Alpha's Fated Passion: An Omegaverse Why Choose Romance (Omega for the Alphas: Fated Flames Book 3)

"Learn statistics without fear! Build a solid foundation in data analysis. Be confident that you understand what your data are telling you and that you can explain the results to others! I'll help you intuitively understand statistics by using simple language and deemphasizing formulas. This guide starts with an overview of statistics and why it is so important. We proceed to essential statistical skills and knowledge about different types of data, relationships, and distributions. Then we move to using inferential statistics to expand human knowledge, how it fits into the scientific method, and how to design and critique experiments. Learn the fundamentals of statistics: Why is the field of statistics so vital in our data-driven society? Interpret graphs and summary statistics. Find relationships between different types of variables. Understand the properties of data distributions. Use measures of central tendency and variability. Interpret correlations and percentiles. Use probability distributions to calculate probabilities. Learn about the normal and binomial distributions in depth. Grasp the differences between descriptive and inferential statistics. Use data collection methodologies properly and understand sample size considerations. Design and critique scientific experiments-whether it's your own or another researcher's. Free access to downloadable datasets to follow along with the examples." -- Provided by publisher Prepare for an Adventure! 11 The Importance of Statistics 14 Draw Valid Conclusions 15 Avoid Common Pitfalls 16 Make an Impact in Your Field 17 Protect Yourself with Statistics 18 Statistics versus Anecdotal Evidence 18 A scientific study of the weight loss supplement 22 How Statistics Beats Anecdotal Evidence 23 Organization of this Book 24 Data Types, Graphs, and Finding Relationships 26 Quantitative versus Qualitative Data 27 Continuous and Discrete Data 28 Continuous data 28 Histograms: Distributions 29 Scatterplots: Trends 30 Time Series Plots 32 Discrete data 33 Bar Charts 34 Qualitative Data: Categorical, Binary, and Ordinal 34 Categorical data 35 Binary data 36 Ordinal data 37 Next Steps 39 Histograms in More Detail 39 Central Tendency 41 Variability 42 Skewed Distributions 43 Identifying Outliers 45 Multimodal Distributions 46 Identifying Subpopulations 47 Comparing Distributions between Groups 49 Histograms and Sample Size 51 Boxplots vs. Individual Value Plots 52 Individual Value Plots 53 Boxplots 54 Using Boxplots to Assess Distributions 55 Example of Using a Boxplot to Compare Groups 56 Two -Way Contingency Tables 57 Cautions About Graphing 60 Manipulating Graphs 60 Drawing Inferences About a Population Requires Additional Testing 63 Graphing and Philosophy 63 Automatic versus Manual Graph Scales 64 When You Should Change Graph Scales 66 Don’t Limit Yourself by Always Using Automatic Scaling 67 Summary and Next Steps 68 Summary Statistics and Relative Standing 71 Percentiles 72 Special Percentiles 73 Calculating Percentiles Using Values in a Dataset 74 Definition 1: Greater Than 76 Definition 2: Greater Than or Equal To 76 Definition 3: Using an Interpolation Approach 76 Measures of Central Tendency 77 Mean 79 Median 81 Comparing the mean and median 83 Mode 84 Finding the mode for continuous data 86 Which One to Use? 87 Measures of Variability 87 Why Understanding Variability is Important 88 Example of Different Amounts of Variability 89 Range 91 The Interquartile Range (IQR) . . . and other Percentiles 92 Using other percentiles 93 Variance 94 Population variance 94 Sample variance 94 Example of calculating the sample variance 95 Standard Deviation 96 Which One to Use? 98 Comparing Summary Statistics between Groups 98 Correlation 99 Interpreting Correlation Coefficients 101 Examples of Positive and Negative Correlation Coefficients 103 Graphs for Different Correlation Coefficients 103 Discussion about the Scatterplots 105 Interpreting our Height and Weight Correlation Example 106 Pearson’s Measures Linear Relationship 107 Correlation Does Not Imply Causation 107 How Strong of a Correlation is Considered Good? 109 Summary and Next Steps 110 Probability Distributions 111 Discrete Probability Distributions 113 Types of Discrete Distribution 114 Binomial and Other Distributions for Binary Data 114 Assumptions for Using Probability Distributions for Binary Data 115 Binomial Distribution 116 Geometric Distribution 117 Negative Binomial Distribution 118 Hypergeometric Distribution 119 Modelling Flu Outcomes Over Decades 121 How long until my first case of the flu on average? 122 How often will I catch the flu? 123 Continuous Probability Distributions 124 How to Find Probabilities for Continuous Data 125 Characteristics of Continuous Probability Distributions 125 Example of Using the Normal Probability Distribution 126 Example of Using the Lognormal Probability Distribution 127 Normal Distribution in Depth 128 Parameters of the Normal Distribution 130 Mean 130 Standard deviation 130 Population parameters versus sample estimates 131 Properties of the Normal Distribution 132 The Empirical Rule 132 Standard Normal Distribution and Standard Scores 133 Calculating Z-scores 134 Using a Table of Z-scores 137 Why the Normal Distribution is Important 139 Summary and Next Steps 140 Descriptive and Inferential Statistics 143 Descriptive Statistics 144 Example of Descriptive Statistics 145 Inferential Statistics 146 Pros and Cons of Working with Samples 147 Populations 148 Subpopulations 149 Population Parameters versus Sample Statistics 150 Tools for Inferential Statistics 152 Hypothesis tests 152 Confidence intervals (CIs) 153 Regression analysis 154 Properties of Good Estimates 155 Sample Size and Margins of Error 155 Sampling Distributions of the Mean 157 Confidence Intervals and Precision 161 Example: Sample Statistics and CIs for 10 Observations 162 Example: Sample Statistics and CIs for 100 Observations 164 Random Sampling Methodologies 165 Simple Random Sampling 166 Stratified Sampling 167 Cluster Sampling 168 Example of Inferential Statistics 169 Summary and Next Steps 170 Statistics in Scientific Studies 173 Step 1: Research Your Study Area 174 Define Your Research Question 175 Literature Review 176 Step 2: Operationalize Your Study 177 Variables: What Will You Measure? 177 Types of Variables and Treatments 178 Measurement Methodology: How Will You Take Measurements? 178 Create a Sampling Plan: How Will You Collect Samples for Studying? 178 Design the Experimental Methods 179 Step 3: Data Collection 180 Step 4: Statistical Analysis 181 Step 5: Writing the Results 182 Summary and Next Steps 182 Experimental Methods 184 Types of Variables in an Experiment 186 Dependent Variables 186 Independent Variables 186 Causation versus Correlation 187 Confounding Variables 189 Example of Confounding in an Experiment 189 Why Determining Causality Is Important 191 Causation and Hypothesis Tests 192 True Randomized Experiments 193 Random Assignment 194 Comparing the Vitamin Study With and Without Random Assignment 196 Flu Vaccination Experiment 197 Drawbacks of Randomized Experiments 198 Quasi-Experiments 199 Pros and Cons of Quasi-Experiments 200 Observational Studies 201 When to Use Observational Studies 202 Accounting for Confounders in Observational Studies 203 Matching 204 Multiple Regression 205 Vitamin Supplement Observational Study 206 Using Multiple Regression to Statistically Control for Confounders 207 Raw results 207 Adjusted results 207 Evaluating Experiments 209 Hill’s Criteria of Causation 210 Strength 210 Consistency 211 Specificity 211 Temporality 211 Biological Gradient 212 Plausibility 212 Coherence 212 Experiment 213 Analogy 213 Properties of Good Data 213 Reliability 214 Test-Retest Reliability 215 Internal Reliability 215 Inter-rater reliability 216 Validity 216 Data Validity 217 Face Validity 217 Content Validity 218 Criterion Validity 218 Discriminant Validity 219 Experimental Validity 220 Internal Validity 220 Single Group Studies 221 Multiple Groups 223 External Validity 225 Relationship Between Internal & External Validity 229 Checklist for Good Experiments 230 Review 230 Wrapping Up and Your Next Steps 233 Review of What You Learned in this Book 234 Next Steps for Further Study 235 References 237 About the Author 238 Learn statistics without fear! Build a solid foundation in data analysis. Be confident that you understand what your data are telling you and that you can explain the results to others! I'll help you intuitively understand statistics by using simple language and deemphasizing formulas. This guide starts with an overview of statistics and why it is so important. We proceed to essential statistical skills and knowledge about different types of data, relationships, and distributions. Then we move to using inferential statistics to expand human knowledge, how it fits into the scientific method, and how to design and critique experiments. Learn the fundamentals of statistics. Why is the field of statistics so vital in our data-driven society? Interpret graphs and summary statistics. Find relationships between different types of variables. Understand the properties of data distributions. Use measures of central tendency and variability. Interpret correlations and percentiles. Use probability distributions to calculate probabilities. Learn about the normal distribution and the binomial distributions in depth. Grasp the differences between descriptive and inferential statistics. Use data collection methodologies properly and understand sample size considerations. Critique scientific experiments-whether it's your own or another researcher's.