sampling is one of the most economical ways of obtaining a sample for a survey. It consists of selecting clusters of units in a population and then obtaining a simple random sample of these clusters.
15: If a man does not keep pace with his companions, perhaps it is because he hears a different drummer. Let him step to the music which he hears, however measured or far away. | A.Methods of Collecting Data Interview Method – A method where there is a person-to-person contact or exchange of into between the interviewer and interviewee. Questionnaire Method – The researcher was prepared act of questions and information are solicited from the respondents. Registration Method – Gathering of information is enforced by the certain laws such a registration of birth certificate, deaths or marriages. Observation Method – The researchers observes behavior of person or organizations through employing. Telephone Interview - When it is not possible to contact the respondent directly, then interview is conducted through telephone. Experimental Method – Usually used in laboratory or field experiments.
16: Music is the movement of sound to reach the soul for the education of its virtue. | FREQUENCY DISTRIBUTION
17: Methods of Presenting Data The main portion of Statistics is the display of summarized data. Data is initially collected from a given source, whether they are experiments, surveys, or observation, and is presented in one of four methods: Textular Method The reader acquires information through reading the gathered data. Example: Lung cancer is the most killing cancer worldwide Tabular Method Provides a more precise, systematic and orderly presentation of data in rows or columns. Survey results of the ages of students in the Adult Basic Education maths classes are shown in this frequency table. Semi-tabular Method Uses both textual and tabular methods. Graphical Method The utilization of graphs is most effective method of visually presenting statistical results or findings.
18: List of Common Graphs in Statistics Different situations call for different types of graphs, and it helps to have a good knowledge of what graphs are available. Many times the type of data determines what graph is appropriate to use.Qualitative data, quantitative data and paired dataeach use different types of graphs. Seven of the most common graphs in statistics are listed below: 1.Pareto Diagram or Bar Graph - A bar graph contains a bar for each category of a set of qualitative data. The bars are arranged in order of frequency, so that more important categories are emphasized. 2.Pie Chart or Circle Graph - A pie chart displays qualitative data in the form of a pie. Each slice of pie represents a different category. 3.Histogram - A histogram in another kind of graph that uses bars in its display. This type of graph is used with quantitative data. Ranges of values, called classes, are listed at the bottom, and the classes with greater frequencies have taller bars. 4.Stem and Left Plot - A stem and left plot breaks each value of a quantitative data set into two pieces, a stem, typically for the highest place value, and a leaf for the other place values. It provides a way to list all data values in a compact form. 5.Dot plot - A dot plot is a hybrid between a histogram and a stem and leaf plot. Each quantitative data value becomes a dot or point that is placed above the appropriate class values. 6.Scatterplots - A scatterplot displays data that is paired by using a horizontal axis (the xaxis), and a vertical axis (the y axis). The statistical tools of correlation and regression are then used to show trends on the scatterplot. 7.Time-Series Graphs - A time-series graph displays data at different points in time, so it is another kind of graph to be used for certain kinds of paired data. The horizontal axis shows the time and the vertical axis is for the data values. These kinds of graphs can be used to show trends as time progresses.
19: Guidelines for Tables and Graphs All tables and figures should be numbered and have complete descriptive titles. Tables and Figures are numbered separately. The numbers are given in the order of appearance of the tables and figures in the research paper. Titles of tables are placed at the top while those of figures are placed at the bottom. Row and Column headings need to be provided also in tables while axes have to be labeled in the case of graphs. Appropriate units of measurements are also included in the axes label of graphs and row and column headings of tables. The Different levels of the independent variable are placed on the x-axis while the different levels of the dependent variable are placed on the y-axis. Legends must be provided where two or more sets of graphs are placed on the same set of coordinates
20: Without music, life would be a mistake. | Frequency Distrubution In statistics, a graph or data set organized to show the frequency of occurrence of each possible outcome of a repeatable event observed many times. Simple examples are election returns and test scores listed by percentile. A frequency distribution can be graphed as a histogram or pie chart. For large data sets, the stepped graph of a histogram is often approximated by the smooth curve of a distribution function (called a density function when normalized so that the area under the curve is 1). The famed bell curve or normal distribution is the graph of one such function. Frequency distributions are particularly useful in summarizing large data sets and assigning probabilities.
21: Class Limits Class limits are the smallest and largest observations (data, events etc) in each class. Therefore, each class has two limits: a lower and upper. Class Boundaries Class Boundaries are the midpoints between the upper class limit of a class and the lower class limit of the next class in the sequence. Therefore, each class has an upper and lower class boundary. Class Intervals Class interval is the difference between the upper and lower class boundaries of any class. Class Width/ Size - The class width is the difference between the upper and lower limit of that particular class. Class Mark - The class mark is the midpoint of each interval and is the value that represents the whole interval for the calculation of some statistical parameters and for the histogram. Class Frequency Class Frequency means the number of observations belonging to a class interval.
22: After silence, that which comes nearest to expressing the inexpressible is music. | Music can change the world because it can change | Submitted By: | Princess Mae J. Ignacio
23: I need drama in my life to keep making music. | Music is a higher revelation than all wisdom and philosophy. | Submitted To: Ms. Karen Santos | One good thing about music, when it hits you, you feel no pain. | Music doesn't lie. If there is something to be changed in this world, then it can only happen through music.