Descriptive and Inferential Statistics

Descriptive statistics is the term Descriptive given to the analysis of data that and helps describe, show or summarize data ,can either be Inferential graphical or computational. Statistics Descriptive Inferential Statistics allows testing of hy...

Descriptive statistics is the term Descriptive given to the analysis of data that and helps describe, show or summarize data ,can either be Inferential graphical or computational. Statistics Descriptive Inferential Statistics allows testing of hypothesis and and drawing conclusions about a population, based on sample, Inferential modeling relationships within Statistics the data.  Quantitative Data vs Qualitative Data Types of Data Quantitative data can Qualitative data is be counted, measured, descriptive and and expressed using conceptual. It can be numbers. categorized based on traits and characteristics. “Numerical” “Categorical”  A variable is an attribute that describes a person, place, Variables thing, or idea. The value of the variable can "vary" from one entity to another.  According to Scale of Measurement Nominal Ordinal Variables also called categorical variables don’t have a numeric value a property defined by an operation whereby members of cannot be added, subtracted, a particular group of ranked. divided or multiplied. contains things that you can place in order. Gender Color Occupation  According to Scale of Measurement Interval Ratio Variables Interval data is a type of data Has all properties of an interval which is measured along a variable and has a clear scale, in which each point is definition of 0 placed at an equal distance Zero that means the absence or (interval) from one another. none of the thing being measured  According to Functional Relationship Independent Variable Dependent Variable Variables – predictor variable – criterion variable  Correlation is a measure of relationship between two variables. Correlation The degree of relationship between variables is expressed into: 1. Perfect correlation (positive or negative) 2. Some degree of correlation (positive or negative) 3. No correlation  A POSITIVE CORRELATION is a relationship between two variables in which both variables move in the same direction. Therefore, when one variable increases as the other variable increases, or one variable decreases while the other decreases. Correlation A NEGATIVE CORRELATION is a relationship between two variables in which an increase in one variable is associated with a decrease in the other. A ZERO CORRELATION exists when there is no relationship between two variables.  Correlation Coefficient Correlation For perfect correlation, it is either positive or negative represented by +1 and -1. Correlation coefficients, positive or negative, is represented by +.01 to +.99 and -.01 to -.99. The no correlation is represented by 0.  Correlation Coefficient Correlation  Regression analysis is used to estimate the relationships between two or more variables: Independent variables (explanatory variables, or Linear predictors) are the factors that might influence the Regression dependent variable. Dependent variable (criterion variable/response variable/controlled variable) is the main factor you are trying to understand and predict.  Simple Linear Regression Simple linear regression means there is only one independent variable X which changes result on different values for Y. Model/ formula: Linear y = a + bx Regression x – the value of the independent variable, y – the value of the dependent variable. a – is a constant, the y-intercept, which shows the value of y when the value of x=0. On a regression graph, it's the point where the line crosses the y axis. b – the regression coefficient, is the slope of a regression line, which shows the rate of change for y as x changes.  Hypothesis is a statement of prediction of the relationship between or among variables or simply, it is the most specific statement of a problem. Hypothesis Testing The hypothesis can be stated in various ways: a. No existence or existence of a difference between groups b. No existence or existence of an effect of the treatment c. No existence or existence of relationship between the variables  Null Hypothesis The null hypothesis, denoted by Ho, is usually the Hypothesis hypothesis that sample observations result purely from Testing chance. It states no existence of relationship between the variables under study. It is so stated for the purpose of being accepted or rejected.  Alternative Hypothesis Hypothesis The alternative hypothesis, denoted by H1 or Ha, is the hypothesis that sample observations are influenced by Testing some non-random cause. If Ho is rejected, H1 is accepted.  EXAMPLES: Null Hypothesis There will be no significant difference in mean scores between boys and girls Hypothesis in a Reading Achievement Test. The proportion of males will not differ significantly from the proportion of Testing females in their attitudes toward birth control. The number of men and women who participate in sports is equal. Alternative Hypothesis There will be a significant difference in mean scores between boys and girls in a Reading Achievement Test. The proportion of males differs significantly from the proportion of females in their attitudes toward birth control. The number of men and women who participate in sports is not equal.  Results from a statistical test will fall into one of two regions: the rejection region— which will lead you to reject the null hypothesis, or the acceptance region, Hypothesis where you provisionally accept the null hypothesis. Testing Acceptance Region Critical Value* Critical Value*  Critical Value A critical value is a point (or points) on the scale of the test statistic beyond which we reject the null hypothesis, and, is derived from the level of significance α of the test. Hypothesis Testing Acceptance Region Critical Value* Critical Value* Test Statistic vs Critical Value (Computed value) Acceptance Region Critical Value* Critical Value* If the computed value ( test statistic computed as a result of the statistical test applied to the data )that is within +critical value and –critical value falls within the region of acceptance, the null hypothesis is to be accepted.  Significance Level Hypothesis The significance level, also denoted as alpha or α, probability of rejecting the null hypothesis when it is Testing true. It is a criterion for determining whether a test statistic is statistically significant. In practice, the most commonly used alpha values are 0.01, 0.05, and 0.1, which represent a 1%, 5%, and 10%, respectively.  P-value (Probability value) vs Significance Level In a hypothesis test, the p-value is compared to the significance level to decide whether to reject the null hypothesis. If the p value is higher than the significance level, the null Hypothesis hypothesis is accepted, and the results are not statistically significant. Testing If the p value is lower than the significance level, the results are interpreted as rejecting the null hypothesis and reported as statistically significant. For our example, the p-value (0.031) is less than the significance level (0.05), which indicates that results are statistically significant. TYPES OF STATISTICAL TESTS Statistical tests are used to analyze data and make inferences about a population based on sample data. These tests can be categorized based on the type of data and the objective of the analysis.  t-Tests are hypothesis tests that assess the means of t-TEST one or two groups. The t test tells how significant the differences between groups are.  The Independent Samples t Test (Two-Sample t-Tests ) Two group means are different. The Independent Samples t Test t-TEST compares the means of two independent groups in order to determine whether there is statistical evidence that the associated population means are significantly different. The research question is: Is there a https://datatab.net/ statistically significant difference between the mean values of two groups?  The Independent Samples t Test (Two-Sample t-Tests ) Example : t-TEST Do students who learn using Method A have a different mean score than those who learn using Method B? Measuring the weight of people who have been on a diet and people who have not been on a diet.  The Paired Samples t –Test (Dependent t-Test) Paired means are different. The Paired Samples t-Test t-TEST compares two means that are from the same individual, object, or related units. The research question is: Is there a statistically significant difference between the mean value of two https://datatab.net/ dependent groups?  The Paired Samples t –Test (Dependent t-Test) A measurement taken at two different times (e.g., pre- test and post-test with an intervention administered t-TEST between the two time points) A measurement taken under two different conditions (e.g., completing a test under a "control" condition and an "experimental" condition) Measurements taken from two halves or sides of a subject or experimental unit (e.g., measuring hearing loss in a subject's left and right ears).  ANOVA (F-test)can be used to determine if there is a statistically significant difference between the means of ANOVA groups, due to some influence factor. (Analysis of Variance) Factor Variable Response Variable Independent Dependent variable Variable  Independent Dependent variable Variable ANOVA Factor Variable Response Variable (Analysis of Variance) Level 1 Level 2 Level 3 A level is some aspect of a factor; these are what we called groups or treatments in the one factor analysis.  Effects of tea on weight loss ANOVA Independent Dependent variable Variable (Analysis of Variance) Types of Tea Weight Loss Green Tea Black Tea No Tea  ANOVA ANOVA (Analysis of Variance) One –Way Two-Way ANOVA ANOVA Used to determine Used to determine how two how one factor affects factors affect a response variable, and to determine a response variable. whether or not there is an interaction between the two factors on the response variable.  Examples: Factor Variable Response Variable ANOVA Types of Tea Weight Loss One-Way Learning Modality Exam Score Blood Pressure Medication Type Reduction  Factor #1 Variable Two-Way Response Variable ANOVA Factor #2 Variable Two-way ANOVA determines whether the interaction effect between the two factors is statistically significant. The separate effects are called main effects while the combined effects are called interaction.  Examples: Types of Tea Two-Way Weight Loss Gender ANOVA Fertilizer Type Crop Yield Crop Type  The Chi-Square Test of Independence is a statistical test used to determine whether two categorical variables are related. If two variables are related, the probability Chi-Square of one variable having a certain value is dependent on Test the value of the other variable. Examples: Test whether gender affects pet preference Determine if there is a relationship between gender on an individual and the level of education that they have obtained. Men’s voting preferences (Republican, Democrat) differ significantly from women’s preferences.  Identify the statistical tool most appropriate to use to test each of these hypotheses. t-Test (Independent) There will be a significant difference in mean score between boys and girls in a Reading Achievement Test. t-Test (Paired) The performance of Grade 7 students in the initial test will differ significantly from their performance in the final test. ANOVA (One Way) There is a significant difference in the average life of four brands of batteries.  Identify the statistical tool most appropriate to use to test each of these hypotheses. ANOVA (Two Way) There will be no difference in verbal creative thinking among high ,average and low mental ability of boys and girls. ANOVA (Two Way) There will be no interaction effect of exposure and non-exposure to reach out activities and the socio- economic status on the social responsibility of the teachers. Chi-Square There is a significant relationship between gender on an individual and the level of education that they have obtained.