Having trouble running Jest tests: `SyntaxError: Unexpected token <`

I know this may have been posted before, but I'm really stuck as to why my tests aren't working in my React project. Here's my .babelrc file:

{
    "presets": ["react", "es2015", "stage-0"],

    "plugins": [
        "transform-runtime",
        "add-module-exports",
        "transform-decorators-legacy"
    ],

    "env": {
        "development": {
            "plugins": [
                "typecheck",
                ["react-transform", {
                    "transforms": [{
                        "transform": "react-transform-catch-errors",
                        "imports": ["react", "redbox-react"]
                    }]
                }]
            ]
        },
        "test": {
            "presets": ["es2015", "react", "stage-0"],
            "plugins": [
                "transform-runtime",
                "add-module-exports",
                "transform-decorators-legacy"
            ]
        }
    },
}

and here is my Jest setting in package.json

  "jest": {
    "moduleFileExtensions": [
      "js",
      "jsx",
      "json"
    ],
    "moduleNameMapper": {
      "SameAsOtherPax": "<rootDir>/app/pages/ExampleTest.js"
    },
    "moduleDirectories": [
      "app",
      "node_modules"
    ]
  },

The error that I'm getting is Test suite failed to run... SyntaxError: Unexpected token <.

From what I can tell about that error, the files that it is trying to run have JSX/ES6 code in them... and it doesn't know how to transpile that? Which is weird because I've told it to do just that in the .babelrc. I have also provided Jest with the appropriate moduleDirectories.

Any help would be greatly appreciated.