Basic Concepts in Statistics 1 By Ahlam Lee

Contents • Variable vs. Constant • Types of Variables - Independent vs. Dependent Variable in Research Questions - Continuous, Ordinal, and Nominal Variable • Parametric vs. non-Parametric tests. • Methods of sampling

• A Variable is a measured characteristics that can vary and assume different values or levels (e. g. , age, height, gender, political affiliation) --- a changeable value depending on people and situation. • A Constant is a measured characteristics that has only one value (e. g. , The number of month in a year, the number of hours in a day, 5, etc) --- a fixed value.

Independent Variable Time Spent Studying Independent Variable Dependent Variable Test Score Dependent Variable -A variable that stands alone and isn’t - Is a changeable variable that is changed by the other variables. affected (or caused) by an independent variable. - called an explanatory or predictable - Represents the output or effect. variable that can explain or predict a - A variable that depends on other dependent variable. factors (independent variables). - called response or predicted variable – Outcome(s) of a study

- (Time Spent Studying) influence (Test Score). IV DV - (Social Economic Status) affects (student academic achievement). IV DV - (Teacher Professional development) has an effect on (student test scores) IV DV “(Independent variable) causes a change in (Dependent Variable)” Reference: https: //nces. ed. gov/nceskids/help/user_guide/graph/variables. asp

• Identify the independent and dependent variables in the following description of an experiment: Researchers investigated the effects of project-based learning activities on student science achievement scores. “(Independent variable) causes a change in (Dependent Variable)” (Project-based learning activities) cause a change in (science achievement scores) IV: Project-based learning activities DV: Student science achievement scores

Questions • “Is having the death penalty available for punishment associated with a reduction in violent crime? ” • “Does student performance in schools depend on the amount of money spent per student, the size of the classes, or the teachers’ salaries? ”

Questions The following is a hypothesis for a study: • “There will be a statistically significant difference in graduation rates of at-risk-high school seniors who participate in an intensive study program as opposed to at-risk-highschool seniors who do not participate in the intensive study program. ” (La. Fountain & Bartos, 2002, p. 57).

Questions The following is a description of a study: • “A director of residential living on a large university campus is concerned about the large turnover rate in resident assistants. In recent years, many resident assistants have left their positions before completing even 1 year in their assignments. The director wants to identify the factors that predict commitment as a resident assistant (defined as continuing in the position a minimum of 2 years). The director decides to assess knowledge of the position, attitude toward residential policies, and ability to handle conflicts as predictors.

Independent and dependent variables Continuous Variable Nominal Variable Ordinal Variable Independent and dependent variables

Definition Continuous Variable Can take on a wide range of values and contains an infinite number of small increments. : interval scale or ratio scale Examples Height, age, salary, temperature Note *** Theoretically, those examples are IQ score, ACT/SAT/GRE considered discrete variables, but for scores. practical purposes for analyzing data, the test scores are considered continuous variables. Nominal Variable Is a categorical variable that has no numerical meaning Gender, Race, Political Affiliation, marital status, etc Ordinal Variable Is a categorical variable that has a numerical meaning. Ordinal variable has a level or rank that can be naturally ordered. Survey questionnaire: How do you feel about this lecture? 1 = Awful 2 = Poor 3 = Ok 4 = Good 5 = Excellent Note: In statistical analysis, ordinal variable is often considered as a continuous variable.

Parametric vs. non-Parametric tests Dependent Variable Continuous Variable Ordinal Variable Nominal Variable Parametric Tests Non-Parametric tests T-test Whitney Mann U Test, Whitney Mann Rank Test, and Signed Test Chi-Squared test Pearson correlation Kendall and Spearman correlation linear regression ANOVA Ordinal regression Logistic regression

Population Sample The term, “population”, represents all possible observations that can be included in a particular study. However, when conducting a study, we (researchers) cannot access entire population. Thus, we (researchers) want to select a portion of the population which is referred to the term, “sample”.

Example: • Researchers randomly selected 200 teachers and asked their perspectives about their school climates. Sample: 200 teachers Population: All teachers who work at the school.

• Agresti, A. , & Finley, B. (2009). Statistical methods for the social Sciences (4 th ed. ). Upper Saddle River, NJ: Pearson. • Creswell, J. W. (2012). Educational Research: Planning, conducting, and evaluating quantitative and qualitative research 4 th ed. Boston, Pearson. • Heppner, P. P. , Kivlighan, D. M. , Jr. , & Wampold, B. E. (1999). • La. Fountain, R. M. , & Bartos, R. B. (2002). Research and statistics made meaningful in counseling and student affairs. Pacific Grove. CA: Brooks/Cole. • Ravid, R. (2011). Practical Statistics for Educators. Rowman & Littlefield Publishers, Inc.