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# Statistics

### intro hypothesis testing, hypothesis testing with means, statistical significanc

Question | Answer |
---|---|

what is the definition of hypothesis testing? | a systematic procedure for deciding whether the results of a research study, which examines a sample, support a hypothesis which applies to a population |

what is the logic of hypothesis testing? | 1. assume IV has no effect on DV 2. conduct a study to gather data that leads to rejection of this assumption 3. conclude IV does have effect on DV |

Step 1 of Hypothesis testing? | Restate question as a research hypothesis and null hypothesis about the populations |

Step 2 of hypothesis testing? | Determine characteristics of the comparison distribution. Assume a normal distribution where to population parameters are µ and σ. |

Step 3 of hypothesis testing? | Determine your cutoff sample. Also known as the critical value (Zcrit) on the comparison distribution at which the null hypothesis should be rejected |

Step 4 of hypothesis testing? | Determine your samples obtained score on the comparison distribution; Zobt |

Step 5 of hypothesis testing? | Decide whether to reject the null hypothesis. |

What is µ? | the mean of the distribution of means |

What is µ1? | the mean of the research population |

What is µ2? | the mean of the comparison population |

what is the z score for a p<.05 significance level of a one-tailed test? | ± 1.64 |

What is the score for a p<.01 significance level of a one tailed test? | ± 2.33 |

What is the formula to find the samples obtained score? | z=(X-µ)÷σ |

What is a direction research hypothesis? | predicting a particular direction direction of difference between the research and null hypothesis. Also called a one-tailed hypothesis test |

What is a non direction research hypothesis? | predicting a difference between the populations without stating direction. Also known as a two tailed test |

What is the score for a p<.05 significance level for a two-tailed test? | ±1.96 |

What is the score for a p<.01 significance level for a two-tailed test? | ±2.57 |

What is the definition of the distribution of means? | of samples of a given size from a particular population |

The characteristics of any distribution of means are determined by? | 1. the parameters of the population distribution of individuals 2. number of individuals in each sample randomly drawn from the population |

Rule #1 of the distribution of means? | the mean of a distribution is the same as the mean of the population of individuals. µM= µ |

Rule #2a of the distribution of means? | the variance of a distribution of means is the variance of the population of individuals divided by the number of individuals in each sample σ2M=σ2÷N |

Rule #2b of the distribution of means? | the standard deviation of a distribution of means is the square root of the variance of the distribution of means σM=√σ2÷N. Also called the standard error |

Rule #3 of the distribution of means? | the shape of means is approximately normal if either (a) each sample if N=30 or more individuals or (b) the distribution of the population of individuals is normal to begin with |

µM=? | The mean of the distribution of means |

µ=? | the mean of the population of individuals |

σM2=? | Variance of the distribution of means |

σ2=? | population variance |

N=? | number in each sample |

What is the central limit theorem? | a statement about the characteristics of the sampling distribution of means of random samples from a given population. describes characteristic cs of the distribution of values we would obtain if we could draw infinite # of random samples. |

What is the Z test? | a hypothesis testing procedure in which there is a single sample and the population parameters of mean and variance are known |

Formula for the Z test? | Z= (M-µM)÷σM |

What is point estimate? | the best estimate of the population mean is the sample mean |

What is the standard error of the mean? | it is the same as σM the standard deviation of the sampling distribution of means |

What does SE tell you? | how much the means of samples are typically in error as estimates of the mean of the population of individuals |

What is Interval Estimate? | an estimate of the range of possible means that are likely to include the population mean with a certain degree of confidence |

What is another name for the interval estimate? | Confidence Interval |

What is step 1 for figuring confidence limits? | figure the standard error |

What is step 2 for figuring confidence limits? | figure the raw scores for 1.96 SE (95%CI) or 2.57 SE (99%CI) above and below the mean |

What are decision error? | possible correct and incorrect decisions in hypothesis testing |

What does effect size do? | indicates the extent to which two populations do not overlap as a result of the experimental procedure |

What is the amount of overlap influenced by? | by predicted mean difference and population SD. SE size adjusts the difference between means for the SD. |

What is the formula for effect size? | d= µ1-µ2÷σ |

What are properties of effect size? | increases when there is a greater difference between means. increases when there is a smaller SD in the population |

what number indicates a small effect size? | 0.20 |

what number indicates a medium effect size? | 0.50 |

What number indicates a large effect size? | 0.80 |

What is meta-analysis? | statistical method for combining the effect size from many different studies |

What is statistical power? | refers to " the probability that the study will produce a statistically significant result if the research hypothesis is true |

Power=? | 1 - β (that is , beta or Type II error) |

gather needed information (a) µM (b) population predicted 1 mean (c)σM | |

What is step two to calculate power? | figure the raw score cut-off point on the comparison distribution to reject the null hypothesis |

What is step three to calculate power? | |

What is step four to calculate power? | Using the normal curve table, figure the probability of getting a score more extreme than that Z score |

What are five e ways to increase power? | Increase the intensity of the experimental procedure, use less diverse population, use standardized testing and/or more precise measurement, use larger sample size, use a more lenient level of signifiance ∝ |

Created by:
taylorjud