Testing Means: The Related-Samples t Test
A hypothesis test for related samples (samples that are not independent) Related Samples: Participants are either observed in more than one treatment or matched on common characteristics
Two types of Research Designs for Related Samples:
1. Repeated-Measures Design
2. Matched Pairs Design
-Each participant is observed multiple times
-You can use a pre-post design or a within-subject design
-Measure the dependent variable before and after treatment
-Observe participants across many treatments but doesn’t have to be before or after a treatment
-participants are selected and then matched based on natural or experimental common characteristics or traits.
-Can only observe two groups with matched participants
-Matching based on experimental manipulation often tests the effect of the traits -requires the trait/characteristic to be measured before matching the pairs -i.e intelligence, eating habits, etc.
-Matching based on natural occurrence matches participants based on preexisting traits, no need to measure traits as with previous
-typical for quasi experiments
-Usually biological or physiological traits
Related Samples t Test:
-Variance is unknown for one or both populations
-Differs from two-independent sample t Test in that the scores are first subtract one score in each pair from the other to get the difference score for each participant Don't forget about the age old question of Fitting the product of service to one or more segments of the broad market in such a way as to set it apart from the competition is called what?
-eliminates source of error that comes with observing different participants in each group/ treatment
- less error increases power of detecting an effect
Two Assumptions made:
1) Normality→ data is normally distributed
2) INdependence within groups
a) Different individuals within each group
Degrees of freedom:
nD= number of difference scores
1) State hypothesis
a) Null makes a statement about the mean difference between the groups b) H0: µD= 0
i) No mean difference
c) H1: µD ≠ 0
ii) there is a mean difference
2) Set criteria for decision
- Usually two-tailed with a= 0.05 Don't forget about the age old question of What are the two things that must be estimated to determine the net realizable value of receivables?
We also discuss several other topics like What product is an important biofuel produced by the countries of indonesia, malaysia, and thailand?
- Calculate degrees of freedom, use this to find critical values in t table If you want to learn more check out What is the main purpose of having administrative agencies?
3) Compute Test Statistic:
-Mean differences in the numerator divided by the estimated standard error in the denominator
-estimates the number of standard deviations in a t distribution that a sample mean difference falls from the population mean difference that was stated in the null hypothesis.
-Need to compute the mean, standard deviation of scores, standard error, and then test statistic. Equation for Mean Difference:
Equation for Variance → Standard Deviation:
Equation for estimated standard error for a distribution of mean difference scores: Equation for test statistic:
4) Make a decision
-Either reject or retain the null
-If t statistic falls beyond the critical values, there is a less than 5% chance of obtaining the null hypothesis, so it is rejected
- If decision is to reject the null, look to calculate effect size
5) Calculate effect size if null is rejected
-Three measures of effect size
1) Cohen’s d
2) Proportion of variance
b) Omega- squared
-Most common measure of effect size
-Measures the number of standard deviations that mean difference scores shifted above or below the population mean difference stated in the null
Proportion of Variance:
-Estimates the proportion of variance in a dependent variable that can be explained by a treatment
Omega- Squared Equation:
Can conclude: x% of the variability in (dependent variable) can be explained by (treatment).