Statistical Tests: T-tests, ANOVA, Regression, Chi-square

• Statistical tests are vital for data analysis, helping determine data significance by comparing it to a known population or assessing differences between samples.
• The importance of statistical tests lies in:
  • Providing evidence for hypotheses regarding data.
  • Reducing errors in data-based conclusions, aiding in error identification during collection.
  • Allowing inferences about populations from sample data to make predictions.

Types of Statistical Tests

• T-tests are used to compare two means of continuous data, including independent and paired samples t-tests.
• ANOVA (Analysis of Variance) compares the means of three or more groups to find significant differences.
• Regression Analysis helps determine relationships between two continuous variables for predictions.
• Chi-square tests assess significant differences between expected and observed frequencies in categorical data.
• Correlation analysis identifies the strength and direction of relationships between two variables.
• Mann-Whitney U Test compares two independent groups to determine significant differences.
• Kruskal-Wallis H Test compares three or more independent groups for significant differences.
• Wilcoxon Signed-Rank Test compares two related samples to assess significant differences between them.

Statistical Analysis Techniques

• Statistical analysis is a tool for businesses and organizations to interpret data and guide decisions.
• It involves collecting, organizing, and analyzing data to recognize patterns and trends across various industries and applications.
• It can be used to predict, simulate, create models, and reduce risk

Main Types of Statistical Analysis

• Descriptive statistical analysis uses numbers to describe data set qualities and condenses data for simple interpretation via data visualization.
• Inferential statistical analysis draws conclusions about a larger population based on a sample group, validating generalizations and accounting for errors.
• Associational statistical analysis identifies relationships among multiple variables, allowing researchers to make inferences and predictions using sophisticated software.

Other Types of Statistical Analysis

• Predictive analysis uses algorithms and machine learning to forecast future events/behavior from new and historical data.
• Prescriptive analysis guides organizational decision-making by identifying the best choice among various options using data analysis tools.
• Exploratory data analysis identifies patterns, trends, relationships, validating assumptions, testing hypotheses, and detecting missing data.
• Causal analysis determines causation to understand why events occur for quality assurance and guiding future decisions.

Statistical Analysis Process

• Data Collection: Gathering data through primary/secondary sources like surveys or CRM software, ensuring sample representativeness.
• Data Organization: Cleaning by identifying and removing duplicates/inconsistencies to ensure analysis accuracy.
• Data Presentation: Arranging data for easy analysis and determining the most effective presentation method using descriptive statistics.
• Data Analysis: Manipulating data sets to find patterns, trends, and relationships through inferential and associational statistical techniques, using software for efficiency.
• Data Interpretation: Providing conclusive results and presenting them accessibly through charts, reports, and dashboards

Common Statistical Analysis Methods

• Mean: This is calculated by summing numbers and dividing by quantity and determines the central data point.
• Standard deviation: Determining this helps determine data dispersion
• Regression: This technique is used to find a relationship between depent and independent variables.
• Hypothesis testing: This tests the conclusion validity

Scenario 1

• Description: Determining a correlation between hours studied and exam score.
• Appropriate Test: Pearson Correlation Coefficient and Linear Regression are appropriate tests
• Reasoning: Both use constant variables

Scenario 2

• Description: Determining the relationship between rank and exam score
• Appropriate Test: Spearman's Rank Correlation is most appropriate
• Reasoning: Spearman's correlation measures the relationship between variables when one is considered ranked or the relationship is non-linear

Scenario 3

• Description: Comparing exam scores of two different teaching methods
• Appropriate Test: Mann-Whitney U Test
• Reasoning: This is used to compare two independent groups when data isn't normally distributed or when working with ordinal data

Data Comparison

• Continuous Data:
  • Independent Samples: t-test (2 groups, normal data), ANOVA (3+ groups, normal data), Mann-Whitney U or Kruskal-Wallis (non-normal data).
  • Related Samples: Paired t-test (normal data), Wilcoxon signed-rank test (non-normal data).
• Categorical Data: Chi-square test (association between variables).

Groups and Profile Types

• Two Groups: t-test, Mann-Whitney U test, Chi-square test.
• Three or More Groups: ANOVA, Kruskal-Wallis test.
• Nominal (Unordered): Gender, car type (Chi-square tests).
• Ordinal (Ordered): Education level, satisfaction (non-parametric tests).

Illustrative Examples

• Comparing test scores by learning style: use ANOVA or Kruskal-Wallis.
• Comparing customer satisfaction by age group: use Kruskal-Wallis test.
• Comparing car preferences by gender: use Chi-square test.

Sampling

• Feasibility: Sampling is often more feasible because of the time constraints etc of analyzing the whole population.
• Efficiency: Sampling allows researchers to gather data from smaller groups

Key Definitions

• Sampling Frame: A listing the population
• Representative Sample: This accurately reflects population characteristics
• Sampling Bias: This indicates the sample does not accurately represent the population and leading to distorted sample results

Sampling Methods

• Probability Sampling: Every member has a known chance to be selected in order to minimize bias.
  • Types: random, stratified, cluster, and systematic sampling.
• Non-Probability Sampling: Here, the probability is unknown but more susceptible to bias.
  • Types: convienience, purposive, quota, snowball

Descriptive Statistics

• Mean (Average): calculated using =AVERAGE(range).
• Median: calculated using =MEDIAN(range).
• Mode: calculated using =MODE.SNGL(range)
• Standard Deviation: calculated using =STDEV.S(range) or =STDEV.P(range).
• Variance: calculated using =VAR.S(range) or =VAR.P(range).
• Range: calculated using MAX(range) - MIN(range).
• Percentiles: calculated using =PERCENTILE.INC(range, k)

Inferential Statistics

• T-tests: Compare two group means by using =T.TEST(array1, array2, tails, type)
• ANOVA: Complex formula that uses Data Analysis Toolpak to compare the effectiveness of different factors on crop yield etc.
• Chi-square Test: Is used to test for independence between two categorical variables by using =CHISQ.TEST(actual range, expected range)
• Correlation: Measures relationship strengths and direction.
  • Excel Forumla: =CORREL(arrayl, array2)
• Regression: Is used to model the relationship in many varibales Excel Formula: =LINEST(y_values, x_values)

More Key Info

• Normal Distribution = NORM.DIST(x, mean, standard_dev, cumulative)
• Binomial Distribution = BINOM.DIST(number_s, n, p, cumulative)
• Poisson Distribution = POISSON.DIST(x, mean, cumulative)

Linear Regression

• This assumes a linear relationship from all the variables.
• The key goal is finding the best-fitting line.
  • Formula Example: y = mx + b

Correlation Coefficient (Pearson's r)

• It's often called "r"
• Values and Interperetation: Ranging from -1 to +1 showing degrees of correlation

Non-Parametic Tests

• Parametic tests are used when there's a non-normal pattern
• Excel does not have a direct Mann-Whitney U fuction and will require add ins or calculator manually
• Spearman's Rank Correlation: Measures the correlation between variables when the data is not nessesarily linear

Array Examples

• It returns range of regeession staistics and needs to select cells to properly type.
• You need to select cells to properly enter MODE.MULT

Array Use Reason

• It runs calulations in many ranges and is more effient with doing regular and complex calulations
• All data can be more easily menipulated

Quick Guide/Shortcuts

• CTRL + z = Undo
• CTRL + c = Copy
• CTRL + U = Underline
• F1 = Open excel help etc