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Lecture 12

PSYB01 - Lecture 12 Notes

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Anna Nagy

PSYB01 - Lecture 11 UNDERSTANDING RESEARCH RESULTS: STATISTICAL INFERENCE SAMPLES AND POPULATIONS  Inferential statistics necessary because results of a given study are based on data obtained from a single sample from a population.  Allows conclusions on the basis of sample data. INFERENTIAL STATISTICS  Allows researchers to make inferences about the true difference in the population means (effect of independent variable) on the basis of the sample data.  Provides the probability of the difference between means reflecting random error rather than a real difference. NULL AND RESEARCH HYPOTHESES  Null Hypothesis (H ):0Population means are exactly equal  Research Hypothesis (H ): Population means are not equal 1 STATISTICAL SIGNIFICANCE  Null hypothesis is rejected when there is a very low probability that the obtained results could be due to random error.  Statistical significant result: one that has a very low probability of occurring if the population means are equal (thus, difference in sample means very unlikely due to random error) PROBABILITY  Probability provides a quantitative description of the likely occurrence of a particular event.  Probability is conventionally expressed on a scale from 0 to 1; a rare event has a probability close to 0, a very common event has a probability close to 1. Examples  When flipping a coin, there are two possible outcomes, heads or tails. What is the probability of the coin landing with heads up?  Another example using a deck of cards: What is the probability of selecting a 9 from a deck of cards? Probability in Statistical Inference  Probability that the difference between means in the sample will occur if there is no actual difference in the population  If probability very low, reject the possibility that chance or random error responsible for the difference in means  Probability in Statistical Inference  How unlikely does the result have to be to be deemed significant?  Decision rule regarding unlikelihood of event determined prior to collecting data  Probability required for significance is called the alpha level (.05 most common in psychological research (sometimes .01))  Thus, at α=.05 results considered significant when there is 5% or less chance that the results were due to random error in one sample from the population. Sampling Distributions  If you compute the mean of a sample of 20 numbers, the value you obtain will not equal the population mean exactly.  If you sampled sets of 20 numbers over and over again (computing the mean for each set), you would find that some sample means come much closer to the population mean than others. Some would be higher than the population mean and some would be lower.  Imagine sampling 20 numbers and computing the mean over and over again, say about 1,000 times, and then constructing a relative frequency distribution of those 1,000 means. This distribution of means is a very good approximation to the sampling distribution of the mean. Sample Size The more observations sampled, the more likely you will obtain an accurate estimate of the true population value. EXAMPLE: THE t AND F TESTS  Uses probability to decide whether to reject the null hypothesis.  Steps:  Specify null hypothesis and research hypothesis.  Specify the significance level that you will use to decide whether to reject the null hypothesis (alpha level; .05)  Decide on most appropriate test to use. T-Test Dog Patting Group 65 68 78 74 73 80 58 84 50 58 Mean=68.8
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