Hypothesis Testing And The Distribution Of Means PSY3200 Uni ✓ Solved

Hypothesis Testing And The Distribution Of Means PSY3200 Unit 4

In this unit we will be taking the concept of the normal distribution and finally connecting it with an experiment. We will do this in a process known as hypothesis testing. Hypothesis testing is a procedure used to see if a hypothesis supports a particular theory; it uses the normal curve, probability, and sampling. The steps for hypothesis testing are as follows: Identify your populations and state your hypotheses; identify the characteristics of the comparison distribution; determine the cutoff score at which you would reject your null hypothesis; calculate your test score; compare your test score to the cutoff score and decide whether you would reject your null hypothesis or not.

Step 1 requires us to do 2 parts. The first thing we will need to do for hypothesis testing is to define our populations. To do this we always state (1) who is in this particular group, and (2) what we are measuring. It is important for this not to state what we think will happen, that is for the hypothesis. The other half of step 1 is to state our hypotheses, and we will have two of them: the research hypothesis and the null hypothesis.

Step 2 is to identify the characteristics of the comparison distribution. In order to see if the experiment worked, we must compare it to those who did not receive the manipulation to check if there is a difference. Step 3 is to find the cutoff score for the comparison distribution. In this step, we ask: at what point is our score different enough from the comparison distribution to say it was caused by our independent variable? The key to step 3 is to find the Z scores that will give us that answer.

Step 4 is to solve the final equation. In this case we are solving for Z. Step 5 we compare the Z scores from step 3 (the cutoff) to step 4 (your Z score) and we decide if we would reject or fail to reject the null hypothesis.

In our example, we often compare a sample to a population. We take a group of people from a population, apply a manipulation and see how they compare to the population they came from. A single group to represent the population isn't ideal as we could have a group of outliers, so by getting multiple samples, we have a better chance of being a good representation.

The final part of the unit will briefly discuss the concept of power, which is the probability you will reject your null hypothesis when you are supposed to.

Paper For Above Instructions

Hypothesis testing plays a crucial role in psychological research, enabling researchers to determine whether their findings statistically support their hypotheses. It is fundamental to validate the results of experimental designs. This paper will explore the hypothesis testing process, characterized by the analysis of the distribution of means, utilising two-tailed and one-tailed tests as appropriate. Furthermore, it will illustrate these concepts through practical applications relevant to psychological studies.

Understanding Hypothesis Testing

The process of hypothesis testing begins with the formulation of two competing statements: the null hypothesis (H0) and the alternative hypothesis (H1). The null hypothesis states that there is no effect or no difference between groups, serving as a baseline to which the alternative hypothesis can be compared. The alternative hypothesis posits that there is a significant effect or difference. For example, if one were to hypothesize that a new therapy improves mental health outcomes better than a standard therapy, the null hypothesis would state that both therapies yield the same outcomes, while the alternative would state that the new therapy performs better (Aron, Coups, & Aron, 2013).

Steps in Hypothesis Testing

Step 1: Define the populations and hypotheses. In the provided survey indicating an average of 8.4 hours of homework per week, we might have two populations; those being surveyed now and those surveyed in 1995. The hypotheses can be stated as:

• H0: μ = 8.4 (There is no change in homework hours)
• H1: μ ≠ 8.4 (There is a change in homework hours)

Step 2: Identify the characteristics of the comparison distribution. This typically involves calculating the mean and standard deviation of the population to allow for a Z-score analysis.

Step 3: Determine the cutoff score associated with your chosen alpha level (α). For a significance level of α = 0.05 in a two-tailed test, your critical Z-scores would be ±1.96. This implies that if your computed Z-score falls beyond these cutoff scores, you reject the null hypothesis.

Step 4: Calculate the Z-score using a formula adjusted for the sample. For instance, if the sample mean is 7.1 with a population standard deviation of 3.2 over a sample size of 100, the computed standard error would be σm = σ/√n = 3.2/√100 = 0.32. The Z-score can be calculated using:

Z = (M - µ) / σm = (7.1 - 8.4) / 0.32 = -4.06.

Step 5: Compare the calculated Z-score against the critical Z-scores from Step 3. With a Z of -4.06, which is less than -1.96, we reject the null hypothesis and conclude that there has been a significant change in the amount of time spent on homework by children.

Further Applications in Hypothesis Testing

Applying similar methodologies can reveal variations in various psychological attributes, such as the impact of treatments on mental health. For instance, in the example involving schizophrenics staying for an average of 85 weeks, the hypotheses would be:

• H0: μ = 85 (The technique has no effect)
• H1: μ

Using the same approach as outlined above, you would calculate if the average stay for patients under the new technique (78 weeks) significantly deviates from the general population's average. In this case, the analysis shows a significant reduction in stay duration, thus supporting the new technique's efficacy.

Using Practical Examples

Numerous studies can replicate this hypothesis testing framework in assessing various psychological outcomes, including the vocabulary skills of children with and without siblings. By utilizing differing samples and means, one can formulate hypotheses based on perceived differences and apply calculated Z-scores accordingly.

Understanding the power of a test also plays an essential role in hypothesis testing. Power is the probability of correctly rejecting the null hypothesis when it is false. It can be influenced by factors such as sample size, effect size, and significance level. As a practical note, larger sample sizes increase the likelihood of detecting a true effect when it exists (Aron et al., 2013).

Conclusion

In conclusion, hypothesis testing provides a systematic framework for evaluating research data in psychology. By methodically following each step, researchers can make informed decisions about the validity of their hypotheses in light of their findings. The integration of Z-scores, population attributes, and careful consideration of both one-tailed and two-tailed tests are crucial for robust and reliable inferential statistics in psychological research.

References

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