Hypothesis Testing PDF

Psychological Statistics Hypothesis Testing A hypothesis test is a statistical method that uses The first and most important of the two sample data to evaluate a hypothesis about a hypotheses is called the null p...

Psychological Statistics Hypothesis Testing A hypothesis test is a statistical method that uses The first and most important of the two sample data to evaluate a hypothesis about a hypotheses is called the null population. hypothesis. The null hypothesis states First, we state a hypothesis about a that the treatment has no effect. population. Usually, the hypothesis The null hypothesis is identified by the concerns the value of a population symbol H0. (The H stands for parameter. hypothesis, and the zero subscript Before we select a sample, we use the indicates that this is the zero-effect hypothesis to predict the hypothesis.) characteristics that the sample should The alternative hypothesis (H1) states have. that there is a change, a difference, or Next, we obtain a random sample from a relationship for the general the population. population. In the context of an Finally, we compare the obtained experiment, H1 predicts that the sample data with the prediction that independent variable (treatment) does was made from the hypothesis. If the have an effect on the dependent sample mean is consistent with the variable. prediction, we conclude that the hypothesis is reasonable. But if there 2. Setting Criteria for Decision is a big discrepancy between the data Eventually the researcher will use the and the prediction, we decide that the data from the sample to evaluate the hypothesis is wrong. credibility of the null hypothesis. The The goal of the hypothesis test is to data will either provide support for the determine whether the treatment has null hypothesis or tend to refute the null any effect on the individuals in the hypothesis. population. In particular, if there is a big discrepancy between the data and the Steps in Hypothesis Testing hypothesis, we will conclude that the hypothesis is wrong. 1. State the Hypothesis Example: effects) and specificity (avoiding false For our example, the null hypothesis states that the positives) red shirts have no effect and the population mean The choice of 0.05 corresponds to a is still μ = 15.8 percent, the same as the population confidence interval of approximately mean for waitresses wearing white shirts. If this is 95%. This means researchers can be true, then the sample mean should have a value confident that if they were to repeat the around 15.8. Therefore, a sample mean near 15.8 study multiple times, 95% of the is consistent with the null hypothesis. On the other calculated confidence intervals would hand, a sample mean that is very different from contain the true population parameter. 15.8 is not consistent with the null hypothesis. This level of confidence is generally deemed sufficient for many scientific 3. The Alpha Level inquiries The alpha level (or significance level) is a crucial concept in hypothesis 4. Critical Region testing, representing the probability of The critical region (also known as the making a Type I error, which occurs rejection region) is the set of values for when the null hypothesis is incorrectly the test statistic that would lead to rejected while it is actually true. This rejecting the null hypothesis. probability is denoted by 𝛼. If the calculated test statistic falls within Set by common values such as 0.05 this region, it indicates that the (5%), 0.01 (1%), or 0.10 (10%) observed data is sufficiently extreme depending on the context of the test under the null hypothesis, prompting and the acceptable risk of error. rejection of the null hypothesis An alpha level of 0.05 indicates a 5% For example, if you set an alpha level risk of committing a Type I error, of 0.05, this means that 5% of the meaning there is a 5% chance of distribution will be in the critical region. rejecting the null hypothesis when it is This corresponds to extreme values in actually true. either tail of the distribution for two- This level is often considered tailed tests or one tail for one-tailed acceptable in many research contexts, tests. providing a reasonable trade-off between sensitivity (detecting true The Type of Errors  1. A Type I (False Positive) error occurs For example, it may state that one variable is when a researcher rejects a null greater than or less than another variable, hypothesis that is actually true. In a indicating a clear expected outcome (e.g., "As sleep typical research situation, a Type I deprivation increases, cognitive performance error means the researcher concludes decreases"). that a treatment does have an effect when in fact it has no effect. Directional tests are referred to as one-tailed tests → Incorrectly rejecting the null because they focus on one tail of the distribution. hypothesis. This means that the critical region for rejecting the → Example: Failure of the drugs to null hypothesis is located entirely in one direction take an effect. (Placebo effect) (either positive or negative). 2. A Type II (False Negative) error Example: In psychological research, a directional occurs when a researcher fails to reject hypothesis might state: "Participants who receive a null hypothesis that is really false. In cognitive training will perform better on memory a typical research situation, a Type II tasks than those who do not receive training." This error means that the hypothesis test clearly indicates that the expectation is for has failed to detect a real treatment improvement in performance due to training effect. → Failing to reject the null Type of Directional Test hypothesis when it's actually false. A. One-Tailed Test: This test evaluates whether a → Example: Failure of the parameter is either greater than or less than a psychiatrist to detect. certain value, focusing on one direction. It can be classified as: Hypothesis for Directional Test 1. Left-Tailed Test: Tests if the parameter is less than a specified A directional test, also known as a one-tailed test, value. is a type of hypothesis test where the researcher 2. Right-Tailed Test: Tests if the specifies the expected direction of the effect or parameter is greater than a specified relationship between variables. value B. Two-Tailed Test: This test assesses whether a parameter is significantly different from a specified Effect Size value, without specifying a direction. It checks for both increases and decreases, making it more Effect size is a numerical value that expresses the general. strength of the relationship between two variables or the size of the difference between groups. Critical Region One-Tailed Test: Has one critical region where A large effect size means that research finding has the entire alpha level (e.g., 0.05) is allocated. This practical significance, while a small effect size means that all statistical power is focused in one indicates limited practical applications tail of the distribution, making it easier to detect an effect in that direction. Cohen's d: Measures the standardized difference Two-Tailed Test: Contains two critical regions, between two means, where, 𝑋1 and 𝑋2 each receiving half of the alpha level (e.g., 0.025 are the sample means, and 𝑆 is the pooled in each tail for an alpha of 0.05). This requires standard deviation. Cohen's d values are more extreme results to achieve significance, as interpreted as small (0.2), medium (0.5), or large the critical values are split between both tails. (0.8) effects. Proper Usage Standardized Difference (Cohen, 1988) One-Tailed Test: Appropriate when there is a Effect Size D % Variance strong theoretical basis or prior evidence Small 0.2 1 suggesting that an effect will occur in one Medium 0.5 6 direction. For example, if a new drug is expected Large 0.8 16 to improve recovery times compared to a placebo, a right-tailed test would be suitable Formula: Two-Tailed Test: Suitable when researchers want to detect any significant difference, 𝑋1 − 𝑋2 𝑑 = regardless of direction. This is common in 𝑠 exploratory research where any change (increase or decrease) is of interest, such as testing whether a new teaching method affects student performance compared to traditional methods.