Unit IV ST 2 PDF

Unit IV  Hypothesis testing Develop the Research question Develop the research hypothesis State it as a Statistical hypothesis Test the hypothesis Was it a good idea Next question  Four elements of research question Patient or Population - What or who is the questi...

Unit IV  Hypothesis testing Develop the Research question Develop the research hypothesis State it as a Statistical hypothesis Test the hypothesis Was it a good idea Next question  Four elements of research question Patient or Population - What or who is the question about Intervention or exposure - What is being done or what is happening to the population or patients Comparisons - What could be done instead of interventions Outcomes - How does the intervention affect the population or patients  P – population, patients, or problem I – intervention or indicator being studied C – comparison group O – outcome of interest  Between the ages of five and 18, are children of parents with diagnosed mental health issues at increased risk of depression or. anxiety compared with children of parents with no diagnosed mental health issues? P (population being studied) children parents with diagnosed mental I (indicator or intervention) health issues children of parents with no C (comparison group) diagnosed mental health issues increased risk of depression or O (outcome of interest) anxiety  Defining the hypothesis Definition: “A well defined hypothesis crystalizes the research question and influence the statistical tests that will be used in analyzing the results” What is hypothesis A tentative statement that proposes a possible explanation to some phenomenon or an event A useful hypothesis is testable statement which may include a prediction Any procedure you follow without an hypothesis is not an experiment  How to format the hypothesis IF and THEN Specify a tentative relationship IF skin cancer is related to Ultra Violet light, THEN people with high exposure of UV light will have a high frequency of skin cancer Dependent variable Independent variable If some students eat breakfast before school and others do not, then the ones who do eat breakfast will have better grades in their morning classes, because their brains have more energy to think.  How to Disprove the hypothesis Collect all the evidences If the evidence is supporting current hypothesis then hold the hypothesis to be provisionally True If the evidence does not support hypothesis reject the hypothesis and develop the new one. Statistical testing uses Null hypothesis No difference unless unlikely event Alternative hypothesis a difference  Statistical Hypothesis Testing Define the problem State the Null hypothesis (H0) State the Alternative hypothesis (H1) Collect a sample of data to gather evidence Calculate test statistics observed value – hypothesized value Test Statistics = ________________________________ Standard error of observed value Relate test Statistics to known distribution to obtain P value Interpret the P-value  Defining the Problem The Null hypothesis assumes no effect H0 There is no treatment effect in the population of interest The alternative hypothesis opposite of Null hypothesis H1: there is a treatment effect in the population of interest  Example for Hypothesis What is hypothesis If a person drinks cranberry juice then there will be a reduction in the recurrence of Urinary Tract Infection (UTI) Statistical Hypothesis Null: There are no difference in recurrence rates of UTI among population who drink cranberry juice Alternative: There is difference in the recurrence rates in the population  How do we choose the Test Statistics What is the measurement of interest For example: Means or Proportions What is the distribution of the measurement For example: Normal or Skewed How many groups of patients are being studied For example: 1,2,3 or more than Are they independent groups or paired  Interpretation of P-value The probability of getting test statistics as large as or longer than, the one obtained in the sample if the Null hypothesis were True It is the probability that our results occurred by chance  Example Past research data from a period of over several years states that the average life expectancy of whales is 100 years. A researcher at a laboratory wishes to test this hypothesis. To that end they procure a sample of life spans of several whales. What is the null hypothesis and the alternative hypothesis that this researcher will establish?  Example Past research data from a period of over several years states that the average life expectancy of whales is 100 years. A researcher at a laboratory wishes to test this hypothesis. To that end they procure a sample of life spans of several whales. What is the null hypothesis and the alternative hypothesis that this researcher will establish? H0: The average life expectancy of whales is exactly equal to 100 years. Ha: The average life expectancy of whales is not equal to 100 years.  Examples of Mean Hypotheses Example 1: In the year 2020, the mean body weight of new born babies in Saudi Arabia was more than 3 kg with standard deviation of 1.2 kg. A pediatrician believe that due to some lack of balanced diet among the Saudi women, the body weight of new born babies in 2021 is less than 3 kg. Q: Identify the H0 and Ha in the above mentioned example?  Examples of Mean Hypotheses Example 1: In the year 2020, the mean body weight of new born babies in Saudi Arabia was more than 3 kg with standard deviation of 1.2 kg. A pediatrician believe that due to some lack of balanced diet among the Saudi women, the body weight of new born babies in 2021 is less than 3 kg. Q: Identify the H0 and Ha in the above mentioned example? Answer: H0 : μ ≥3 kg Ha : μ < 3 kg  Examples of Mean Hypotheses Example 2: Doctors believe that the average teen sleeps on average no longer than 10 hours per day in Saudi Arabia. However, a researcher believes that teens on average sleep longer. Q: Identify the H0 and Ha in the above mentioned example?  Examples of Mean Hypotheses Example 2: Doctors believe that the average teen sleeps on average no longer than 10 hours per day in Saudi Arabia. However, a researcher believes that teens on average sleep longer. Q: Identify the H0 and Ha in the above mentioned example? Answer: H0 : μ ≤ 10 hours Ha : μ > 10 hours  Examples of Proportion Hypotheses Example 1: A pharmaceutical company reported that at least 60% of the diabetes patients responded to Diabex (Metformin). Doctors in Diabetic center of King Fahd Hospital contradict with the statement and claim the response rate quite less than the reported one. Q: Identify the H0 and Ha in the above mentioned example?  Examples of Proportion Hypotheses Example 1: A pharmaceutical company reported that at least 60% of the diabetes patients responded to Diabex (Metformin). Doctors in Diabetic center of King Fahd Hospital contradict with the statement and claim the response rate quite less than the reported one. Q: Identify the H0 and Ha in the above mentioned example? Answer: H0 : p ≥ 0.60 Ha : p < 0.60  Examples of Proportion Hypotheses Example 2: Breast cancer ranked first among the females in Saudi Arabia, accounting for up to 25% of all newly diagnosed female cancers in the year 2018. Q: Identify the H0 and what will the possible Ha in the above mentioned example?  Examples of Proportion Hypotheses Example 2: Breast cancer ranked first among the females in Saudi Arabia, accounting for up to 25% of all newly diagnosed female cancers in the year 2018. Q: Identify the H0 and what will the possible Ha in the above mentioned example? Answer: H0 : p ≤ 0.25 Ha : p > 0.25  Data and variables One variable per DATA: the answers to questions or column measurements from the experiment VARIABLE = measurement which varies between subjects e.g. height or gender One row per subject  Inference Two ways to make inference Estimation of parameters * Point Estimation (X or p) * Intervals Estimation Hypothesis Testing To compare any two or more variables or groups and to estimate the population values from the sample values Inferential statistics is used. There are two types 1. Estimation (Confidence Interval) 2. Test of Significance (Testing of Hypothesis)  Estimation To estimate the population parameter using the sample value with some confidence interval (C.I) is called estimation. For Mean, 95% C.I = Mean ± Zα/2 x SE, where SE= SD / √n = 22 ± 1.96 x 1.22 = 19.6 to 24.4 For Proportions, 95% C.I = P ± Zα/2 x SE, where SE = √ {PQ / n} = 0.8 ± 1.96 x 99.2 = 0.3 to 1.5  EXAMPLE: You conducted a study on the heights of 100 students in your school. The sample mean height is 165 cm with a standard deviation of 8 cm. Calculate a 95% confidence interval for the population mean height, and explain what it means in the context of your study. 95% C.I = Mean ± Zα/2 x SE ,, = 165 ± 1.96(8/√100) = (163.2, 166.8) ,163.2 TO 166.8 This means that you can be 95% confident that the true average height of all students in your school falls within this range.  EXAMPLE In a study involving 300 patients, 200 reported experiencing pain relief after taking a new painkiller. Calculate a 95% confidence interval for the proportion of patients in the population who may experience pain relief with this medication, and explain what this interval signifies in the context of your study.  Statistic Parameter Mean: X estimates ____ Standard deviation: s estimates ____ Proportion: p estimates ____ from entire from sample population Population Point estimate Interval estimate I am 95% Mean confident that  Mean, , is is between 40 & X = 50 unknown 60 Sample  Standard Error S Quantitative Variable SE (Mean) = n p(1-p) Qualitative Variable SE (p) = n  Statistics Inferential Statistics Descriptive Statistics Hypothesis testing Summarize mean / proportion (incidence / prevalence) Comparison of means Comparison of proportions ( incidences / prevalences)  Methods in Test of Significance Comparison of two independent means or proportions – Student t-test and paired means Paired t-test Relationship between two quantitative variables – Correlation Coefficient Linear relationship between two quantitative variables – Regression Analysis Comparisons involving several population means – Analysis of Variance (ANOVA)  Hypothesis testing A statistical method that uses sample data to evaluate a hypothesis about a population parameter. It is intended to help researchers differentiate between real and random patterns in the data.  Hypotheses Research Question Is there a (statistically) significant difference between male and female students with respect to their math achievement? Null Hypothesis There is no (statistically) significant difference between male and female students with respect to their math achievement. Alternative Hypothesis There is a (statistically) significant difference between male and female students with respect to their math achievement.  Variation (i) Chance Variation (ii) Effect Variation The difference that we might find between the boys’ and girls’ exam achievement in our sample might have occurred by chance, or it might exist in the population.  Decision Table TRUTH Null Hypothesis RESEARCH FINDINGS True False Null Hypothesis True  Type II Error () False Type I Error ()  Type I Error : The null hypothesis is true, but we reject it. The probability of a Type I Error is called  and is set at 0.05. Type II Error : The null hypothesis is false, but we fail to reject it. The probability of a Type II Error is called . Making Decisions: Test of Hypothesis Ho is True Ho is NOT True Accept Ho   Type II error Reject Ho   Type I error  =probability of Type I error (level of significance)  =probability of Type II error 1- =Power  P - Value Probability of getting a result as extreme as or more extreme than the one observed when the null hypothesis is true. When our study results in a probability of 0.01, we say that the likelihood of getting the difference we found by chance would be 1 in a 100 times. It is unlikely that our results occurred by chance and the difference we found in the sample probably exists in the populations from which it was drawn.  ‘P’ as a significance level P < 0.05 result is statistically significant P > 0.05 result is not statistically significant. These cutoffs are arbitrary & have no specific importance.  When should we use T-test? The conditions for using t-test are: 1-σ is unknown. 2- n