REVIEWER STATS PDF - Statistics Notes

Statistics - comes from the Italian word “statista” which means statement. German word, “statiska” which means political state. Descriptive statistics - totality of methods and treatments employed in the collection, description, and analysis of numerical data. The purpose of...

Statistics - comes from the Italian word “statista” which means statement. German word, “statiska” which means political state. Descriptive statistics - totality of methods and treatments employed in the collection, description, and analysis of numerical data. The purpose of a descriptive statistics is to tell something about the particular group of observation. Inferential Statistics - logical process from sample analysis to a generalization or conclusion about a population. Constant - characteristics of data that does not vary Variable - characteristics of data that can take of different values either in quantity or in equality. Data - Facts or figures, which are numerical or otherwise, collected with a definite purpose are called data. Types of Data: Quantitative Data - represent numerical value, can be numerically computed. Qualitative Data - These represent some characteristics or attributes. These depicts descriptions that may be observed but cannot be computed. Primary Data - Data collected for first time. Secondary Data - Data that is sourced by someone other than the user. Discrete Data - can take only specific value. Continuous Data - data that can take values from a given range. Frequency Distribution Table - a list, table, or graph that displays the frequency of various outcomes in a sample of data. Ungrouped - used for small data set. Grouped - used for large data set. Scales of Measurement: Nominal Scale - measurement in which a number is assigned to represent something or someone; it provides no additional information. Nominal data are discrete variables. Example: Gender, Civil status, Seasons Ordinal Scale - measurement that conveys only that some value is greater or less than another value. It is used in ranking and considered discrete variables. Example: Student grades, Employee rank, Class standing Interval Scale - measurement that have no true zero and are distributed in equal units. Example: Temperature, Calendar Time, Ratio Scale - measurements that have true zero value and are distributed in equal units. Example: Weight, Age, Salary Data Collection 1. Interview 2. Observation 3. Focus Groups  4. Experimental 5. Documents and Records 6. Questionnaire/Surveys Frequency Table - is an excellent device for making larger collections of data much more intelligible. A frequency table is so named because it list categories of scores along with their corresponding frequencies. Steps to Draw Frequency Distribution Table 1. Arranged the raw data in ascending order 2. Determine the classes: ❖ Find the highest and lowest value. ❖ Find the range. ❖ Determine the number of classes. (2k>n) ❖ Determine the class interval or width ❖ Set the individual class limits ❖ Set the class boundaries in each class. (-.5 and +.5 HV LV) 3. Determine the frequency of each class limits 4. Determine the relative frequency (f/n x 100%) 5. Determine the cumulative frequency (frequency plus next frequency) 6. Determine the midpoints. Class Class Frequency Relative Cumulative Midpoint Limits Boundaries Frequency Frequency 1-3 0.5 - 3.5 3 (3/38 x 100%) 3 (3+6) 2 = 7.89% 4-6 3.5 - 6.5 6 (6/38 x 100%) 9 5 = 15.79% 7-9 6.5 - 9.5 10 26.31% 19 8 10-12 9.5 - 12.5 5 13.16% 24 11 13-15 12.5 - 15.5 5 13.16% 29 14 16-18 15.5 - 18.5 9 23.68% 38 17 ci= 3 n = 38 Histogram - Chart that plots the distribution of a numeric variable’s values as a series of bars. Frequency Polygon - graph that displays the data using points which are connected by lines. It is almost identical to a histogram, which is used to compare sets of data or to display a cumulative frequency distribution. It uses a line graph to represent quantitative data. Cumulative Frequency Polygon - a graph that displays the cumulative frequencies for the classes in a frequency distribution.  Computing Sample Size and Sampling Techniques Yamane (1967) - provided a simplified formula to calculate the sample size. Margin of Error - the value which quantifies possible sampling error Sampling Techniques Census - count or measure of an entire population Sampling - process of selecting sample Random Sampling or probability sampling - refers to a process of selecting samples whose members had equal chance of being selected from the population. 1. Simple random sampling ot Lottery sampling - Selecting of n sample size using random numbers. - Example: In a class with 50 students and you need 5 students. You assigned number for students from 1 through 50 then select 5 numbers randomly from 1 - 50. Those 5 random numbers that you will get, is now the representative of the class. 2. Stratified Sampling - Samples are obtained by dividing the population into subgroups or strata according to some characteristics relevant to the study. (There can be several subgroups.) Then subjects are selected from each subgroup. - Example: Given the population of students enrolled in statistics class. Applying Yamane’s Formula it is suggested that sample size should be 345. 3. Cluster Sampling - Dividing the population into sections or clusters and then selecting one or more clusters and using all members of the sample. This is usually used for a wide geographical area and naturally occurring subgroups, each having similar characteristics. - Example: Someone wants to know the opinion of people of Antipolo City regarding the response of the local Government on the Pandemic. There are 6 Barangays in the city. One can randomly select 4 barangays and ask their opinions. That will be the response of the people of the city of Antipolo. Measures of Central Tendency - A single value that attempts to describe a set of data by identifying the central position within that set of data. - Sometimes called measures of central location. - Also called as summary statistics. Measures of Dispersion or Variability - A measure that characterized the data set of how it is distributed, varied, or how far each element is from some measure of central tendency. - Most common measures of dispersion are the range, standard deviation, and variance Measures of Position - Method by which the positions that a particular data value has within a given data set can be identified. - We commonly refer to this measure of position as quantiles or fractiles. Quantiles - a score distribution where the scores are divided into different equal parts. There are three kinds of quantiles: ❖ Quartile ( 4 equal parts ) ❖ Decile ( 10 equal parts ) ❖ Percentile ( 100 equal parts ) Discovery of the equation for a normal distribution: ❖ 1733 - Abraham DeMoivre, French mathematician, derived an equation for a normal distribution based on the random variation of the number of heads appearing when a large number of coins were tossed. ❖ About 100 years later, Pierre Laplace in France and Carl Gauss in Germany, derived the equation of the normal curve independently and without any knowledge of DeMoivre’s work. ❖ In 1994, Karl Pearson found that DeMoivre had discovered the formula before Laplace or Gauss. Normal Distribution - a continuous, symmetric, and bell-shaped distribution of a random variable. Can be used to describe, at least approximately, any variable that tends to cluster around the mean.