CHAPTER 13: UNDERSTANDING RESEARCH RESULTS- STATISTICAL

INFERENCE

SAMPLES AND POPULATIONS

•Inferential statistics are necessary because the results of a given study are

based on data obtained from a single sample of research participants.

•If researchers ever study entire populations; their findings are based on

sample data.

•In addition to describing sample data, we want to make statements about

populations.

oWould the results hold up if the experiment were conducted repeatedly,

each time with a new sample?

Definition of Inferential Statistic: statistics designed to determine whether

results based on sample data are generalizable to a population

•Used to determine whether we can, in fact, make statements that the results

reflect what would happen if we were to conduct the experiment again and

again with multiple samples.

oWhether we can infer that the difference in the sample means reflects

a true difference in the population means.

Example: People in one state might tell you that 57% prefer the Democratic

candidate and that 43% may favor the Republican candidate for office.

•Reports say that these results are accurate to within 3 percentage points,

with a 95% confidence level.

•The researchers are very confident that if they were able to study the entire

population rather than a sample, the actual percentage who preferred the

Democratic candidate would between 60% and 54%

•The percentage preferring the Republican would be 46% and 40%

•Researcher could predict with a great deal of certainty that the Democratic

candidate will win because there is no overlap in the projected population

values.

INFERENTIAL STATISTICS

•Equivalence of groups is achieved by experimentally controlling all other

variables or by randomization.

•The assumption is that if the groups are equivalent, any differences in the

dependent variable must be due to the effect of the independent variable.

(usually valid)

•It is also true that the difference between any two groups will almost never be

zero.

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oThere will be some difference in the sample means, even when all of

the principles of experimental designs are utilized; this happens

because we are dealing with samples rather than populations.

•Random or chance error will be responsible for some difference in the means

even if the independent variable had no effect on the dependent variable.

•THE POINT IS THAT THE DIFFERENCE IN THE SAMPLE MEANS

REFLECTS ANY TRUE DIFFERENCEIN THE POPULATION MEANS,

PLUS ANY RANDOM ERROR.

•Inferential statistics give the probability that the difference between means

reflects random error than a real difference.

NULL AND RESEARCH HYPOTHESIS

•Statistical inference begins with a statement of the null hypothesis and a

research (or alternative) hypothesis.

Null Hypothesis: The hypothesis used for statistical purposes that the variables

under investigation are not related in the population, that any observed effect

based on sample results is due to random error.

•

(null hypothesis) : the population mean of the no-model group is equal to

the population mean of the model group

•Independent variable had no effect

• Used because it is very precise

oThe population means are exactly equal

oPermits us to know precisely the probability of the outcome of the

study occurring if the null hypothesis is correct.

oThe null hypothesis is rejected when there is a low probability that the

obtained results could be due to random error.

This is what is meant by statistical significance.

•

Statistical significance: Rejection of the null hypothesis when

an outcome has a low probability of occurrence (usually .05 or

less) if, in fact, the null hypothesis is correct.

•Significance is a matter of probability.

•

•Research Hypothesis: The hypothesis that the variables under

investigation are related in the population- that the observed effect based on

sample data is true in the population.

•(research hypothesis): The population mean of the no-model group is

not equal to the population mean of the model group

•Independent variable did have an effect.

•

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•LOGIC OF THE NULL HYPOTHESIS

•If we can determine that the null hypothesis is incorrect, then we accept the

research hypothesis as correct.

•Acceptance of the research hypothesis means that the independent variable

had an effect on the dependent variable.

•

•PROBABILITY AND SAMPLING DISTRIBUTIONS

•Probability- The likelihood that a given event (among a specific set of

events) will occur.

We all use probabilities frequently in everyday life.

oExample: the weather forecaster says there is a 10% chance of rain

today; this means that the likelihood of rain is very low.

Probability in statistical inference is used in much the same way.

The probability that an event (in this case, a difference between means in the

sample) will occur if there is no difference in the population.

•

•PROBABILITY: THE CASE OF ESP

The use of probability in statistical inference can be understood intuitively

from a simple example;

oExample: you test your friend on their ESP (extrasensory perception)

You test your friend by doing 10 trials and of showing them 5

cards with different symbols on each card; you show these cards

twice in a random order in 1 trial

The null hypothesis is that only random error is operating

The research hypothesis is that the number of correct answers

shows more than random or chance guessing

You can reasonably say that that the person will get 1/5 answers

right

•You can expect small deviations away from the expected 2

answers correct per trial

oHow unlikely does a result have to be before we decide it is significant?

A decision rule is determined prior to collecting the data

oThe probability required for significance is called the alpha level

Most common alpha level probability is used is 0.05

•The outcome is considered significant when there is a 0.05

or less probability of obtaining the results; only 5/100

chances that the results were due to a random error

•

•Sampling Distribution

•You can infer using intuition that getting 7/10 answers vs. 2/10 answers

correct on the ESP experiment is unlikely

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