handout week 1 course Renske Doorenspleet 1 Chapter 1 -A. The role of statistics in the research process -B. Statistical applications -C. Types of variables

handout week 1 course Renske Doorenspleet 2 A. The Role Of Statistics  Statistics are mathematical tools used to organize, summarize, and manipulate data.  Data are scores on variables. Information expressed as numbers (quantitatively).

handout week 1 course Renske Doorenspleet 3 Variables  Traits that can change values from case to case.  Examples: Age Gender Race Social class

handout week 1 course Renske Doorenspleet 4 Case The entity from which data is gathered. Examples  People  Groups  States and nations

handout week 1 course Renske Doorenspleet 5 The Role Of Statistics:Example  Describe the age of students in this class.  Identify the following: Variable Data Cases Appropriate statistics

handout week 1 course Renske Doorenspleet 6 B. Statistical Applications  Two main statistical applications: Descriptive statistics Inferential statistics

handout week 1 course Renske Doorenspleet 7 Descriptive Statistics  Summarize variables one at a time.  Summarize the relationship between two or more variables.

handout week 1 course Renske Doorenspleet 8 Descriptive Statistics  Univariate descriptive statistics include: Percentages, averages, and various charts and graphs. Example: On the average, students are 20.3 years of age.

handout week 1 course Renske Doorenspleet 9 Descriptive Statistics  Bivariate descriptive statistics describe the strength and direction of the relationship between two variables. Example: Older students have higher grades.  Multivariate descriptive statistics describe the relationships between three or more variables. Example: Grades increase with age for females but not for males.

handout week 1 course Renske Doorenspleet 10 Inferential Statistics  Generalize from a sample to a population. Population includes all cases in which the research is interested. Samples include carefully chosen subsets of the population.

handout week 1 course Renske Doorenspleet 11 Inferential Statistics  Voter surveys are a common application of inferential statistics. Several thousand carefully selected voters are interviewed about their voting intentions. This information is used to estimate the intentions of all voters (millions of people). Example: The Conservative candidate will receive about 42% of the vote.

handout week 1 course Renske Doorenspleet 12 C. Types Of Variables  In causal relationships: CAUSE  EFFECT independent variable  dependent variable  Discrete variables are measured in units that cannot be subdivided.  Continuous variables are measured in a unit that can be subdivided infinitely.

handout week 1 course Renske Doorenspleet 13 Level Of Measurement  Nominal variables- Scores are labels only, they are not numbers, e.g. gender  Ordinal - Scores have some numerical quality and can be ranked from more to less, e.g. items that measure opinions and attitudes  Interval-ratio - Scores are numbers, e.g. education and age

handout week 1 course Renske Doorenspleet 14 Level of Measurement  Different statistics require different mathematical operations (ranking, addition, square root, etc.)  The level of measurement of a variable tells us which statistics are permissible and appropriate.

handout week 1 course Renske Doorenspleet 15 CHAPTER 2 Basic Descriptive Statistics: Percentages, Ratios and rates, Tables, Charts and Graphs

handout week 1 course Renske Doorenspleet 16 Percentages and Proportions

handout week 1 course Renske Doorenspleet 17 Percentages and Proportions: Example  What % of social science majors is male? of (whole) = all social science majors  = 229 is (part) = male social science majors  97 (97/229) * 100 = (.4236) * 100 = 42.36% 42.36% of social science majors are male

handout week 1 course Renske Doorenspleet 18 Ratios  Compare the relative sizes of categories.  Compare parts to parts.  Ratio = f 1 / f 2 f 1 - number of cases in first category f 2 number of cases in second category

handout week 1 course Renske Doorenspleet 19 Ratios  In a class of 23 females and 19 males, the ratio of males to females is: 19/23 = 0.83 For every female, there are 0.83 males.  In the same class, the ratio of females to males is: 23/19 = 1.21 For every male, there are 1.21 females.

handout week 1 course Renske Doorenspleet 20 Percentage Change  Measures the relative increase or decrease in a variable over time.

handout week 1 course Renske Doorenspleet 21 Frequency Distributions  Report the number of times each score of a variable occurred.  The categories of the frequency distribution must be stated in a way that permits each case to be counted in one and only one category.

handout week 1 course Renske Doorenspleet 22 Graphs And Charts  Pie and bar graphs and line charts present frequency distributions graphically.  Graphs and charts are commonly used ways of presenting “pictures” of research results.

handout week 1 course Renske Doorenspleet 23 Sample Pie Chart: Marital Status (N = 20)

handout week 1 course Renske Doorenspleet 24 Marriage And Divorce Rates Over Time How would you describe the patterns?