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No chapter abstract available.

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Statistics is the process of collecting, analyzing, presenting and interpreting data with an aim of deriving conclusions. Statistics is also the process of learning from data. Population is the total collection of elements of interest in a particular study, e.g. COVID-19 patients in Kenya. There are two types of population: finite and infinite. Finite is a population that is known. For example, the total number of students in a given class is known. Infinite is a population that is not known. Data are collected facts and figures. Data can also be defined as the values of a variable. Elements are entities on which data are collected. A variable is a characteristic of interest for the element. Variables can be continuous or discrete and in some cases variables can be dependent, independent, intervening or moderating. Data can be classified as either cross-sectional or time series especially when analyzing data.

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One must collect data so that collected data can be analyzed to generate meaningful information to answer the specific questions of interest. The commonly used methods for collecting data are: questionnaires, experiments, interviews, focused group discussions (FGDs) and observation check lists. There are several reasons that may lead to one choosing a particular data collection method. Data preparation is the process of cleaning and transforming the raw collected data before conducting the data analysis. When data are properly prepared then analysis will be more efficient with limited errors and inaccuracies. Data preparation process can be a tedious process since it involves fixing errors and enriching the data so that it has minimal errors. The process of deriving meaningful information from the collected data using statistical software. The type of data (either quantitative or qualitative) determines the type of analysis and the choice of statistical software.

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Statistical Package for Social Sciences (SPSS) current version is Version 27. These are the features that don’t change when we switch from Data View to Variable View and vice versa. There are some letters that are underlined and they present the keyboard short cut for exercising the specific function. File menu contain all of the options found in file menu including saving data or graphs output or previously saved files. Data menu allows changes into the data editor. Some of the important features include Spilt Files for splitting the file by grouping variable or Select Cases which is used to conduct analysis for selected sample of cases. Other features include defining variable properties, sorting cases, sorting variables, transposing, merging data sets, aggregating data or weighing cases. Transform menu is used to manipulate some of the variables in some way on the basis of existing variables.

Pages: 90

Summaries of data which may be tabular, graphical or numerical are referred to as descriptive statistics. The analyzed data can be presented using tables (frequency tables), graphs/charts and numerical measures. Frequency distribution is a tabular summary of data showing the items in groups or classes and the number of times those items are appearing (frequency of items). A Histogram displays data using continuous bars. Histogram displays the shape and spread of continuous/numerical data. A cumulative frequency curve is a graph of cumulative frequencies (on y-axis) against the class limits on (x-axis). A scatter plot is a two-plot relating values two different numerical variables on both the x-axis and y-axis. A cumulative frequency curve is a graph of cumulative frequencies (on y-axis) against the class limits on (x-axis). The coefficient of variation measures how spread out values are in a dataset relative to the mean.

Pages: 64

No chapter abstract available.

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Probability is a numerical measure of likelihood (certainty or uncertainty) that an event will occur. The value of probability lies between 0 (0%) and 1 (100%). Experiment is a process that generates well-defined outcomes. Experiment is an act that can be repeated under given conditions. For example, tossing a coin will generate outcomes of either having head or tail, sitting for an exam, attending a job interview, etc. A sample space for an experiment is the set of all experimental outcomes. An Events is a collection of sample points. An event is a possible outcome of an experiment or a result of atrial or an observation. The subjective method of assigning probabilities is used when one cannot assume that the experimental outcomes are equally likely and when little relevant data are available. Subjective probability comes from the person's intuition or reasoning.

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A random variable is a variable whose values are associated with some probability of being observed. A random variable represents outcomes of random experiments represented by uppercase variable such as X. A random variable can be classified as being either discrete or continuous. A discrete random variable is a random variable whose possible values can be listed. A continuous random variable is one that can assume any numerical value in an interval or collections of intervals. Binomial distribution is one of the discrete probability distributions. Binomial distribution is used when there are only two outcomes. The Poisson distribution is another discrete probability distribution. The chi-square distribution is a distribution that is used to solve statistical tests/inference involving contingency tables and can be used to test if a sample of data came from a population with a specific distribution.

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Sampling is the process/an act of selecting a representative sample from the population. There are two types of sampling methods, probability and nonprobability sampling methods. In probability sampling every element has equal chance of being selected. Probability sampling is also known as random sampling. Probability sampling methods include: simple random sampling, systematic sampling, stratified sampling and cluster sampling. In nonprobability sampling every element has no equal chance of being selected (the method is biased with more errors). The nonprobability sampling method is also known as non-random sampling. The nonprobability sampling methods include: judgmental sampling, convenience sampling, snowball sampling and quota sampling. Probability distribution of sample proportion p- of sample size n. If the sample proportions p- is a random variable, the sampling distribution of p- is the probability distribution of all possible values of the sample proportion p-.

Pages: 160

No chapter abstract available.

Pages: 38

Inferential statistics is part of statistics that enables one to generalize about a population based upon information obtained from a sample. This is done through Estimation and Test of Hypothesis, which are the two major branches of inferential statistics. Inferential statistics has two branches: parametric statistics and nonparametric statistics. A good estimator should be unbiased, consistent and efficient. An unbiased estimator of a population parameter is an estimator whose expected value of the sample mean equals the population mean. An unbiased estimator is said to be a consistent estimator if the difference between the estimator and the parameter grows smaller as the sample size grows larger. A point estimate of a population parameter is a single value of a statistic being used to estimate the population parameter. An interval estimate is defined by two numbers, between which a population parameter is said to lie.

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Testing Hypothesis is part of statistical inference that uses statistic to make decisions and conclusions about hypothesized values of a population. A hypothesis is a tentative assumption about the distribution of a phenomenon that a research intends to establish. There are three types of hypotheses: Research hypotheses, Statistical Hypotheses and Substantive hypotheses. In order to test hypotheses, business researchers formulate their research hypotheses into statistical hypotheses. There are two types of statistical hypotheses: Null hypothesis and alternative hypothesis. The null hypothesis, denoted by H0, is usually the hypothesis that sample observations result purely from chance. Depending on the situation, hypothesis tests about a population parameter may take one of three forms: Two use inequalities in the null hypothesis; the third uses an equality in the null hypothesis. There are two approaches can be used to make decision about the Null hypothesis: Critical value approach and p-value approach.

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In this section, we will conduct a hypothesis testing procedure by applying the necessary statistical tests in the appropriate steps.

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In this section, we will conduct a hypothesis testing procedure by applying the necessary statistical tests in the appropriate steps.

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An experimental design is a plan and a structure to test hypotheses in which the researcher either controls or manipulates one or more variables. It contains independent and dependent variables. In an experimental design, an independent variable may be either a treatment variable or a classification variable. A treatment variable is a variable the experimenter controls or modifies in the experiment. A classification variable is some characteristic of the experimental subject that was present prior to the experiment and is not a result of the experimenter's manipulations or control. Independent variables are sometimes also referred to as factors. Experimental designs are analyzed statistically by a group of techniques referred to as analysis of variance (ANOVA). The completely randomized design contains only one independent variable, with two or more treatment levels, or classifications. A completely randomized design is analyzed by a one-way ANOVA. The one-way ANOVA, provides methods for comparing the means of more than two populations.

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A variable that has a chi-square distribution if its distribution has the shape of a special type of right-skewed curve is called a chi-square curve. There are two types of chi-square tests: Chi-square goodness-of-fit test and Chi-square test for independence. The chi-square goodness of fit test statistic is a nonparametric test hat is used to make statistical inferences about the equality of population proportions for three or more populations. It can also be used to check if the data are consistent with the specified distribution. The chi-square test for independence is used to determine whether an association exists between two categorical variables, e.g. to determine if there is a statistical and significant relationship between gender (male or female) and employment status (i.e. employed or not employed). It is also known as chi-square test for association.

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Correlation analysis is used to determine the strength and direction of relationship/association between two numerical/quantitative variables. There are two types: Pearson product moment and Spearman rank. This chapter discusses inferences in correlation using Statistical Package for Social Sciences (SPSS). Regression analysis is a mathematical measure of the average relationship between dependent and independent(s) numerical variables. In linear regression, there are two types of variable: independent and dependent. Dependent variable is the outcome variable and is usually denoted by y, e.g. salary. Independent variable is the variable that is resulting into the outcome and is usually denoted by x, e.g. years of experience. There are two types of linear regression analysis: simple linear and multiple linear regression analysis. The F-test in the regression ANOVA is used to determine if there is a statistical significant linear relationship between dependent/outcome variable (quantitative) and independent/predictor variable (quantitative).

Pages: 100

No chapter abstract available.

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A nonparametric test is a statistical test, in which specific assumptions are not made about the population parameter. The researcher has no idea regarding the population parameters. It is not based on underlying assumptions, and it does not require a knowledge of a population's distribution. The test is mainly based on differences in medians. Nonparametric tests are also known as distribution-free tests. Sign test is used to test the null hypothesis that the median of a distribution is equal to some hypothesized value k. The test is based on the direction or the data are recorded as plus and minus signs rather than numerical magnitude, hence it is called Sign test. Kruskal-Wallis H test is used instead of a one-way analysis of variance (ANOVA) to find out if two or more medians are different. Ranks of the data points are used for the calculations, rather than the data points themselves.

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Time series is an ordered sequence of values of a variable at equally spaced time intervals. Time series may be measured continuously or discretely. Time series data are data gathered collected sequentially over time on a given characteristic. A lag of time series is created when the time base is shifted by a given number of periods. Lags of a time series are often used as explanatory variables to model the actual time series itself. This is because the state of the few back time series periods may still has an influence on the series current state. The simple moving average of the time series can be used to estimate the trend component of a non-seasonal time series described by the additive model. Simple moving average is one of the averaging techniques for “smoothing out” the irregular fluctuations in the time series data. Exponential smoothing can be used to make short-term forecasts for time series data.

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Statistical Process Control (SPC) is a method of quality control which employs statistical methods to measure, monitor and control a process. It uses a scientific visual method to monitor, control and improve the process by eliminating points that are out of control. SPC has three parts: Statistics, Process and Control. Statistics is the process of collecting, analyzing, presenting and interpreting data with an aim of drawing information from the data. SPC aims to optimize continuous improvement by using statistical tools to analyze data, make inferences about process behavior, and then make appropriate decisions. SPC assumes that all processes are subject to variation. A Control chart is one of the main techniques of SPC. The control chart is a graphical display of quality characteristics that have been measured or computed from a sample versus the sample number or time. X-bar S charts are control charts used to examine the process mean and standard deviation over the time.