R&EH Exam 3

make sure to draw out diagrams on cheat sheet.

what is a hypothesis?

• a hypothesis is an educated guess about a relationship between variables.

• It provides a clear, testable statement that can be examined using data.

• it is the foundation of scientific research.

the role of hypothesis testing

• hypothesis testing allows us to determine if observed results are due to chance or a real effect.

• we compare the sample data to what we would expect if there were no real relationship (the null hypothesis).

• helps ensure research findings are scientifically valid.

population

the entire group being studied (e.g., all college students in the U.S.).

sample

a subset of the population used for research (e.g., 200 randomly selected students).

sampling error

the difference between the sample statistics and the population parameters.

probability sample methods

• simple random sampling

• stratified random sampling

• clustered sampling

• systematic sampling

non probability sample methods

• convenience sampling

• snowball sampling

• quota sampling

• purposive or judgmental sampling

higher sampling error

less precise results

lower sampling error

more reliable conclusions

the importance of generalizability

• generalizability = how well findings apply to a larger population.

• a representative sample ensures accurate conclusions.

• biased samples reduce research credibility.

what is the Null Hypothesis (H0)?

• the null hypothesis (H0) states that there is no effect or relationship between variables.

• it acts as the default assumption in research.

• example:

  • “There is no difference in test scores between students who sleep 6 hours vs. 8 hours.”

examples of Null Hypotheses

• “No difference between 9th and 12th graders on a memory test.”

• “No relationship between reaction time and problem-solving ability.”

• “No association between parental involvement and income.”

what is the Research Hypothesis (H1)?

• the research hypothesis (H1) states that there is a relationship or effect.

• it is the hypothesis researchers are trying to support with evidence.

• there are two types of research hypotheses:

  • 1. Directional

  • 2. Nondirectional

Nondirectional Research Hypotheses

• reflect a difference, but the direction is not specified.

• use a two-tailed test.

• H1: X1 doesn’t equal X2

Directional Research Hypotheses

• reflect a difference, and the direction is specified.

• use the one-tailed test.

• H1: X1> X2 or H1: X1<X2

Null Hypothesis

• no relationship between variables

• refers to the population

• indirectly tested

• written using Greek symbols

• implied hypothesis

Research Hypotheses

• relationship between variables

• refers to the sample

• directly tested

• written using roman symbols

• explicit hypothesis

good hypotheses should:

1. be stated in declarative form.

2. posit a relationship between variables.

3. reflect a theory or a body of literature on which they are based.

4. be brief and to the point and

5. be testable.

Why Probability?

• the normal curve provides us with a basis of understanding the probability associated with any possible outcome.

• basis for determining the degree of confidence that an outcome is “true”.

  • E.g., are changes in student scores due to a particular intervention that took place or by chance alone?

The Normal Curve

• AKA the bell-shaped curve/

• Visual representation of a distribution of scores.

• Characteristics of Normal Curve:

  • Mean, median, and mode are equal to one another.

  • Perfectly symmetrical about the mean.

  • Tails are asymptotic (get closer to horizontal axis but never touch it).

The z Score

• a standard score

• z is the z score

• x is the individual score

• x bar is the mean of the distribution.

• s is the distribution’s standard deviation.

• result of dividing the amount that a raw score differs from the mean of the distribution by the standard deviation.

The z Score

• Scores below the mean are negative (left of the mean), and those above are positive (right of the mean).

• A z score is the number of standard deviation the raw score is from the mean.

• z scores across different distributions are comparable.

What z Scores Represent

• the areas of the curve that are covered by different z scores:

  • encompassed by different values of standard deviation or z scores.

  • represents the probability of a certain score occurring.

what z Scores Really Represent

• knowing the probability that a z score will occur can help you determine how extreme a z score you expect before determining that a factor other than chance produced the outcome.

Hypothesis Testing and z Scores

• any event can have a probability associated with it.

• Probability values help determine how “unlikely” the event might be.

• The key is that something has less than 5% chance of occurring, and you have a significant result.

Fat and Skinny Frequency Distributions

• Average value

• Variability

• Skewness

• Kurtosis

Variability

Skewness

Kurtosis