Statistics: Sampling and Hypothesis Testing

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Questions and Answers

Why do researchers typically choose to take a sample from a population instead of measuring the entire population?

It simplifies the data analysis process.

Measuring the whole population is often too costly and time-consuming. (correct)

Samples are always more accurate than full population measurements.

It eliminates sampling errors completely.

In hypothesis testing, what does a type 1 error signify?

Rejecting the null hypothesis when it is true. (correct)

Accepting the null hypothesis when it is false.

Failing to detect an actual effect of the IV on the DV.

Finding no significant differences when they exist.

What is the significance level commonly set in psychological research?

0.01

0.10

0.15

0.05 (correct)

What does the mean of multiple sample means indicate regarding the population mean?

It gets closer to the population mean than any individual sample mean. Signup and view all the answers

How is a p-value used in hypothesis testing?

To estimate the likelihood that results are due to chance. Signup and view all the answers

What is an advantage of a between-subject design in experimental research?

It eliminates the impact of order effects. Signup and view all the answers

What typically happens to sampling error as the sample size increases?

Sampling error decreases as the sample size increases. Signup and view all the answers

Which of the following best describes continuous data in SPSS?

Data that can take any value in a range. Signup and view all the answers

What does a t statistic measure in the context of comparing means?

The ratio of variance explained by the independent variable to unexplained variance Signup and view all the answers

What is the primary purpose of the Shapiro-Wilk test?

To determine if data is normally distributed Signup and view all the answers

In which situation would a non-parametric test be preferred over a parametric test?

When data does not meet the assumptions required for a parametric test Signup and view all the answers

What does a p-value less than 0.05 indicate in the context of the Shapiro-Wilk test?

Data is significantly different from the normal distribution Signup and view all the answers

Which of the following best describes a between-subject design?

Different subjects are assigned to each condition Signup and view all the answers

Which assumption is NOT required for conducting a one-sample t-test?

Data must have a standard deviation above zero Signup and view all the answers

Which graphical representation is most useful for assessing the normality of data?

Histogram Signup and view all the answers

Study Notes

Target Population and Sampling

Studying an entire target population is usually impossible due to time, cost, and logistical challenges.
A representative sample is used instead.
A sample accurately reflects the population if it's representative.
Sampling error arises from the difference between a sample mean and the population mean.
Larger sample sizes reduce sampling error and provide more reliable estimates of the population mean.

Sampling Error

Sampling error is the difference between a sample mean and the population mean.
Taking an average of multiple samples reduces sampling error.
Smaller samples have a higher probability of high or low scores, resulting in greater variability in sample means and higher sampling error.
Larger samples result in less variability in sample means and lower sampling error.

Hypothesis Testing

Experimental hypothesis: The independent variable (IV) affects the dependent variable (DV).
Null hypothesis: There is no effect of the IV on the DV.
Inferential statistics assess the probability of obtaining results if the null hypothesis is true.

Type I and Type II Errors

Type I error: Concluding there's an effect when there isn't.
Type II error: Concluding there's no effect when there is.

P-values

P-value represents the probability of obtaining results by chance if the null hypothesis is true.
P-values range from 0 to 1.
A low p-value (e.g., p < 0.05) suggests a low probability of the results being due to chance.
This probability threshold for significance (alpha level) is 0.05 in psychology.

Experimental Design

Between-subjects design: Different participants in each condition. This method avoids order effects but is less powerful than within-subjects designs.
Within-subjects design: The same participants experience all conditions. This design can be more powerful but is susceptible to order effects.

Analyzing Continuous Data

Continuous data (scale data in SPSS) use means and standard deviations.

T-tests

T-tests compare means across groups or with a specific value.
The t-statistic is a ratio of the variation between conditions to variation within conditions.
T-test results indicate whether the difference between groups or conditions is statistically significant.

Comparing Means and Significance

Parametric tests have assumptions.
Non-parametric tests can be used for data that don't meet parametric test assumptions.

Normality Testing (Shapiro-Wilk Test)

Data normality is a crucial assumption for many statistical tests.
The Shapiro-Wilk test assesses the probability that the data distribution is normal.
A high p-value (p > 0.05) in the Shapiro-Wilk test suggests normality.
A small p-value (p < 0.05) indicates the data are significantly different from a normal distribution.

One-Sample T-test

Compare sample data to a single value (e.g., national average).
Requires independent, continuous, and normally distributed data.

Reporting T-test Results

Describe data handling.
Report descriptive statistics (mean, standard deviation).
Explain the chosen statistical test.
State the assumptions (e.g., normality, independence).
Present test statistic, degrees of freedom, and p-value.
Example format: T(df) = value, p = value.

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Description

Explore the essential concepts of target population, sampling methods, and the significance of sampling error. This quiz will also cover hypothesis testing, including both experimental and null hypotheses. Test your knowledge on these foundational statistical principles.