Testing Hypotheses

Basic Research Designs• Descriptive Designs:

– Descriptive Studies: thoroughly describe a single variable in order to better understand it

– Correlational Studies: examine the relationships between two or more quantitative variables as they exist with no effort to manipulate them

• Inferential Designs:– Quasi-Experimental Studies: make comparisons

between naturally-occurring groups of individuals– Experimental Studies: make comparisons between

actively manipulated groups

Population With

Parameters

Chain of Reasoning in Inferential Statistics

Sample With

Statistics

Random Selection

Probability

SamplingDistributions

Of the Statistics

Inference

Inferential Reasoning

• Population: group under investigation

• Sample: a smaller group representing the population– A sample that has been randomly

selected should be representative of the population

Random Selection

Inference

Hypothesis Testing

• Hypothesis Testing: the process of using inferential procedures to determine whether a hypothesis is supported by the results of a research study

Hypothesis Testing

• Conceptual Hypothesis: a general statement about the relationship between the independent and dependent variables

• Statistical Hypothesis: a mathematical statement that can be shown to be supported or not supported. It is designed to make inferences about a population or populations.

Hypothesis Testing

• In psychological research, no hypotheses can be proven to be true.

• Modus Tollens: a procedure of falsification that relies on the fact that a single observation can lead to the conclusion that the premise or prior statement is incorrect– Null Hypothesis (H0): statements of equality (no relationship; no

difference); statements of opposing difference– Alternative (Research) Hypothesis (H1 or HA): a statement that

there is a relationship or difference between levels of a variable; statements of inequality

Types of Research Hypotheses• Nondirectional Research

Hypothesis: reflects a difference between groups, but the direction of the difference is not specified (two-tailed test) – H1: X ≠ Y

• Directional Research Hypothesis: reflects a difference between groups, and the direction of the difference is specified (one-tailed test) – H1: X > Y

– H1: X < Y z = 1.645p = .05

z = -1.96 µ z = 1.96p = .025 p = .025

µ

Rejecting the Null Hypothesis

• Alpha Level (α): the level of significance set by the researcher. It is the confidence with which the researcher can decide to reject the null hypothesis.

• Significance Level (p): the probability value used to conclude that the null hypothesis is an incorrect statement– If p > α cannot reject the null hypothesis– If p ≤ α reject the null hypothesis

Determining the Alpha Level

• Type I Error (α): the researcher rejects the null hypothesis when in fact it is true; stating that an effect exists when it really does not

• Type II Error (β): the researcher fails to reject a null hypothesis that should be rejected; failing to detect a treatment effect

Determining the Significance Level (Probability)

• The distribution used to determine the probability of a specific score (or difference between scores) is determined by multiple factors.

• Regardless of the distribution used, the logic and process used to determine probability is essentially the same.

• All statistical distributions mimic the function of the standard normal distribution.

The Normal Curve

• Three Main Characteristics: 1. Symmetrical: perfectly

symmetrical about the mean; the two halves are identical

2. Mean = Median = Mode3. Asymptotic Tail: the tails

come closer and closer to the horizontal axis, but they never touch

The Normal Distribution and the Standard Deviation

• In the normal distribution…– 68% of scores fall between +/-

1 standard deviations– 95% of scores fall between +/-

2 standard deviations– 99.7% of scores fall between

+/- 3 standard deviations• It is possible to determine the

probability of obtaining any given score (or any differences between scores).

The Normal Curve and Probability• The normal distribution is the

most commonly used distribution in behavioral science research.

• The scores of variables can be converted to standard z-scores, which can be used to determine the probability of a specific score.

• All probabilities are a number between 0.0 and 1.0, and given all possible outcomes of an event, the probabilities must equal 1.0.

µ z = 1.645

µ z = 1.645

z-scores

• z-score: represents the distance between an observed score and the mean relative to the standard deviation; a score on an assessment expressed in standard deviation units

• Formula:– z = X – M

s– z = X – µ

σ

More Curves and Probability

µ z = 1.282 p = .10

µ z = 1.645 p = .05

µ z = 2.326 p = .01

z = -1.645 µp = .05