Exam 2 research methods 2

Four steps of hypothesis testing

1) State the hypothesis and select an alpha level Ho/H1 2) locate the critical region 3) compute the test statistics (Z-score) 4) make a decision

Define a Type I error and a Type II error and explain the consequences of each.

A Type I error is rejecting a true null hypothesis (deciding that there is a treatment effect when there is not). A Type II error is failing to reject a false null hypothesis (failing to detect a real treatment effect).

1 tail keywords

Anything that represents a direction for example weaker, stronger, strength, higher, lower

What is central limit theorem?

Describes the distribution of sample mean by identifying three basic characteristics that describe any distribution: 1)shape 2)central tendency 3)variability

Babcock and Marks (2010) reviewed survey data from 2003-2005, and obtained an average of μ=14 hours per week spent studying by full-time students at 4-year colleges in the United States. To determine whether this average has changed in the past 10 years, researcher selected a sample of n=64 of today's college students and obtained an average of M= 12.5 hours . If the standard deviation for the distribution is o=4.8 hours per week, does this sample indicate a significant change in the number of hours spent studying? Use a two-tailed test with alpha=.05.

Ho: μ=14 (there has been no change). H1: μ not=14 (the mean has changed). The critical region consists of z-scores beyond ±1.96. For these data, the standard error is 0.6 and . Reject the null hypothesis. There has been a significant change in study hours.

A Sampling distribution

Is a distribution of statistics obtained by selecting all the possible samples of a specific size from a population

definition of a hypothesis testing

Is a statistical method that uses sample data to evaluate a hypothesis about a population. Simply put: hypothesis test uses a sample to draw a conclusion about the population. Hypothesis testing helps to prevent type one and type two errors.

The distribution of sample

Is the collection of sample means for all the possible random samples of a particular size (n) that can be obtained from a population.

2 tail keywords

Nondirectional for example the difference between it will always say there's a difference between two without stating what direction the difference is going in.

Type II error

Occurs when a researcher fails to reject a null hypothesis that is really false. In type II error you're failing to reject the null hypothesis; you're saying that there is no effect but really there is an effect

What is the difference between standard deviation and standard error?

Standard deviation: distance from the mean, Low variability equals closely clustered around the mean High variability equals larger distribution from the mean Standard error: measures how much standard error distance is expected on average between sample mean and population mean

The relationship between alpha level and critical region

The alpha level is the baseline or boundary that shows you where the critical level begins and ends. Is a probability value that is used to define the concept of "very unlikely" in a hypothesis test. The alpha level is Between critical area (far from mean) and noncritical area (closer to the mean) Critical region = one tail = one critical region 2 tail = two critical regions

What is the critical region

The critical region is on the far side of the alpha score away from the positive or negative mean.

Shape

The distribution of sample means is normal if either one of the following two conditions is satisfied: (1)The population from which the samples are selected is normal. (2)The size of the samples is relatively large (around or more). 1st step in central limit theorem

The mean of the distribution of sample means

The expected value of sample mean equal to the population mean Sample mean = population mean

Identify the four steps of a hypothesis test as presented in this chapter.

The four steps are: (1)State the hypotheses and select an alpha level (2)Locate the critical region (3)Compute the test statistic (4)Make a decision

Central Tendency.

The mean of the distribution of sample means is identical to the mean of the population from which the samples are selected. The mean of the distribution of sample means is called the expected value of M. 2nd step in central limit theorem

Variability

The standard deviation of the distribution of sample means is called the standard error of M and is defined by the formula Standard error measures the standard distance between a sample mean (M) and the population mean μ .

Standard error

The standard error tells how much error to expect if you are using a sample mean to represent a population mean. It is a Measure of how much distance is expected on average between a sample mean and a population mean Distance between M and M It's basically the error and sampling

What is the logic of F-ratio

Used in ANOVA F - ratio has the same basic structure as the T statistic that is based on variance instead of sample mean difference. F = ratio of two variances estimates variance between treatments F= -------—----------------------- Variance within treatments

When comparing more than two treatment means, why should you use ANOVA instead of using several test?

You would have to do independent t-test several times to compare all groups to each other with every T test bias is added. More variable = more mistakes More mistakes makes it bias so you need to use ANOVA ANOVA Measures variance.

The meaning of the numerator when you calculate the Z obtained value? The meaning of the denominator when you calculate Z obtained value?

You're basically going to use the formula to solve for Z the numerator is sample mean minus population mean and the denominator is standard error

The value of the z-score in a hypothesis test is influenced by a variety of factors. Assuming that all other variables are held constant, explain how the value of z is influenced by each of the following: a) Increasing the difference between the sample mean and the original population mean. b) Increasing the population standard deviation. c) Increasing the number of scores in the sample.

a) A larger difference will produce a larger value in the numerator which will produce a larger z-score. b) A larger standard deviation will produce larger standard error in the denominator which will produce a smaller z-score. c)A larger sample will produce a smaller standard error in the denominator which will produce a larger z-score.

standard error measures

how much discrepancy you should expect, between a sample statistic and a population parameter.

Statistical inference

involves using sample statistics to make a general conclusion about a population parameter Thus, standard error plays a crucial role in inferential statistics.

What factors

large n small pop standard deviation Large difference between population and sample mean

Type I error

occurs when a researcher rejects a null hypothesis that is actually true. Reject the null hypothesis you're saying there is an effect when there is not an effect.

The distribution of sample means is defined as

the set of Ms for all the possible random samples for a specific sample size (n) that can be obtained from a given population. Because the distribution of sample means tends to be normal, we can use these z-scores and the unit normal table to find probabilities for specific sample means. In particular, we can identify which sample means are likely and which are very unlikely to be obtained from any given population.

The location of each M in the distribution of sample means can be specified by

z-score