2. Probability Testing.docx

CRITICAL READING: CORNELL NOTES Probability Testing Name: Date: 10 September 2023 Section: Lecture 2 Period: Questions/Main Ideas/Vocabulary Notes/Answers/Definitions/Examples/Sentences Quantitative Research Methods We use research in psychology to ask questions about different aspect...

CRITICAL READING: CORNELL NOTES Probability Testing Name: Date: 10 September 2023 Section: Lecture 2 Period: Questions/Main Ideas/Vocabulary Notes/Answers/Definitions/Examples/Sentences Quantitative Research Methods We use research in psychology to ask questions about different aspects of behaviour, psychological functioning, cognitive processes, etc. Quantitative approaches differ from qualitative approaches in that they employ statistical tests to analyse the data. Involves collecting and analysing numerical data to describe patterns and relationships, make comparisons, test hypotheses, models and other types of predictions. Quantitative Research Process Define a research question. What is the relationship between perfectionistic attitudes and problematic eating behaviours? Do different study approaches result in different academic outcomes? Use an experiment or survey or other means to collect numerical data. Apply an appropriate statistical test(s). Correlations, regressions, t-tests, ANOVA, non-parametric tests. Interpret the outcome of the statistical tests to see what it tells us about the research question. Statistics & Decision-Making There are different pieces of information that we obtain from statistical tests that allow us to make decisions about the research question. Did we find what we were expecting to find or something different? Did we find anything at all or is it inconclusive? One important piece of information is the effect size. An effect size can tell us about things such as the strength of a relationship, or the magnitude of any observed differences. Examples: r, r2, eta, cohen’s d. Did we find what we were expecting to find or something different? Did we find anything at all or is it inconclusive? Another piece of important information we can take from many statistical tests is the p-value. A p-value represents a probability. For example, if we are talking about an event occurring: If p = 1, it will definitely happen (100%). If p = 0, it will definitely not happen (0%). Most of the p-values we see associated with statistical tests range somewhere between 0 and 1. Interpreting p-Values In relation to our statistical tests, a p-value tells us if a given result is statistically significant. We determine this by comparing the p-value to a decision criterion that we call an α-value. By convention, in psychological research, we set α to .05. If our p-value is less than α, we say the test is statistically significant. Null-Hypothesis Significance Testing (NHST) NHST is the interpretive framework in which the majority of statistical analysis occurs in quantitative psychological research. For any given research question, we can formulate two hypotheses: The null hypothesis (H0) says there is no effect. The alternative hypothesis (H1) says there is an effect. We observe an effect in our sample. Because the properties of sampling distributions are well known, we can determine the probability of making an observation at least as strong as this if the null hypothesis was true. If p < .05, we reject the null hypothesis, and say the effect is significant. If we set our α to p = .05, then this is like saying that we are accepting that 5% if the time, the true population is zero, and what we have observed is simply due to chance. Population & Sample What the p-value actually represents is the probability of observing a correlation as strong as what has been found in our sample if the true population correlation was zero. Population: This contains all of the members of the group we are interested in. We rarely actually have access to the population (think about how many undergraduate psychology students there are in the world. How would we test them all?). Sample: This is a subset of the population. This is what we actually have access to and generally we want to generalise from what we find in the sample to the wider population. Sampling Error Our ability to generalise from the sample to the population is limited by the potential effect of sampling error. Sampling error doesn’t mean we have made a mistake or done something wrong when collecting our sample. Sampling error is just what happens when we take a sample from a population. It is the difference between our observed sample statistic and the actual population parameter. We could measure the height of everyone in this room and calculate the mean. This would be the population mean height for this lecture theatre. If I randomly chose 10 of you and calculated the mean height, would it be exactly the same as the mean for the whole class? Any time we take a sample from a population, there will be some degree of sampling error. Sometimes this error will be large and sometimes it will be small. Sampling Distribution If we were to plot a histogram of correlation values, the sampling distribution would show. Most of the time, the sample statistic is close to the population parameter, but sometimes it is much stronger and sometimes much weaker. Properties of Sampling Distributions The mean of the sampling distribution is a really good estimate of the true population parameter. Regardless of the shape of the population distribution, if we take enough samples, the sampling distribution will be approximately normal in shape. Normal distributions are also called probability distributions because there is a probability associated with every value under the distribution. The larger the sample size, the closer to normal it becomes. The larger the sample size, the lower the degree of sampling error. As the sample size increases, the sampling distribution converges to the normal, and the degree of sampling error decreases. Because of this, we know the associated probability of finding a given test statistic (for a give sample size) if the null hypothesis were true. There are families of probability distributions for different test statistics.