Statistical Treatment

• Parametric Assumptions – assumptions which refer to a quantity that is calculated from data and describes a population
• Independent, unbiased samples - Two samples are independent if the sample values selected from one population are NOT related or somehow paired or matched with the sample values selected from the other population.
• Data normally distributed - A normal distribution, sometimes called the bell curve, is a distribution that occurs naturally in many situations. For example, the bell curve is seen in tests like the SAT and GRE. The bulk of students will score the average (C), while smaller numbers of students will score a B or D. An even smaller percentage of students score an F or an A. This creates a distribution that resembles a bell (hence the nickname). The bell curve is symmetrical. Half of the data will fall to the left of the mean; half will fall to the right.
• Equal variances - Variance refers to the data spread or scatter. Statistical tests, such as analysis of variance (ANOVA), assume that although different samples can come from populations with different means, they have the same variance. Equal variances (homoscedasticity) is when the variances are approximately the same across the samples.
• Continuous Data - Continuous Data can take any value (within a range).
• Discrete - can only take certain values.
• Chi-square test - used to determine if there is a significant relationship between two nominal (categorical) variables.*
• True independent variable - occurs when subjects arrive for the study and the experimenter randomly assigns them to groups.
• Regression Analysis - a set of statistical processes for estimating the relationships among variables*
• Correlational Analysis - a method of statistical evaluation used to study the strength of a relationship between two, numerically measured, continuous variables*
• Parametric - rely on assumptions about the shape of the distribution (i.e., assume a normal distribution) in the underlying population and about the form or parameters (i.e., means and standard deviations) of the assumed distribution.
• Non-parametric - rely on no or few assumptions about the shape or parameters of the population distribution from which the sample was drawn.
• Pearson's Product Moment Correlation - evaluates the linear relationship between two continuous variables. A relationship is linear when a change in one variable is associated with a proportional change in the other variable. For example, you might use a Pearson correlation to evaluate whether increases in temperature at your production facility are associated with decreasing thickness of your chocolate coating.
• Spearman’s Rank-Order Correlation - evaluates the monotonic relationship between two continuous or ordinal variables. In a monotonic relationship, the variables tend to change together, but not necessarily at a constant rate. The Spearman correlation coefficient is based on the ranked values for each variable rather than the raw data.
• Spearman correlation is often used to evaluate relationships involving ordinal variables. For example, you might use a Spearman correlation to evaluate whether the order in which employees complete a test exercise is related to the number of months they have been employed.
• Equal Variance - when the variances are approximately the same across the samples.
• Brown and Smythe’s test - The Brown-Forsythe (B-F) Test is for testing the assumption of equal variances in ANOVA.
• Bartlett’s test - used to test that variances are equal for all samples. It checks that the assumption of equal variances is true before running certain statistical tests like the One-Way ANOVA. It’s used when you’re fairly certain your data comes from a normal distribution.
• Means -  average of a set of data
• Paired t-test - means that you will look at the differences between the two groups. This test first calculates the difference from one group to the other, and runs a one-sample t test. (difference of two groups)
• Unpaired t-test - means that you simply compare the two groups. So, you will build a model for each group (calculate the mean and variance), and see whether there is a difference. Data transformation - replacement of a variable by a function of that variable: for example, replacing a variable x by the square root of x or the logarithm of x. In a stronger sense, a transformation is a replacement that changes the shape of a distribution or relationship.
• Mann-Whitney U - used to compare differences between two independent groups when the dependent variable is either ordinal or continuous, but not normally distributed.
• Wilcoxon Rank sums test - a nonparametric alternative to the two sample t-test which is based solely on the order in which the observations from the two samples fall.
• Analysis of Variance (ANOVA) - is a statistical method used to test differences between two or more means.
• Post-hoc test - means to analyze the results of your experimental data. They are often based on a familywise error rate; the probability of at least one Type I error in a set (family) of comparisons.
• Tukey’s test - to figure out which groups in your sample differ. It uses the “Honest Significant Difference,” a number that represents the distance between groups, to compare every mean with every other mean.
• Bonferroni’s test - This multiple-comparison post-hoc correction is used when you are performing many independent or dependent statistical tests at the same time.
• Kruskal-Walis - used when the assumptions of one-way ANOVA are not met. 
• Dunn’s test - a post hoc (i.e. it’s run after an ANOVA) non parametric test (a “distribution free” test that doesn’t assume your data comes from a particular distribution).
• Fmax test - is a test for homogeneity of variance. In other words, the spread (variance) of your data should be similar across groups or levels. (compare variances)
• Descriptive Statistics: the analysis of data that helps describe, show or summarize data in a meaningful way such that, for example, patterns might emerge from the data.
• Inferential Statistics: includes all the techniques used in analyzing the sample data that will lead to generalizations about a population from which the sample came from (Añez-Tandang, 2019).
• DESCRIPTIVE STATISTICS

  ➢Measures of Central Tendency (Mean, Median, Mode)

  ➢Measures of Dispersion (Variance, Standard Deviation, Coefficient of Variation, etc)

  ➢Measures of Position (Quantiles, Min, Percentiles, etc) ➢Measures of Shape (Skewness, Kurtosis, etc)
• CHARTS AND GRAPHS

  ➢ Line Chart – used for trends and changes over a period of time such as trends in stocks, changes in the amount of rainfall or annual unemployment rates.

  ➢ Bar Graphs – used to show magnitude of variables or show distribution of data points.

  ➢ Pie Chart – used to show percentage or proportional data. It is only meaningful if the sum of the individual parts add up to a whole.

  ➢ Scatter Plot – used to show spread of distribution of data. It can also show relationship when a scatter plot contains a regression line.
• Summary of Statistical Treatment

  A) Mcnemar

  B) Fisher

  C) Cochran q-test

  D) Chi square

  E) Wilcoxon rank

  F) Mann-Whitney U-test

  G) Friedman

  H) Kruskal-Wallis

  I) Analysis of Variance

  J) Repeated Measures Anova

  K) Uncorrelated

  L) Correlated

  
• Summary of Statistical Treatment

  A) Chi-square

  B) Spearman's

  C) Pearson's

  
• Summary of descriptive statistic

  A) Qualitative

  B) Nominal

  C) Ordinal

  D) Quantitative

  E) Distribution Disregarded

  F) Distribution not normal

  G) Normal distribution

  H) Mode Frequency Percentage

  I) Median

  J) Mean

  K) Interquartile range

  L) range

  M) standard deviation