T-Tests: Comparing Two Groups

• Introduction to Statistical Tests
  • Goal is to understand when and how to use common statistical tests.
  • Tests covered will include T-test, ANOVA, Chi-Square, and Repeated Measures ANOVA.
  • Focus will be on when to use the tests, how to run them, and how to report the results in APA style.

T-Test

• Use to compare two groups on a continuous variable (comparing two means).
• Useful for questions like, "Do males and females differ in exam scores?"
• Type: Independent Samples T-Test, which involves two separate groups.
• Steps:
  • Check normality using the Shapiro-Wilk test.
  • Run the T-test.
  • Look at the p-value to decide if the difference is significant.
  • Check equality of variances using Levene's test.
• APA Style Reporting includes reporting the means, standard deviations, the t-statistic, degrees of freedom, and p-value, for example: An independent samples t-test showed that exam scores were significantly higher for males (M = 82.5, SD = 6.3) than for females (M = 78.1, SD = 7.2), t(48) = 2.25, p = .029

One-Way ANOVA

• Used to compare 3 groups on a continuous variable which involves three means.

Measures of Central Tendency

• Measures of central tendency, also called averages, give an idea about the concentration of values in the central part of a distribution.
• Measures tell where the majority of values in the distribution are located.
• Examples: Arithmetic mean (average), median (middle value), and mode (most frequent value).

What is APA Style?

• A set of guidelines created by the American Psychological Association for writing research papers and reporting results, especially in the social sciences.
• Why use APA style?
  • Keeps research clear and consistent.
  • Makes it easy for others to understand and replicate your work.
  • Widely used in psychology, education, and nursing.
• Main components of APA Style:
  • Formatting (margins, font, spacing).
  • In-text citations and a reference list.
  • Reporting statistics.
  • Headings, tables, and figures.
• Reporting statistics in APA style includes always reporting:
  • Test type (t, F, x², etc.).
  • Degrees of freedom in parentheses.
  • The test statistic value.
  • The p-value.
  • Any relevant descriptive stats (M, SD, etc.).
• Use italics for statistical symbols (e.g., t, p, F).
• Example: An independent samples t-test found a significant difference in scores, t(38) = 2.45, p = .019

APA Style for Captions for Tables and Figures

• Tables:
  • Numbered (e.g., Table 1)
  • Title italicized, flush left, above the table
  • Notes below the table if needed.
  • Example: table with summary of participant demographics
• Figures (charts, graphs, photos):
  • Numbered (e.g., Figure 2)
  • Title and caption below the figure
  • Italicize the word "Figure" and the number
  • Example: Figure shows Mean Test Scores by Age Group

Non-Probability Sampling

• Members are selected from the population in some nonrandom manner.
• Each member of the population has an unknown probability of selection.
• Example types include convenience, judgmental/purposive, quota, and snowball sampling.

Regression Analysis

• Regression allows you to estimate how a dependent variable changes based on the change in an independent variable(s).
• Types of regressions: include simple linear regression, logistic regression, and multiple regression.

Correlation

• Correlation helps to describe the relationship between two variables.
• Helps to understand the degree (strong/weak) and direction (positive/negative) of the relationship.
• Used with variables measured on interval, ordinal, and ratio levels.
• Correlation does not equal causation; correlation indicates a relationship, but not necessarily a cause-and-effect.
• When changes in one variable cause another variable to change, this is a causal relationship.
• The most important thing to understand is that correlation is not the same as causation - sometimes two things can share a relationship without one causing the other.
• Correlation is when two factors (or variables) are related, but one does not necessarily cause the other.
• Causation is when one factor (or variable) causes another.
• The third variable and directionality problems are two main reasons why correlation isn't causation.

Measuring and Reporting Correlation

• The most frequently used bivariate correlational procedure is called Pearson's product-moment correlation (Pearson's r).
• Pearson's r is used when each of the two variables is quantitative and measured to produce raw scores.
• Correlation coefficient denoted 'r' - normally between -1.00 and +1.00.

Correlation on a graph

• Correlation (r) measures the direction and strength of the linear relationship between two quantitative variables.
• r = 0 indicates no correlation, r > 0 indicates a positive association, and r < 0 indicates a negative association.
• The sign indicates the nature of the relationship.
• Size of Correlation and Interpretation
  • .90 to 1.00 (-.90 to -1.00): Very high positive (negative) correlation
  • .70 to .90 (-.70 to -.90): High positive (negative) correlation
  • .50 to .70 (-.50 to -.70): Moderate positive (negative) correlation
  • .30 to .50 (-.30 to -.50): Low positive (negative) correlation
  • .00 to .30 (.00 to -.30): negligible correlation

Simple Linear Regression

• Involves one predictor variable and one response variable.
• Aims to see how well scores on the dependent variable can predicted from data on the independent variable.

Probability

• Probability (p) is the likelihood or chance of an event occurring, with 0 ≤ P(E) ≤ 1.
• P(E) refers to the probability of event E occurring.
• Probability is a number between 0 and 1.
• The sum of the probabilities of all possible outcomes is 1.
• Probability of an event occurring is 1
• Probability of an event NOT occurring is 0 (impossible).

Hypothesis Testing

• Conducted ONLY with quantitative data.
• Two types of hypotheses: Null Hypothesis (Ho) and Alternative Hypothesis (Ha).
• Null Hypothesis (Ho):
  • Proposes NO differences between the means of the variables of interest (negative statement).
  • This is the assumption we want to test (the assumption that we are trying to reject).
• Alternative Hypothesis (Ha):
  • Often called the research hypothesis; proposes differences EXIST between the means of the variables of interest (positive statement).

Selecting and Interpreting Significance Level

• With a small p-value we reject Ho, and small P-values are strong evidence against Ho.
• P-value of 0.05 or less is typically considered statistically significant.
• Relationships between p-value and support for Ho:
  • Greater than 10% - very weak to none against Но
  • Between 10%-5% weak
  • Between 5% - 1% - strong
  • Less than 1%-very strong
• Do not reject the null hypothesis if it falls within the region of area 0.95.
• The higher the level of significance, the higher is the probability of rejecting the null hypothesis when it is true.

Types of Sampling

• Probability sampling: the sample is selected at random. Everyone in the population has an equal chance of getting selected.
• Non-probability sampling: Sample selection based on the subjective judgment of the researcher. Not everyone has an equal chance to participate.

Stratified Random Sampling

• Stratified random sampling is a method of sampling that involves the division of a population into smaller subgroups known as strata.
• The strata are formed based on members' shared attributes or characteristics, such as income or educational attainment.
• Has numerous applications and benefits, such as studying population demographics and life expectancy.

Simple Random Sampling

• Each individual in the population has an equal chance of selection into the sample
• Ways to use Simple Random Sampling include:
  • The lottery method.
  • Random-number table.
  • Software program.

Cluster Random Sampling

• Researchers divide the population into multiple groups (clusters) for research.
• Instead of taking all groups we select a sample of these groups and we call each group as a cluster such as schools or classes.

Non- Probability Sampling Types

• Convenience Sampling are the most conveniently available people for the researcher.
• Judgmental/Purposive Sampling has the sample is selected based on the opinion of an expert.
• Quota Sampling has a researcher wants to study the career goals of male and female employees in an organization.
• Snowball Sampling (Referral or Chain Sampling) has participants select new members to their respective group

Relative Risk

• Probability that a given individual or individuals will develop a specific condition
• Estimates the likelihood that a specific condition will occur

Risk Assessment

• Those at risk have the greatest potential to develop a problem because of presence or absence of factor
• Relative Risk (RR) is comparing the probability of a disease within exposed group vs non exposed group
• RR=1: Risk in exposed equal to risk in non-exposed (no association)
• RR>1: Risk in exposed is greater than risk in non-exposed: possible causal effective
• RR<1: Risk in exposed is less than risk in non-exposed: maybe protective