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Intro to Hypothesis Testing

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PSYC 210
Cathy Mc Farland

Chapter 4 – Intro to Hypothesis Testing 1 Hypothesis testing – procedure for deciding whether the outcome of a study (results for a sample) supports a particular theory or practical innovation (which is thought to apply to a population)  Hypothesis – prediction, often based on informal observation, previous research, or theory, that is tested in a research study o Research hypothesis – statement in hypothesis testing about the predicted relation between populations (often a prediction of a difference between population means); proposes a relationship about two variables o Null hypothesis – statement about a relation between populations that is the opposite of the research hypothesis; statement that in the population there is no difference (or a difference opposite to that predicted) between populations; a hypothesis that proposes no relationship or difference between two variables THE RESEARCH HYPOTHESIS AND NULL HYPOTHESIS ARE COMPLETE OPPOSITES. F ONE IS TRUE,THE OTHER CANNOT BE . RESEARCH HYPOTHESIS IS ALSO KNOWN AS THE ALTERNATE HYPOTHES(THE ALTERNATIVE TO THE NULL HYPOTHE),EVEN THOUGH THE RESEARCH HYPOTHESIS IS WHAT WE ARE CONCERNED ABOU. Theory – set of principles that attempt to explain one or more facts/relationships/events; psychologists often derive specific predictions from theories that are then tested in research studies Population mean  µ Population SD  δ Null hypothesis  H 0 Sample mean  M Sample SD  SD Alternate hypothesis  H 1 Hypothesis-Testing Process: Step 1: Restate the question as a research hypothesis and a null hypothesis about the populations.  The researchers are interested in the effects on babies in general. The purpose of studying samples is to know about populations. That is why it’s useful to restate the hypothesis in terms of a population. Population 1 = babies who receive the experimental treatment (vitamin) = experimental group  Population 1: Babies who take the specially purified vitamin. Population 2 = comparison baseline of what is already known about babies in general = control group  Population 2: Babies in general (i.e., babies who don’t take the vitamin). Prediction A: Population 1 babies will on the average walk earlier than Population 2 babies. Population 1 mean is lower (babies receiving the special vitamin walk earlier) than the mean of Population µ. < µ ) 1 2  The difference between populations = research hypothesis Prediction B: Population 1 babies will on average not walk earlier than Population 2 babies. There is no age difference at which Population 1 and 2 babies start walking; they start at the same time, on averagµ1(=µ 2 Chapter 4 – Intro to Hypothesis Testing 2  The populations aren’t different in the way predicted; opposite of the research hypothesis; a lack of difference between populations = null hypothesis Step 2: Determine the characteristics of the comparison distribution. Hypothesis testing involves figuring out the probability of getting a particular result i0 H is true.  Babies in Population 2 (babies in the general population) have µ = 14 and δ=3. If H 0s true, Population 1 = Population 2. This means that both populations have µ = 14, δ = 3, and follow normal curves. In the hypothesis-testing process, you need to find the probability that you could have gotten a sample score as extreme as what you got (i.e., a baby walking very early) if your sample was from a population with a distribution if the H 0ere true.  Comparison distribution – distribution used in hypothesis testing that represents the population situation if the H0is true; the distribution to which you compare the score based on your sample’s results. Step 3: Determine the cutoff sample score on the comparison distribution at which the null hypothesis should be rejected. Before conducting, you should set a target against which you will compare your result: how extreme the sample score would have to be for it to be too unlikely that they could get such an extreme score if the H0were true  The cutoff sample score – point in hypothesis testing, on the comparison distribution at which, if reached or exceeded by the sample score, you reject the null hypothesis (aka critical value) Researchers generally reject the H if the probability of getting a sample this extreme (if the H were true) is less 0 0 than 5% (p < .05); some use a cutoff of 1% (p < .01).  Conventional levels of significance (p < .05, p < .01) – widely used significance levels  When a sample score is so extreme that researchers reject the H (conclusion = results concur with H ), 0 1 the result is said to be statistically significant Step 4: Determine your sample’s score on the comparison distribution Carry out the study and get the results for your sample. Calculate the Z score for the sample’s raw score based on the µ and δ of the comparison distribution. Going back to the baby walking example...  The baby who was given the specially purified vitamin started walking at 6 months.  Of the comparison distribution to which we are comparing the results µ=14 and δ=3  A baby who walks at 6 months is 8 months below the population mean. o 2⅔ standard deviations below the µ o Z score for this sample baby on the CD is -2.67 [Z = (6 – 14)/3 = -2.67]. Step 5: Decide whether to reject the null hypothesis. Compare your actual sample’s Z score (Step 4) to the cutoff Z score (Step 3).  In the example, the actual result was -2.67. Suppose the researchers decided that they would reject the H 0f the sample’s Z score < -2. Since -2.67 is below -2, the researchers would reject the H0. If the researchers reject the null hypothesis, the research/alternate hypothesis remains. o In this example, the research team would conclude that the results of their study support the research hypothesis that babies who take the specially purified vitamin walk earlier than babies in general. Chapter 4 – Intro to Hypothesis Testing 3 Implications of Rejecting or Failing to Reject the Null Hypothesis: Two points about conclusions you can make from the hypothesis-testing process: ONE: When you reject the 0 , it means that your results support the research hypothesis. You can’t say that it proved the hypothesis. Research studies are based on the probability being low of getting your re0ult if the H were true. You can say (when you rejec0 H ) the results are statistically significant , “support” or “provide evidence for” the research hypothesis. TWO: When the result isn’t extreme enough to reject the null hypothesis, you don’t say that the result supports or proves the null hypothesis. You say that they aren’t statistically significant or inconclusive. Say there was a difference in the populations but the results weren’t strong enough to rej0ct the H , the results are still inconclusive. The Basic Logic of Hypothesis Testing, including the Logic for the Example of the Effect of a Specially Purified Vitamin on the Age that Babies Begin to Walk Basic Logic Baby Example Focus of Research Sample is studied Baby given specially purified vitamin and age of walking is observed. Is the baby’s walking age typical of Question Is the sample typical of the general population? babies in general? Very unlikely Could be Very unlikely Answer ↓ ↓
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