Data Analysis using Statistics and Hypotheses Testing.pdf
- 1. RESEARCH IN DAILY LIFE 2 Data Analysis Using Different Statistics and Hypotheses Testing
- 2. Life Performance Outcomes I am Courageous, Resourceful EXPLORERS & PROBLEM SOLVERS
- 3. Essential Performance Outcomes Seek out issues, possibilities, and sources of related information willingly for further investigation and development.
- 4. Intended Learning Outcomes Seek out issues, possibilities, and sources of related information through Data Analysis Using Different Statistics and Hypotheses Testing for further investigation and development.
- 5. Steps in Quantitative Data Analysis 1. Preparing the Data ▪ Coding System ▪ Data Tabulation 2. Analyzing the Data
- 6. Test Statistics - Is a mathematical formula that allows researchers to determine the likelihood of obtaining sample outcomes if the null hypotheses were true. - The value of the test statistic is used to make a decision regarding the null hypothesis.
- 7. Statistical Tests Univariate Descriptive Central Tendency Mode - the most commonly occurring value ex: 6 people with ages 21, 22, 21, 23, 19, 21 – mode = 21 Median • the center value ex: 6 people with ages 21, 22, 24, 23, 19, 21 line them up in order form lowest to highest 19, 21, 21, 22, 23, 24 and take the center value - mode =21.5
- 8. Statistical Tests Central Tendency Mean - the mathematical average ex: mean age = age of person one + age of person two + age of person three, etc./number of people Variance - a measure of how spread out a distribution is. It is computed as the average squared deviation of each number from its mean
- 9. Statistical Tests Central Tendency Standard Deviation ▪ how much scores deviate from the mean ▪ it is the square root of the variance ▪ it is the most commonly used measure of spread
- 10. Bi-and Multivariate Inferential Statistical Tests Chi Square - compares observed frequencies to expected frequencies ▪ ex: Is the distribution of sex and voting behavior due to chance or is there a difference between the sexes on voting behavior? t-Test - looks at differences between two groups on some variable of interest; the IV must have only two groups (male/female, undergrad/grad) ▪ ex: Do males and females differ in the amount of hours they spend shopping in a given month?
- 11. Bi-and Multivariate Inferential Statistical Tests ANOVA - tests the significance of group differences between two or more groups; the IV has two or more categories. ▪ ex: Do NSAT scores differ for low-, middle-, and high-income students? ANCOVA - same as ANOVA, but adds control of one or more covariates that may influence the DV ▪ ex: Do NSAT scores differ for low-, middle-, and high-income students after controlling for single/dual parenting?
- 12. Bi-and Multivariate Inferential Statistical Tests MANOVA - same as ANOVA, but you can study two or more related DVs while controlling for the correlation between the DV; if the DVs are not correlated, then separate ANOVAs are appropriate ▪ ex: Does economic status affect reading achievement, math achievement, and overall scholastic achievement among 6 graders? MANCOVA - same as MANOVA, but adds control of one or more covariates that may influence the DV ▪ ex: Does economic status affect reading achievement, math achievement, and overall scholastic achievement among 6 graders after controlling for social class?
- 13. Bi-and Multivariate Inferential Statistical Tests Correlation - used with two variables to determine a relationship/association; do two variables covary?; does not distinguish between independent and dependent variables ▪ ex: Amount of damage to a house on fire and number of firefighters at the fire Multiple Regression - used with several independent variables and one dependent variable; used for prediction; it identifies the best set of predictor variables. ▪ ex: IVs drug use, alcohol use, child abuse DV, suicidal tendencies
- 14. Hypothesis testing or significance testing - Is a method for testing a claim or hypothesis about a parameter in a population, using data measured in a sample. - In this method, we test some hypothesis by determining the likelihood that a sample statistic could have been selected, if the hypothesis regarding the population parameter were true. Data Analysis Using Different Statistics and Hypotheses Testing
- 15. FOUR STEPS TO HYPOTHESIS TESTING Step 1: State the hypotheses. ▪ We begin by stating the value of a population mean in a null hypothesis, which we presume is true. ▪ Keep in mind that the only reason we are testing the null hypothesis is because we think it is wrong. We state what we think is wrong about the null hypothesis in an alternative hypothesis.
- 16. FOUR STEPS TO HYPOTHESIS TESTING Step 2: Set the criteria for a decision. ▪ To set the criteria for a decision, we state the level of significance for a test. ▪ Likewise, in hypothesis testing, we collect data to show that the null hypothesis is not true, based on the likelihood of selecting a sample mean from a population (the likelihood is the criterion).
- 17. FOUR STEPS TO HYPOTHESIS TESTING Step 3: Compute the test statistic ▪ A test statistic tells us how far, or how many standard deviations, a sample mean is from the population mean. The larger the value of the test statistic, the further the distance, or number of standard deviations, a sample mean is from the population mean stated in the null hypothesis.
- 18. FOUR STEPS TO HYPOTHESIS TESTING Step 4: Make a decision ▪ We use the value of the test statistic to make a decision about the null hypothesis. The decision is based on the probability of obtaining a sample mean, given that the value stated in the null hypothesis is true. ❑ Reject the null hypothesis. ❑ Retain the null hypothesis
- 19. FOUR STEPS TO HYPOTHESIS TESTING Step 4: Make a decision ▪ When the p value is less than 5% (p < .05), we reject the null hypothesis. We will refer to p < .05 as the criterion for deciding to reject the null hypothesis, although note that when p = .05, the decision is also to reject the null hypothesis. ▪ When the p value is greater than 5% (p > .05), we retain the null hypothesis. The decision to reject or retain the null hypothesis is called significance.
- 20. Example: Table 1 Reason for Involvement in Evaluation Stage Chi-square test yield a p-value of .00001 which is smaller than the significance level alpha = 0.05. This result rejects the null hypothesis and accepts the alternative hypothesis that there is a significant association between the project participants’ reason for participation in the evaluation stage. Reason for Participation Evaluation Statistical Test Value Interpre- tation No Yes Economic 27 7 Chi-Square .00001 Significant Personal 11 17 Social Service 53 5