Chapter 13 psy 102

The odds of correctly rejecting the null hypothesis when it is false are always equal to:

(1 - beta ) also referred to as the 'power' of the statistical test

The odds that we will fail to reject the null hypothesis when that is the correct decision.

(1-alpha)

Steps to analyzing any set of data

1. We organize it 2. We summarize it 3. We apply a statistical test to interpret our results

significance level

A criterion for deciding whether to reject the null hypothesis or not.

Statistical inference

A statement made about a population and all its samples based on the samples observed

Non-directional hypothesis

A statement that predicts the difference between treatment groups without predicting the exact pattern of results

Alternative hypothesis (H,)

A statement that the data came from different populations; the research hypothesis, which cannot be tested directly

One Tail Test/ Directional Test

A statistical procedure used when a directional prediction has been made; the critical region of the distribution of the test statistic is measured in just one tail of the distribution

two-tailed test

A statistical procedure used when nondirectional prediction has been made the critical region of the distribution of the test statistic is divided over both tales of the distribution

There is no way to directly test the;

Alternative hypothesis (which states that the data came from different populations.)

Parametric test

Are preferred by researchers requiring interval and ratio scales. Because they are more powerful. Representing a relationship between treatment effects and variability.

nominal

By category Ex. Gender: male, female, other

the precise value of beta;

Cannot be measured.

Raw data

Data recorded as an experiment is run; the responses of individual subjects

Proving something means

Establishing the truth of it by presenting evidence and logical argument.

As the amount of variability in the distribution goes up, The critical regions:

Fall further from the center of the distribution.

Variability

Fluctuation in data can do be defined numerically as range, variance, or standard deviation. Variability is the amount of fluctuation observed in scores on a dependent variable.

Frequency distribution

Graphing a frequency distribution you should mark off all possible values of the dependent variable along the X or horizontal axis frequencies are marked off on the ordinance the Y or vertical axis.

3 ways Beta can be reduced by...

Increasing sample size, reducing the variability in our sample data (for instance by controlling extraneous variables or using a within subjects or matched groups design), & using more powerful statistical tests called 'parametric tests.'

Populations that have high variability on the dependent measure are more likely To have:

Large differences in distribution

Parametric tests

Make certain assumptions about the parameters of the population represented by our samples. Example, normally distributed data, comparable variability across groups, interval or ratio scale data.

statistical significance

Meeting the set criterion criterion for significance; The data do not support the no hypothesis confirming a difference between the groups that occurred as a result of the experiment

When we have a directional hypothesis, we make a:

One tailed test: the 5% critical region is located in just one tale of the distribution.

A nondirectional hypothesis is:

One that does not predict the exact pattern of results - the direction of the effect will we will produce through the experimental manipulation.

Critical Region

Portion of the tail(s) of the distribution of a test statistic extreme enough to satisfy the researchers criterion for rejecting the null hypothesis- for instance the most extreme 5% of a distribution where P < .05 is the chosen significance level

The simplest Measure of variability:

Range is the difference between the largest and smallest scores in a set of data.

Unnecessary sources of variation in an experiment will:

Reduce the chances of rejecting the no hypothesis, and increase the chances of a type error.

When the experiment is over, we would like to be able to____________ By showing that the effect produced by the independent variable led to real differences in the responses of the groups.

Reject the null hypothesis

Standard deviation

Square root of the variance; measures the average deviation of scores about the mean thus reflecting the amount of variability in the data

Directional hypothesis

Statement that predicts the exact pattern of results that will be observed; such as which treatment group will perform best

Inferential statistics

Statistics that can be used as indicators of what is going on in a population; also called a test statistic.

Test statistic

Statistics that can be used as indicators of what is going on in the population and can be used to evaluate results; also called inferential statistics

Measures of central tendency

Summary statistics that describe what is typical of a distribution of scores including mean median and mode

The probability of making a Type 1 error is represented by :

The Greek letter alpha

The probability of making a type 2 error is represented by;

The Greek letter beta

In a common sense way, variability is;

The amount of change your fluctuation we see in some thing.

The odds of finding significance are affected by two factors:

The amount of variability in the data and whether that we have a directional or non-directional hypothesis.

Mean

The arithmetical average computed by dividing the sum of the group scores by the total number of scores; a measure of central tendency

Variance

The average squared deviation of scores from there mean; a more precise picture a very abilities in the range

Range

The difference between the largest and smallest scores in a set of data; a rough indication of the amount of variability in the data

Mode

The most frequently occurring score in a distribution measure of central tendency

finding a statistically significant effect requires very large differences between the mean scores from different treatment groups in the experiment:

The population has high variability

Median

The score that divides the distribution in half so that half of the scores in the distribution fall above the median house below; a measure of central tendency

Critical regions are:

The shaded areas of the curves

An advantage of using a one tailed test:

The size of the critical region is larger and closer to the center of the distribution, making it easier for differences between means to be large enough to fall there.

Descriptive statistics

The standard procedures used to summarize and describe data quickly and clearly; summary statistics reported for an experiment including mean range and standard deviation

Significance level

The statistical criterion for deciding whether to reject the no hypothesis or not, typically p<.05

When using a directional hypothesis and a one tailed test:

Treatment effects do not need to be as dramatic, we can get the significant results more easily.

Making a_______ Error is generally considered to be less serious than making a_______ error.

Type 2 =less serious than , making a Type 1 error.

The independent variable has produced an effect, but we are unable to detect it ...describes:

Type 2 error

Whenever we have a nondirectional hypothesis:

Use a two-tailed test

The odds of making a type one error are equal to the

Value that we choose as the significance level for rejecting the null hypothesis

Experimental error

Variation in subjects scores produced by uncontrolled extraneous variables in the experimental procedure experiment or bias or other influences on subjects not related to effects of the independent variable

When we obtain a large value of a test statistic:

We are more likely to be able to reject the no hypothesis, the more likely that the independent variable produced to change in subjects responses

Testing the null hypothesis. Until we can determine otherwise;

We assume an independent variable has no effect.

Evaluate the data from a psychological experiment

We carry out a statistical test to determine whether the independent variable probably caused changes in the dependent variable from one treatment condition to another.

Larger differences between means of samples are required to reject the null hypothesis:

When there is more variability.

Null Hypothesis (H0)

a statement that the performance of treatment groups is so similar that the groups must belong to the same population; a way of saying that the experimental manipulation had no important effect

Summary data

descriptive statistics computed from the raw data of an experiment, including the measures of central tendency and variability

Type 2 error

failing to reject a false null hypothesis (false negative)

Type 1 error

rejecting the null hypothesis when it is true (false positive)

the most common interpretive strategies in statistical hypothesis testing are:

supported by null hypothesis significance testing, reporting P values, and including effect sizes and confidence intervals.