Psych 2220 Exam 2

What are the six steps of hypothesis testing?

1. Identify the population, comparison distribution and assumptions 2. State the null and research hypotheses (in words and symbolic notation) 3. Determine the characteristics of the comparison distribution 4. Determine the critical values (cutoffs) that indicate the points beyond which we will reject the null hypothesis 5. Calculate the test statistic 6. Make a decision, reject or fail to reject the null hypothesis; Reject if the test statistic is beyond the cutoffs and fail to reject if if the test statistic is not beyond the cutoffs.

Give three reasons why z scores are useful

1. Standardization 2. 3.

Distribution of Means

A distribution composed of many means that are calculated from all possible samples of a given size, all taken from the same population.

Cohen's d

A measure of effect size that assesses the difference between two means in terms of standard deviation, not standard error.

Statistical Power

A measure of the likelihood that we will reject the null hypothesis, given that the null hypothesis is false

Z distribution

A normal distribution of standardized scores.

Meta-analysis

A study that involves the calculation of a mean effect size from the individual effect sizes of many studies.

Point Estimate

A summary statistic from a sample that is just one number used as an estimate of the population parameter.

Standardization

A way to convert individual scores from different normal distributions to a shared normal distribution with a known mean, standard deviation, and percentiles.

Critical Region

Area in the tails of the comparison distribution in which the null hypothesis can be rejected.

Interval Estimate

Based on a sample statistic and provides a range of plausible values for the population parameter.

How is calculating a percentile for a mean from a distribution of means different from doing so for a score from a distribution of scores?

Calculating a percentile for a mean requires knowing what the sampling distribution of means looks like. It also requires knowing the sample size to estimate the standard error. The central limit theorem helps us know the shape, mean and spread of such a distribution.

Assumption

Characteristic that we ideally require the population from which we are sampling to have so that we can make accurate inferences

Why do we calculate confidence intervals?

Confidence intervals add details to the hypothesis test. Specifically, they tell us a range within which the population mean would fall 95% of the time if we were to conduct repeated hypothesis tests using samples of the same size from the same population.

What are critical values and the critical region?

Critical Values (cutoffs) are the test statistic values beyond which we reject the null hypothesis; the critical region refers to the area in the tails of the distribution in which the null hypothesis will be rejected if the test statistic falls there.

Relate effect size to the concept of overlap between distributions

If two distributions overlap a lot, then we would probably find a small effect size and not be willing to conclude that the distributions are necessarily different. If they don't overlap much, this would be evidence for a larger effect size or a meaningful difference between them.

Explain how increasing alpha increases statistical power.

Increasing alpha increases the critical region, possibly making it easier to detect an effect (higher power).

Central Limit Theorem

Refers to how a distribution of sample means is a more normal distribution than a distribution of scores, even when the population distribution is not normal.

What does statistically significant mean to statisticians?

Reject the null hypothesis because the pattern in the data differed from what we would expect by chance; doesn't necessarily mean the finding is important or meaningful, it only means that we are justified in believing that the pattern in the data is likely to reoccur.

Normal Curve

Specific bell-shaped curve that is unimodal, symmetric, and defined mathematically. Describes the distributions of many variables. As the size of a sample approaches the size of the population, the distribution resembles a normal curve (as long as the population is normally distributed).

What effect does increasing the sample size have on standard error and the test statistic?

Standard Error: Decreases as sample size increases Test Statistic: Increases as sample size increases

What is the difference between standard deviation and standard error?

Standard deviation is the measure of spread for a distribution of scores in a single sample or in a population of scores. Standard error is the standard deviation (or measure of spread) in a distribution of means of all possible samples of a given size from a particular population of individual scores.

Critical Value

Test statistic value beyond which we reject the null hypothesis; often called a cutoff.

In statistics, what do we mean by assumptions?

The characteristics we ideally require the population from which we are sampling to have so that we can make accurate inferences.

How does the size of a sample of scores affect the shape of the distribution of data?

The distribution of sample scores approaches normal as the sample size increases, assuming the population is normally distributed.

Why does the standard error become smaller simply by increasing the sample size?

The greater the sample size, the closer your sample is to the actual population itself; If you take a sample that consists of the entire population you actually have no sampling error because you don't have a sample, you have the entire population.

What point on the normal curve represents the most commonly occurring observation?

The highest point (the mean)

What are the mean and standard deviation of the z distribution?

The mean is 0 and the standard deviation is 1

Standard Error

The name for the standard deviation of a distribution of means. Standard Deviation/Square Root of Sample Size

What does a z statistic- a z score based on a distribution of means- tell us about a sample mean?

The z statistic tells us how many standard errors a sample mean is from the population mean.

What specific danger exists when reporting a statistically significant difference between two means?

There may be a statistically significant difference between group means, but the difference might not be meaningful or have a real-life application.

Why do researchers typically used a two-tailed hypothesis test rather than a one-tailed hypothesis test?

Two-tailed tests are more conservative; use one-tailed tests only when the researcher is certain the effect cannot go in the other direction or is uninterested in the result if it did.

What does it mean to say an effect-size statistic neutralizes the influence of sample size?

Using an effect size like Cohen's d standardizes the effect regardless of sample size. It's not influenced by sample size.

How do we calculate the percentage of scores below a particular positive z score?

We add the percentage between the mean and the positive z score to 50% which is the percentage of scores below the mean

What is a percentile?

the percentage of scores that fall below a certain point on a distribution

When we look up a z score on the z table, what information can we report?

the probability of getting anything equal to or lesser than the value you chose

What are the five steps to create a confidence interval for the mean of a z distribution?

1. Draw a normal curve with the sample mean in the center 2. Indicate the bounds of the confidence interval on either end, and write the percentages under each segment of the curve. 3. Look up the z statistics for the lower and upper ends of the confidence interval in the z table. (Always -1.96 and 1.96 for a 95% confidence interval around a z statistic) 4. Convert the z statistics to raw means for each end of the confidence interval 5. Check your answer; each end of the confidence interval should be exactly the same distance from the sample mean.

List five factors that affect statistical power. For each, indicate how a researcher can leverage that factor to increase power.

1. Increasing the alpha level 2. Performing a one-tailed test rather than a two-tailed test 3. Increasing the sample size 4. Maximizing the difference in the levels of the IV 5. Decreasing variability in the distributions by using, for example, reliable measures and homogeneous samples.

What are three kinds of dirty data and what are their possible sources?

1. Missing Data: test subject can't finish test, accidentally pressed enter without answer, etc. 2. Misleading Data: misinterpretation of question or information 3. Outliers: mistaken reporting of data by participants, inaccurate data entry, obnoxious response by angry participant etc.

What are three ways to deal with missing data?

1. Replace the missing data point with the mode or mean for that variable (based on other participants' responses) 2.Replace the missing data point with the mode or mean based on that participant's response to other, similar questions 3. Replace the missing data point with a random number within the possible range of numbers

What are the four basic steps of a meta-analysis?

1. Select the topic of interest, and decide exactly how to proceed before beginning to track down studies. 2. Locate every study that has been conducted and meets the criteria. 3. Calculate an effect size, often Cohen's D, for every study. 4. Calculate statistics- ideally, summary statistics, a hypothesis test, a confidence interval, and a visual display of the effect sizes.

Three Assumptions for Parametric Tests

1. The dependent variable is assessed using a scale measure (interval, ratio) 2. The participants are randomly selected; if violated we must be careful when generalizing from a sample to a population 3. The distribution of the population of interest must be approximately normal; at least have a sample size of at least 30.

What sample size is recommended in order to meet the assumption of a normal distribution of means, even when the underlying population of scores is not normal?

30

Traditionally, what minimum percentage chance of correctly rejecting the null hypothesis is suggested in order to proceed with an experiment?

80%

What is a z score?

A z score is a way to standardize data; it expresses how far a data point is from the mean of its distribution in terms of standard deviations.

What are Cohen's guidelines for small, medium and large effects?

According to Cohen's guideline for interpreting the d statistic, a small effect is around 0.2, a medium effect is around 0.5, and a large effect is around 0.8.

Confidence Interval

An interval estimate based on the sample statistic; it includes the population mean a certain percentage of the time if we sample from the same population repeatedly.

Using everyday language, explain why the words critical region might have been chosen to define the area in which a z statistic must fall in order for a researcher to reject the null hypothesis?

Critical region may have been chosen because values of a test statistic describe the area beneath the normal curve that represents a statistically significant result.

What is the goal of a meta-analysis?

Find the mean of the effect sizes from many different studies that all manipulated the same IV and measured the same DV.

What is the difference between a one-tailed hypothesis test and a two-tailed hypothesis test in terms of critical regions?

For a one-tailed test, the critical region (usually 5%, or a p level of 0.05) is placed in only one tail of the distribution; for a two-tailed test, the critical region must be split in half and shared between both tails (usually 2.5%, or 0.025, in each tail)

Two-Tailed Test

Hypothesis test in which the research hypothesis does not indicate a direction of the mean difference or change in the dependent variable, but merely indicates that there will be a mean difference.

One-Tailed Test

Hypothesis test in which the research hypothesis is directional, positing either a mean decrease or a mean increase in the dependent variable, but not both, as a result of the independent variable.

Statistically Significant

If the data differ from what we would expect by chance if there were, in fact, no actual difference.

How can data that are misleading result in missing data?

If the participant didn't give accurate responses due to misinterpretation or giving extreme answers to screw over the study/get it over with then the data can be omitted from the study

Explain how the word normal is used in everyday conversation; then explain how statisticians use it.

In everyday conversation, the word normal is used to refer to events or objects that are common or that typically occur. Statisticians use the word to refer to distributions that conform to a specific bell-shaped curve, with a peak in the middle where most of the observations lie, and symmetric areas underneath the curve on either side of the midpoint. The normal curve represents the pattern of occurrence of many different kinds of events.

In your own words, define the word power- first as you would use it in everyday conversation and then as a statistician.

In everyday language we use the word power to mean either an ability to get something done or an ability make others do things; in statistics it refers to the ability to detect an effect, given that one exists.

In your own words define the word effect- first as you would use it in everyday conversation and then as a statistician.

In everyday language, effect refers to the outcome of a certain situation. Statisticians look at effect sizes which is the size of an outcome.

Effect Size

Indicates the size of a difference and is unaffected by sample size.

Parametric Test

Inferential statistical analysis based on a set of assumptions about the population

Nonparametric Test

Inferential statistical analysis that is not based on a set of assumptions about the population

Standard Normal Distribution

Normal distribution of z scores.

Z Score

Number of standard deviations a particular score is from the mean; x-mean/standard deviation

What is the difference between parametric tests and non-parametric tests?

Parametric tests are based on assumptions while non-parametric tests are not

P level (alpha)

Probability used to determine the critical values (cutoffs) in hypothesis testing

Robust Hypothesis Test

Produces fairly accurate results even when the data suggest that the population might not meet some of the assumptions

File drawer analysis

Statistical calculation, following a meta-analysis, of the number of studies with null results that would have to exist so that a mean effect size would no longer be statistically significant.

How does statistical power relate to Type II errors?

Statistical power is how likely we will reject the null hypothesis given that the null hypothesis is false, which is the probability we won't make a type two error.