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Remind yourself of when an independent t-test would be used. Complete the following statements by typing the missing word.

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An independent t-test is used for a research question that investigates a [[0]] between groups.

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The independent variable should be a [[1]] variable, and the dependent variable would be a [[2]] variable.

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We only use an independent t-test if a [[3]]-participants design is used.

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The independent variable name should be a general name for the variable as a whole (i.e. without specifying any groups or conditions) but specific to the groups that the variable might be divided into.

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The dependent variable name should be specific enough to understand what the value presented in the data represents.

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Identify the variables under investigation in this study. 

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\n

Ability to do maths

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"]}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Hypothesis", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Jenny Hughes", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7275/"}], "tags": [], "metadata": {"description": "", "licence": "None specified"}, "statement": "", "advice": "", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": [], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "1_n_2", "useCustomName": true, "customName": "H0", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

Which of theses is the null hypothesis (H0)

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Which of theses is the (non-directional) experimental hypothesis (H1)

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You can find the number of participants (N) in the independent t-test outputs. 20 participants in each group so 40 participants in total.

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You can find the average/mean and SD for each group in the Explore output ot the independent t-test output

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you can find the median/IQR for each group in the Explore output

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You can find the mean difference in the independent t-test output

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Make sure that all values are reported to two decimal places.

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How many participants took part in this study? [[0]]

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What was the average score for males who took the maths test? [[1]]

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What is the average spread (standard deviation) of maths scores for males who took the maths test? [[2]]

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What is the median score for males who took the maths test? [[3]]

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What is the interquartile range for males who took the maths test? [[4]]

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What was the average score for females who took the maths test [[5]]

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What is the average spread (standard deviation) of maths scores for females who took the maths test? [[6]]

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What is the median score for females who took the maths test? [[7]]

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What is the interquartile range for females who took the maths test? [[8]]

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What is the mean difference in maths scores between the two groups [[9]]

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The dots in the graph represent the position of the mean for each group, which indicates that females had a higher mean score on the maths test compared with males who took the test.

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The less overlap there is between the 95% confidence intervals around the means, the more likely tht there is a significant difference. Because the intervals overlap this difference may not be significant.

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Use the Error bar graph that you obtained to answer the following question.

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On the basis of the error bar graph alone, please select which statement is correct.

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\n
\n
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\n
\n
\n
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Males had a higher mean/average maths test score than females, but this may not be significantly higher because the 95% confidence intervals around the means overlap quite a bit.

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\n
\n
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\n
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\n
\n
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\n
\n
\n
\n

Females had a higher mean/average maths test score than males, but this may not be significantly higher because the 95% confidence intervals around the means overlap quite a bit.

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\n
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\n
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Use the Simple Histograms that you obtained to check the assumptions of normality.

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Is the distribution of this data normal?

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The data for both groups is normally distributed

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\n
\n
\n
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Use the Simple Boxplots that you obtained to answer the following question.

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Are there any extreme scores in the maths test scores for either group?

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Use the Levene's test displayed in the independent t-test output and obtain information to check the assumptions of equal variances

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Complete the following statement.

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Levene's test for equality of variances is [[0]]. We can therefore assume there there are [[1]] differences between the [[2]] in the scores for each group and the assumption of variances has [[3]].

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Independent t-test

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The data was inspected and was judged that the this was normally-enough distributed on histograms with one outlier on the box plots which was considered acceptable, therefore an independent t-test was conducted.

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A maths test was given to male and female participants to see if one gender was better at maths than the other. On the maths test females scored significantly higher (m = 17.05, SD = 2.61) compared to males (m=15.25, SD=2.61; t (38) = 1.67, p = .104). This suggests that the opinion that males are better at maths is correct. (Rebecca: this is not the most appropriate test in my opinion as the extreme outlier will affect the reliability of the test - One of the assumptions has been violated.)

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Mann Whitney U Test

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The data was inspected and was judged that the data for the female participants was not normally distributed from the histogram with one outlier on the boxplot, therefore a Mann-Whitney U test was conducted.

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A maths test was given to male and female participants to see if one gender was better at maths than the other. On the maths test females scored significantly higher (median = 18.00, IQR = 3) compared to males (median = 15.25, IQR = 3.75; U = 110.50, p = .014). This suggests that the opinion that males are better at maths is a myth. 

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Select the test you chose to use. How would you report these results along with a rationale for why the test was chosen. Jot down your answers, then choose the test and reveal answers for feedback.

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SCENARIO
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There is a general tendency for people to think that women are better at languages and art skills, and that men are better at maths and natural sciences. We wanted to know whether men really are better at maths than women, or whether this is just a myth. We asked 20 male and 20 female students to complete a math test. Math scores were calculated by counting the number of correct answers (out of a total of 24 questions).
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Task 1
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Male participants’ scores on the maths test:
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19, 11, 15, 16, 13, 15, 16, 17, 16, 17, 16, 12, 15, 13, 10, 14, 14, 18, 18, 20
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Female participants’ scores on the maths test
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20, 3, 17, 17, 18, 16, 18, 23, 17, 20, 16, 19, 18, 15, 18, 13, 14, 19, 19, 21
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Task 2.
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Math Scores
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Name = Mathscores
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Type = Numeric
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Decimals = 0
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Measure = Scale
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Ensure that the correct information is displayed for the variable Gender:
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Name = Gender
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Type = Numeric
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Decimals = 0
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Values: 1 = Male, 2 = Female
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Measure = Nominal
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Click on the Data View tab and enter the data (you should have 40 rows)
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Task 3  
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Instructions are provided in the Data Exploration: Descriptive Statistics section of the SPSS Guide.
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Task 4: Create aSimple Histogramto visually display the distribution of the data, separately for male and female students.
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Instructions are provided in the Graphical display of data section of the SPSS Guide document.
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Task 5: Obtain aSimple Error bar graphto display the differences in average math score between the groups.
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Instructions are provided in the Graphical display of data section of the SPSS Guide document.
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Task 6: Obtain a Simple Box plot to assess whether there are any outliers or extreme scores.Graphical display of data
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Task 7: Perform the Independent t-test analysis.
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Instructions are provided in the Data Analysis: Inferential Statistics section of the SPSS Guide document.
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You can export any of the images in the Output file, and save it in a folder on your personal computer for later reference.
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Instructions for how to save a picture from the output are provided in the Graphical display of data section of the SPSS Guide 
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After you have finished these tasks, answer the questions in the online test, using the information from the SPSS output.
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Thank you

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