Statistical Analysis PDF

Statistical Analysis EXPERIMENTAL PSYCHOLOGY Prepared by: Hannah Jane Onayan What is Statistical Analysis in Psychology? Statistical analysis in psychology is the process of applying mathematical tools to analyze and interpret psychological data. The Research Process in Experimental...

Statistical Analysis EXPERIMENTAL PSYCHOLOGY Prepared by: Hannah Jane Onayan What is Statistical Analysis in Psychology? Statistical analysis in psychology is the process of applying mathematical tools to analyze and interpret psychological data. The Research Process in Experimental Psychology Step 4. Step 1. Step 2. Step 3. Interpret and Develop a Collection of Analyzing the share the Hypothesis Data Data results Qualitative (Categorical) Data Nominal Data Categorical data that has no intrinsic order to its categories. For example, gender is a nominal variable because the categories (woman, man, transgender, non-binary, etc.) cannot be ordered from high to low Ordinal Data Categorical data that has ordered categories. For example, Olympic medals are an ordinal variable because the categories (gold, silver, bronze) can be ordered from high to low. Other examples of ordinal data include class rank, socioeconomic status, and Likert scales. Quantitative (Numerical) Data Discrete Can only take on certain values, and there are no values in between. Discrete data is countable and finite, and often represents specific observations or categories. Examples include the number of people on a ride, the score on a pair of dice, or a shoe size. Continuous Can take on any value within a given range, and there are an infinite number of values possible. Continuous data often represents a range of information, and is often used to show trends over time. Examples include the heights of a group of adults, the lengths of some leaves, or a dog's weight. Choosing the Right Statistical Test T-test: Comparing the means of two groups. Example: A researcher wants to compare the average test scores of two different teaching methods. Group 1: Students taught with Method A (n=30). Group 2: Students taught with Method B (n=30). ANOVA (Analysis of Variance) : Comparing means across multiple groups. Example: A company wants to compare employee satisfaction scores across three departments: Sales, Marketing, and HR. Group 1: Sales (n=25) Group 2: Marketing (n=30) Group 3: HR (n=20) Choosing the Right Statistical Test Chi-Square Test: Testing categorical data. Example: A survey asks people if they prefer coffee or tea, and their responses are grouped by age category. Age group 1: 18-30 Age group 2: 31-45 Age group 3: 46-60 Age group 4: 60+ Correlation: Measuring the strength of a relationship between two variables. Example: A researcher wants to explore the relationship between hours studied and exam scores. Variable 1: Hours studied (X) Variable 2: Exam score (Y)  Sampling Method Technique sampling refers to the process of selecting a subset of individuals (participants) from a larger population to participate in a study.  Sampling Method Technique Stratified Sampling Random Sampling The population is divided into subgroups (strata) based on a specific Every individual in the population characteristic (e.g., age, gender, has an equal chance of being education level), and participants are selected for the sample. randomly selected from each subgroup. Example: If you’re studying stress Example: If you’re studying levels across different age groups, you memory recall in university might stratify by age (e.g., 18-30, 31- students, you randomly select 45, 46-60) and randomly select participants from a list of all individuals from each age group. students at a university.  Sampling Method Technique Systematic Sampling Convenience Sampling Every nth individual is selected from a Participants are selected based list of the population after choosing a on their easy availability and random starting point. willingness to participate. Example: If you have a list of 1000 Example: If you recruit students and want a sample of 100, participants from your psychology you could randomly select a starting class to study the effect of sleep point and then choose every 10th on concentration, you’re using student (i.e., 1st, 11th, 21st, etc.). convenience sampling.  Sampling Method Technique Purposive (Judgmental) Snowball Sampling Sampling A form of non-probability Participants are selected based on sampling where initial specific characteristics or criteria that participants are chosen, and they are relevant to the research study. then refer other participants who fit the criteria for the study. Example: If you want to study the Example: If you’re researching a effects of chronic anxiety on memory, specific mental health disorder you may purposefully select and the initial participants refer participants who have been others with the same condition. diagnosed with an anxiety disorder.  Sampling Method Technique Cluster Sampling Quota Sampling The population is divided into groups Participants are selected based or “clusters” (e.g., schools, on predetermined quotas for neighborhoods), and then a random specific characteristics (e.g., age, sample of clusters is selected. All gender, ethnicity). Once the individuals within the chosen clusters quotas are filled, no more are then studied. participants are added. Example: If you want equal Example: If you’re studying representation of males and schoolchildren’s behavior in a district, females in your study, you would you might randomly select a few continue recruiting participants schools (clusters) and then study all until you reach the required students within those schools. number of each group. Tips by Ms: Choosing the Right Sampling Method For Convenience: Convenience sampling is quick but should be used cautiously. For Generalizability: Use random sampling or stratified sampling. For Specific Populations: Use purposive sampling or snowball sampling. For Cost and Time Efficiency: : Cluster sampling or systematic sampling can be more practical. Descriptive Statistics in Psychology Mean: Average score (e.g., average memory recall score). Median: Middle value when the data is ordered. Standard Deviation (SD): Measure of variability or how spread out the data is. Range: Difference between the highest and lowest scores. Visuals: Show a histogram or bar chart to visually represent the data distribution.  Interpreting Results P-value: Determines statistical significance. p < 0.05: The result is statistically significant. The null hypothesis is rejected. p ≥ 0.05: The result is not statistically significant. We fail to reject the null hypothesis. Effect Size: How big is the observed effect? Confidence Intervals: Range within which the true population parameter is likely to fall.  P-value (Probability) The p-value tells you how likely it is that the results of your experiment happened by chance. It helps you decide if what you found is something real or just a fluke. A small p-value (≤ 0.05) means the result is unlikely to have happened by chance, so you can say there’s a real effect. A large p-value (> 0.05) means the result could have happened by chance, so you don’t have enough evidence to say there’s a real effect.  P-value (Probability) Example: Imagine you want to test if a new type of cookie recipe tastes better than the regular recipe. 1. Null Hypothesis (H₀): There is no difference in taste between the new and regular cookies. 2. Alternative Hypothesis (H₁): The new cookies taste better than the regular cookies. You ask 100 people to try both cookies and rate them on taste. After analyzing the ratings, you get a p-value of 0.02. What does this mean? A p-value of 0.02 means there’s only a 2% chance the difference in ratings happened by random luck. Since 0.02 is less than 0.05, you can reject the null hypothesis and say, “The new cookie recipe likely tastes better than the regular one.”  P-value (Probability) If the p-value were, for example, 0.10, that would mean there’s a 10% chance the difference in taste could have happened by chance. Since 0.10 is greater than 0.05, you would fail to reject the null hypothesis, meaning you don’t have strong enough evidence to say the new cookie recipe tastes better. Summary: p-value ≤ 0.05: Strong evidence that the new cookies taste better. p-value > 0.05: Not enough evidence to say the new cookies taste better. Thank You